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CENTER OF RESEARCH AND ADVANCED STUDIES
OF THE NATIONAL POLYTECHNICAL INSTITUTE
UNIT IN MERIDA
DEPARTAMENT OF APPLIED PHYSICS
K0
S production at high Q2 in
deep inelastic ep scattering at H1
A dissertation submitted by
Julia Elizabeth Ruiz Tabasco
for the degree of
Doctor in applied physics
Thesis Supervisor
Dr. Jesus Guillermo Contreras Nuno.
Merida, Yucatan, Mexico. May 2010
CENTRO DE INVESTIGACION Y DE ESTUDIOS AVANZADOS
DEL INSTITUTO POLITECNICO NACIONAL
UNIDAD MERIDA
DEPARTAMENTO DE FISICA APLICADA
Produccion de K0
S a Q2 altas en
dispersion ep inelastica profunda en H1
Tesis que presenta
Julia Elizabeth Ruiz Tabasco
para obtener el grado de
Doctora en Ciencias
en la especialidad de
Fısica Aplicada
Director de Tesis
Dr. Jesus Guillermo Contreras Nuno.
Merida, Yucatan, Mexico. Mayo de 2010
All truths are easy to understand once they are discovered;
the point is to discover them.
(Galileo Galilei)
v
Acknowledgements
I enormously thank my parents, Mr. Agustin Ruız y Uex and Mrs. Marıa Eliz-
abeth Tabasco Ruz for the education, for teach me to fight against the obstacles and
do not leave the things without finish them. By their continuous support to all my
decisions with respect to the academic and private life, and for those goodbyes and
good desires accompanied with pretty smiles even when they did not want let me go.
Thanks to my four sisters Nalleli, Adriana, Delmira and Leydi for the shared mo-
ments throughout our years together, especially to Nalle for those talks in which only
stopped laughing until the stomach hurts. Thanks to you and Delmi for give me the
opportunity of being a child again when I play with my nephews. Eternal thanks to
that house of “crazy people” in Tizimın that makes me what I am.
I also want to thank my beloved husband, the Engineer Luis R. Dzib Eliodoro for
his unconditional support, to give me the chance of professional development and to
encourage me to do the things even when everything seemed to be against. For that
optimistic way to live, for helping me to bear my frustrations and deceptions in those
long conversations drinking a beer, but mainly for undertaking with me a nice stage
of life.
Special thanks to my thesis supervisor, Dr. Jesus Guillermo Contreras Nuno for
trust my skills, for answer to my questions not only about the work but to everyone
that I did. For answering to my hundreds of emails when it was not possible to be in
the same place. For the support during the days of anger or desception, for knowing
how to deal with me in spite of my character and to offer me the opportunity to work
with him.
Eternal gratefulness to Dr. Daniel Traynor of the Queen Mary University from
London for accepting to be the supervisor of my analysis during my time at DESY,
for the explanations, comments and constant help in the accomplishment of this thesis
viii
work.
I would also like to thank the members of the H1 Collaboration for the nice time
together, especially to Drs. Hannes Hung, Albert Kutson and Dmitri Ozerov for
their help to solve my doubts with respect to the Monte Carlo programs. To Ms.
Deniz Sunar and Ms. Ana Falkiewicks, as well as to the colleagues Marc del Degan
and Maxime Gouzevitch for the discussions with respect to strangeness physics, the
technical studies necessary to carry out the analysis and the help with commands of
Root and programming in C++.
To Dr. Daniel Pitzl, Dra. Grazyna Nowak, Dra. Karin Daum, Dra. Katja
Krueger, Dr. Stefan Schmitt and Dr. Guenter Grindhammer for the interest de-
posited in this study; the continuous comments, suggestions and requests that en-
riched this analysis, but especially for the attention dedicated to my work during the
days near to the preliminary stamp of my results.
To the High Energy Physics LatinAmerican-European Network program (HELEN)
for the partial economic support during both periods of my stays at DESY. To Dr.
Fridger Schrempp, Dr. Veronica Riquer and Dr. Arnulfo Zepeda for their help with
the steps to get the Helen scholarship.
To the Consejo Nacional de Ciencia y Tecnologıa (CONACYT) for the economic
support during my doctoral studies.
To Mrs. Heidy Lucely Miranda Chable, Maricarmen Iturralde Lorıa and Guadalupe
Aguilar Martınez for the secretarial help during my studies in CINVESTAV. As well
as to Mrs. Alla Grabowsky and Sabine Platz, secretaries of DESY that offered me
their help during my stay there.
To the members of the Department of Applied Physics at CINVESTAV, for the
lessons and the nice time together in the classrooms and outside them.
To Ms. Georgina Espinoza and Mr. Mauricio Romero for their constant help
with computational equipment, that for some strange reason always stopped working
in my hands.
To the Doctors who conform the honorable synod: Dr. Jurgen Engelfried, Dr.
ix
Eduard de la Cruz Burelo, Dr. Francisco Larios Forte, Dr. Juan Jose Alvarado Gil,
and Dr. J. Guillermo Contreras Nuno.
To Ms. Angela Lucati for the beautiful friendship, the tasty apple pies and the
pleasant talks in the office. For her interest in learning Spanish and the enormous
support offered during the time living in Hamburg, but mainly for her patience and
disposition to help during my first days of stay at DESY. To Dr. Andrea Vargas for
her company in the search of Mexican ingredients in Hamburg, for the nice afternoons
cooking in her house and the nice talks that reminded me my country.
To Anastasia Grebenyuk, Tobias Toll, Lluis Marti, Federico Von Samson, Axel
Cholewa, Michal Deak, Zlatka Staykova, Krzysztof Kutak, Albert Kutson and Krzysztof
Nowak for doing the life so funny in Hamburg, for the laughters in the meetings of
’physics and cookies’ and also, why not?, for the discussions of politic, economy,
literature and physics.
And the last in the list but the first in my heart, to my dear friends of the drunk
band: Dulce Valdes, Jose Luis Albornoz, Benjamın Palma, Roberto Ramırez, Miguel
Lopez, Roberto Escalante, Marco Izozorbe, Carlos Perera and Johny Martınez, to
offer me their invaluable friendship and for acceptting me among them, but specially
for letting me be the strange girl.
Agradecimientos
Agradezco enormemente a mis padres, el Prof. Agustın Ruiz y Uex y la Sra.
Marıa Elizabeth Tabasco Ruz por la educacion brindada, por ensenarme a luchar
contra los obstaculos y no dejar las cosas sin terminar. Por el continuo apoyo ape-
sar de mis espontaneas decisiones respecto a la vida academica y privada, e incluso
por esos adioses y buenos deseos acompanados de bonitas sonrisas aun cuando en
el fondo no querıan dejarme ir. Gracias a mis cuatro hermanas Nalleli, Adriana,
Delmira y Leydi por los bonitos momentos que hemos compartido a lo largo de nue-
stros anos juntas, especialmente a Nalle por aquellas ’platicas ’ que se convertıan en
interminables risas hasta que el estomago dolıa. Gracias a tı y a Delmi por darme
la alegrıa de ser nina otra vez al jugar con mis sobrinos. Gracias eternas a esa casa
de locos en Tizimın que me convirtio en lo que ahora soy.
Quiero agradecer tambien a mi esposo el Ing. Luis R. Dzib Eliodoro por su apoyo
incondicional, por darme la oportunidad de desarrollarme profesionalmente y alen-
tarme a realizar las cosas aun cuando todo parece estar en contra. Por esa manera
optimista de vivir, por ayudarme a sobrellevar mis frustraciones y decepciones en
esas largas conversaciones bebiendo una cerveza, pero sobre todo por emprender a mi
lado una linda etapa de la vida.
Gracias especiales a mi supervisor de tesis, el Dr. Jesus Guillermo Contreras
Nuno por confiar en mi capacidad, por contestar a mis interminables preguntas no
solo del trabajo sino todas aquellas que en algun momento formule. Por responder
a mis cientos de emails cuando no era posible coincidir en el mismo lugar. Por el
apoyo durante los dias de enojo o desanimo, por saber como tratar conmigo apesar
de mi caracter y por brindarme la oportunidad de trabajar a su lado.
Un agradecimiento eterno para el Dr. Daniel Traynor de la universidad Queen
Mary de Londres por aceptar ser supervisor de mi analisis durante el tiempo que es-
xii
tuve en DESY, por sus explicaciones, comentarios y constante ayuda en la realizacion
de este trabajo de tesis.
Me gustarıa tambien agradecer a los miembros de la colaboracion H1 por la amable
convivencia, especialmente al Dr. Hannes Hung, Albert Kutson y Dmitri Ozerov
por su ayuda a resolver mis dudas respecto a los programas Monte Carlo. A la
Sritas. Deniz Sunar and Anna Falkiewicks, ası como a los colegas Marc del Degan
y Maxime Gouzevitch por las discusiones respecto a fısica de extraneza, los estudios
tecnicos necesarios para llevar a cabo el analisis y la ayuda con comandos de root y
de programacion en C++.
Al Dr. Daniel Pitzl, Dra. Grazyna Nowak, Dra. Karin Daum, Dra. Katja
Krueger, Dr. Stefan Shmitt y Dr. Guenter Grindhammer por el interes depositado
en este estudio; los continuos comentarios, sugerencias y peticiones que sirvieron
para el enriquecimiento de este analisis, pero especialmente por la atencion prestada
durante los dıas cercanos a la obtencion de estampa preliminar de mis resultados.
Al programa High Energy Physics LatinAmerican-European Network (HELEN)
por el soporte economico parcial durante los dos perıodos de estancia en DESY. Al
Dr. Fridger Schrempp, Dra. Veronica Riquer y Dr. Arnulfo Zepeda por su ayuda
con los tramites para la obtencion de la beca Helen.
Al consejo nacional de ciencia y tecnologıa (CONACYT) por el apoyo economico
durante mis anos de estudios doctorales.
A las Sras. Heidy Lucely Miranda Chable, Maricarmen Iturralde Lorıa y Guadalupe
Aguilar Martınez por la ayuda secretarial durante mi estancia en el CINVESTAV.
Ası como a las Sras. Alla Grabowsky y Sabine Platz, secretarias del DESY que me
brindaron su ayuda durante mi estancia ahı.
A los miembros del departamento de fısica aplicada del CINVESTAV, por las
ensenanzas y convivencia en las aulas y fuera de ellas.
A la Srita. Georgina Espinoza y el Sr. Mauricio Romero por la constante ayuda
con equipos de computo, que por alguna extrana razon siempre se descomponıan en
mis manos.
xiii
A los doctores que conforman el honorable sınodo, Dr. Jurgen Engelfried, Dr.
Francisco Larios Forte, Dr. Juan Jose Alvarado Gil, Dr. Eduard de la Cruz Burelo
y Dr. J. Guillermo Contreras Nuno.
A la Srita. Angela Lucati por la linda amistad, los ricos pasteles de manzana y
las agradables platicas en la oficina. Por su interes en aprender espanol y el enorme
apoyo brindado durante todo el tiempo que vivı en Hamburgo; pero principalmente
por su paciencia y disposicion de ayuda durante mis primeros dias de estancia en
DESY. A la Dr. Andrea Vargas por acompanarme en la busqueda de ingredientes
mexicanos en Hamburgo, por las agradables tardes cocinando en su casa y las platicas
populares que me hacıan recordar mi pais.
A Anastasia Grebenyuk, Tobias Toll, Lluis Marti, Federico Von Samson, Axel
Cholewa, Michal Deak, Zlatka Staykova, Krzysztof Kutak, Albert Kutson and Krzysztof
Nowak por hacer la vida divertida en Hamburgo, por las risas en las reuniones de
’physics and cookies’ y tambien, porque no?, por las discusiones de polıtica, economıa,
literatura y fısica.
Y por ultimo en la lista pero los primeros en el corazon, a mis amigos de la banda
borracha: Dulce Valdes, Jose Luis Albornoz, Benjamın Palma, Roberto Ramırez,
Miguel Lopez, Roberto Escalante, Marco Izozorbe, Carlos Perera y Johny Martınez,
por brindarme su valiosa amistad y aceptarme entre ellos, pero mas que nada por
dejarme ser la chica extrana.
Abstract
The production of K0S mesons is studied using deep-inelastic scattering events
(DIS) recorded with the H1 detector at the HERA ep collider. The measurements
are performed in the phase space defined by the four-momentum transfer squared of
the photon, 145 GeV2 < Q2. The differential production cross sections of the K0S
meson are presented as function of the kinematic variables Q2 and x, the transverse
momentum pT and the pseudorapidity η of the particle in laboratory frame, and as
function of the momentum fraction xBFp and transverse momentum pBF
T in the Breit
Frame. Moreover, the K0S production rate is compared to the production of charged
particles and to the production of DIS events in the same region of phase space. The
data are compared to theoretical predictions, based on leading order Monte Carlo
programs with matched parton showers. The Monte Carlo models are also used for
studies of the flavour contribution to the K0S production and parton density function
dependence.
xv
Resumen
La produccion de mesones K0S es estudiada usando eventos de dispersion inelastica
profunda (DIS) tomados con el detector H1 en el colisionador ep HERA. Las medi-
ciones se realizan en el espacio fase definido por el cuadrado del cuadrimomento
transferido del foton, 145 GeV2 < Q2. Las secciones trasversales diferenciales de la
produccion de K0S se presentan en funcion de las variables cinematicas Q2 y x, el
momento transverso pT y la pseudorapidez η de la partıcula en el marco del labora-
torio, y en funcion de la fraccion de momento xBFp and momento transverso pBF
T en el
marco Breit. Mas aun, la produccion de los mesones K0S se compara a la produccion
de partıculas cargadas y a la produccion de eventos DIS en la misma region de espa-
cio fase. Los resultados se comparan a predicciones teoricas basadas en programas
Monte Carlo de primer orden unidos a cascadas de partones. Los modelos Monte
Carlo tambien se usan para el estudio de la contribucion de sabor a la produccion
de K0S y la dependencia de la funcion de densidad de partones.
Preface
The understanding of the composition of matter and the way it interacts has been,
since a long time ago, the topic of investigation of several physicist whose theoretical
and experimental researches have contributed to the formulation of ideas about the
structure of the atoms. The first models indicated that the protons, neutrons and
electrons are the basic components, but further studies revealed that the proton and
neutrons are formed by other elementary pieces called quarks [1].
In 1969, ideas from Bjorken and Feynman were fundamental for the development
of a model able to explain a nucleon as a particle composed of quarks. The compo-
sition of the nucleon was described through the so called structure functions. This
model, known as the quark parton model or QPM [2] [3], expresses the structure
function F2 as the weighted sum of the momentum distribution of the quarks qi(x)
and antiquarks qi(x) in the nucleon times the square of their electric charge ei:
F2(x) =∑
i
e2i x[qi(x) + qi(x)] (1)
where x is the fraction of the proton momentum carried by the probed quark. The
quarks, in this model, carry only longitudinal momentum.
The proton (uud) is formed by two up u quarks and one down d quark, then:
∫ 1
0
(u(x) − u(x)) dx = 2
∫ 1
0
(d(x) − d(x)) dx = 1. (2)
The QPM interpretation had some success, but further studies [4] showed that
only 50% of the proton momentum is carried by the quarks, then the missing momen-
tum should be carried by another kind of partons with no electric charge. Some time
later, between 1973-78 the gluons were discovered, and quantum chromodynamics
(QCD) was proposed: the QCD age had started.
xix
xx
QCD considers that the quarks carry not only electric charge but also colour
charge. The exchange of colour is mediated by the gluons with spin 1. Due to
the new assumption, QCD also should consider the possibility that quarks radiate
gluons, and the possibility of gluon fluctuations into quarks which is the source of
the sea of quarks inside the proton. These processes complicate the calculations of
proton structure function F2 but good experimental results have been obtained as
shown in Figure 1 where F2 is plotted versus the four-momentum squared of the
transfer photon in the DIS events, Q2. The F2 data for x values around 0.25 is flat
as a function of Q2, this is called Bjorken scaling. For smaller values of x, F2 grows
logarithmically with Q2, this is called scaling violation.
QCD together with the electroweak theory form the so called Standard Model
(SM) which is a very successful theory of elementary particles, in spite of its known
shortcomings.
The SM includes 61 elementary particles, 48 of them of spin 1/2 (or fermions):
36 quarks (the quarks up, down, charm, strange, top and bottom, presented in three
different colors; and their antiparticles) and 12 leptons (the electron, muon, tau, their
neutrinos, and their respective antiparticles) which are classified according to their
way of interaction. The SM explains the forces as resulting from matter particles
exchanging other particles, the mediating particles (12 elementary particles) with
spin 1 (bosons): the photon γ for the very well known electromagnetic force, the W±
and Z0 boson for the weak interactions and the gluon g (8 different gluons) for the
strong interaction. Figure 2 shows the Standard Model of the elementary particles.
The Higgs boson (also considered as elementary particles) is still an hypothetical
particle, that would explain the fundamental mass of the particles.
Hadrons, strongly interacting particles, are classified as mesons or baryons if they
are made of a quark-antiquark pair (qq) or of three quarks (qqq), respectively. The
proton is an stable baryon as far as we know. The nucleon, another baryon, is
relatively stable only when bound in a nuclei. All other hadrons decay very fast, in
a human time scale, so they are not found in ordinary matter. This characteristic is
xxi
10-3
10-2
10-1
1
10
10 2
10 3
10 4
10 5
10 6
1 10 102
103
104
105
Q2 / GeV2
F 2 ⋅
2i
x = 0.65, i = 0
x = 0.40, i = 1
x = 0.25, i = 2
x = 0.18, i = 3
x = 0.13, i = 4
x = 0.080, i = 5
x = 0.050, i = 6
x = 0.032, i = 7
x = 0.020, i = 8
x = 0.013, i = 9
x = 0.0080, i = 10
x = 0.0050, i = 11
x = 0.0032, i = 12
x = 0.0020, i = 13
x = 0.0013, i = 14
x = 0.00080, i = 15
x = 0.00050, i = 16
x = 0.00032, i = 17
x = 0.00020, i = 18
x = 0.00013, i = 19
x = 0.000080, i = 20x = 0.000050, i = 21 H1 e+p
ZEUS e+p
BCDMS
NMC
H1 PDF 2000
extrapolation
H1
Col
labo
ratio
n
Figure 1: Experimental results of the F2 structure function of the proton as functionof the four-momentum squared of the transfer photon Q2 and the proton momentumfraction carried by the struck quark x, compared to NLO calculations in QCD (solidline shows the H1 PDF 2000 [5]). At low Q2, the H1 data are complemented withthe fixed target experiments BCDMS[6] and NMC[7], [8] data.
xxii
Figure 2: Standard model constituents.
one of the issues that makes important their study in particle physics.
This thesis is focused in the research of a meson known as the K0S which belongs
to the family of strange mesons due to the presence of a strange s quark in its
composition.
The first observed mesons were the pion π and the kaon K, in 1947 [9] using a
cloud chamber. The kaon decay was observed by G.D. Rochester and C.C. Butler,
then other mesons were observed in several experiments. The lifetimes differences
of the kaons and the observation of pair production of strange particles from strong
interaction of non-strange hadrons, as that one shown in Figure 3, suggested that
they contain a new quark, the strange quark s, having the same electric charge as
the d quark but higher mass because K and Σ are heavier than π+ and p. Then
a new quantum number, called strangeness, was introduced by M. Gell-Mann and
A. Pais [10]. The strangeness quantum number is conserved in strong, but violated
in weak interactions.
The discovery of hadrons with strangeness quantum number marked the begin-
ning of an exciting age in particle physics which, after more than 60 years, have not
found its conclusion yet. However the studies continue, as the one carried out for
this doctoral thesis whose main goal is the analysis of the lightest strange meson,
xxiii
__
+
p
K+
+
Figure 3: The production of strange particles in the interaction of non-strangehadrons π+ + p → K+ + Σ+.
the K0S, decaying mainly into two pions with opposite electric charges.
The goal of this thesis is to contribute to the strangeness studies throught the
determination of the total and differential cross sections of the K0S meson production
at high Q2 range using HERA II data from 2004 to 2007, since they provide plenty of
statistics making possible the study at this range which was not been possible in the
previous years of HERA operation, and provide valuable information of fundamental
aspects in QCD dynamics, understanding of K0S production, comparison of parton
density functions and strangeness factor values for MC tests.
The thesis is structured as follows. In the first chapter the deep inelastic scattering
and its kinematics are introduced, the main aspects of the theoretical framework in
which the Monte Carlo simulation programs are based can also be found there.
The second chapter consists on the presentation of the K0S meson, the production
mechanisms and the importance of the strangeness studies. Previous results of differ-
ent experiments corresponding to the strange topic are briefly summarized, the most
recent measurements of strange particles by the H1 collaboration are emphasized as
the main introduction to the work presented here.
The third chapter is dedicated to the description of the HERA collider and the
H1 detector components as well as to the explanation of the performance of trackers
and calorimeter detection devices, trigger system and luminosity measurement.
xxiv
The fourth chapter concentrates on the selection criteria of deep inelastic scatter-
ing events. The K0S reconstruction through the identification of its track daughters
and the signal extraction from its invariant mass distribution can also be found in
this chapter. The selection criteria to obtain the charged particle sample needed for
cross section ratios are explained in the last subsection.
Chapter five introduces the procedure to determine the total and differential cross
sections. The main corrections needed in the measurements and the statistical and
systematic uncertainties sources are explained in detail.
The last chapter, number six, is reserved to the results of the K0S production,
differential cross sections in the laboratory and Breit frames, production ratios of
the K0S to charged particle and DIS events, double differential cross section, as well
as complementary studies such as the PDFs dependence and flavour contribution to
the K0S production are shown. The last section presents the conclusions.
Contents
Abstract xv
Resumen xvii
Preface xix
1 Theoretical framework 1
1.1 Deep inelastic scattering . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Theoretical DIS cross section . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Event generators: Monte Carlo programs . . . . . . . . . . . . . . . . 4
1.3.1 Colour dipole model and parton showers . . . . . . . . . . . . 6
1.3.2 Fragmentation and hadronization . . . . . . . . . . . . . . . . 7
1.4 Django and Rapgap Monte Carlo programs . . . . . . . . . . . . . . . 10
1.4.1 Django . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.4.2 Rapgap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2 Strange mesons 13
2.1 What is a K0S meson? . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2 Production of K0S . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.3 Why strangeness studies are important? . . . . . . . . . . . . . . . . 19
2.4 Previous strangeness production studies . . . . . . . . . . . . . . . . 22
2.4.1 At e+e− colliders . . . . . . . . . . . . . . . . . . . . . . . . . 22
xxv
xxvi CONTENTS
2.4.2 At pp and heavy ions collisions . . . . . . . . . . . . . . . . . 23
2.4.3 At ep colliders . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.5 Previous H1 results of strangeness at low Q2 . . . . . . . . . . . . . . 27
2.5.1 Search of resonances . . . . . . . . . . . . . . . . . . . . . . . 27
2.5.2 Analysis of K∗(892) meson production . . . . . . . . . . . . . 30
2.5.3 K0S and Λ studies at low Q2 . . . . . . . . . . . . . . . . . . . 32
3 HERA and the H1 Detector 39
3.1 The HERA collider . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.2 The H1 detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.2.1 Tracker system . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.2.1.1 Central silicon tracker . . . . . . . . . . . . . . . . . 50
3.2.1.2 Central jet chambers . . . . . . . . . . . . . . . . . . 50
3.2.1.3 Central z chambers . . . . . . . . . . . . . . . . . . . 51
3.2.1.4 Central proportional chambers . . . . . . . . . . . . 52
3.2.2 Calorimeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.2.2.1 Liquid argon calorimeter . . . . . . . . . . . . . . . 53
3.2.2.2 Spaghetti calorimeter (SPACAL) . . . . . . . . . . . 55
3.2.3 Luminosity system . . . . . . . . . . . . . . . . . . . . . . . . 56
3.2.4 Trigger system . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4 Selection of DIS events and K0S candidates 59
4.1 Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4.2 Data quality constrains . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.2.1 Run sample selection . . . . . . . . . . . . . . . . . . . . . . . 61
4.2.2 Vertex cuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.2.3 DIS kinematic range . . . . . . . . . . . . . . . . . . . . . . . 63
4.3 Selection of DIS events . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.3.1 Scattered electron energy . . . . . . . . . . . . . . . . . . . . . 64
4.3.2 Scattered electron polar angle and zimpact coordinate . . . . . 64
CONTENTS xxvii
4.3.3 Four-momentum conservation . . . . . . . . . . . . . . . . . . 65
4.4 Reconstruction of K0S candidates . . . . . . . . . . . . . . . . . . . . 65
4.4.1 Track cuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.4.2 Cuts to the K0S candidates . . . . . . . . . . . . . . . . . . . . 67
4.5 Event yield . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.6 Signal extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.7 Selection of charged particles . . . . . . . . . . . . . . . . . . . . . . . 76
5 The measurement of the cross section 77
5.1 Determination of the cross section . . . . . . . . . . . . . . . . . . . . 77
5.1.1 Binning scheme . . . . . . . . . . . . . . . . . . . . . . . . . . 79
5.2 The correction of data . . . . . . . . . . . . . . . . . . . . . . . . . . 80
5.2.1 Control plots . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
5.2.2 Reweighting procedure . . . . . . . . . . . . . . . . . . . . . . 87
5.2.3 Purity and Stability . . . . . . . . . . . . . . . . . . . . . . . 88
5.2.4 Efficiencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
5.2.5 Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
5.3 The systematic uncertainties . . . . . . . . . . . . . . . . . . . . . . . 95
5.3.1 Energy and polar angle of the electron . . . . . . . . . . . . . 98
5.3.2 Luminosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
5.3.3 Topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
5.3.4 Model dependence . . . . . . . . . . . . . . . . . . . . . . . . 101
5.3.5 Track efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . 102
5.3.6 Trigger efficiency . . . . . . . . . . . . . . . . . . . . . . . . . 103
5.3.7 Signal extraction . . . . . . . . . . . . . . . . . . . . . . . . . 103
5.3.8 Branching ratio . . . . . . . . . . . . . . . . . . . . . . . . . . 105
6 Results and conclusions 107
6.1 Total K0s cross section . . . . . . . . . . . . . . . . . . . . . . . . . . 107
6.2 Differential K0s cross section . . . . . . . . . . . . . . . . . . . . . . . 109
xxviii CONTENTS
6.3 Ratios of the differential cross sections . . . . . . . . . . . . . . . . . 110
6.3.1 Differential K0S/h± cross section . . . . . . . . . . . . . . . . . 115
6.3.2 Differential K0s /DIS cross section . . . . . . . . . . . . . . . . 115
6.4 Double differential cross section . . . . . . . . . . . . . . . . . . . . . 119
6.5 Comparison to QCD models . . . . . . . . . . . . . . . . . . . . . . . 119
6.5.1 Parton distribution functions . . . . . . . . . . . . . . . . . . 120
6.5.2 Flavour contribution . . . . . . . . . . . . . . . . . . . . . . . 121
6.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
A Reconstruction methods 129
A.1 The electron method . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
A.2 The hadron method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
A.3 The double angle method . . . . . . . . . . . . . . . . . . . . . . . . 130
A.4 The sigma method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
A.5 The electron-sigma method . . . . . . . . . . . . . . . . . . . . . . . 131
B Multiwire proportional and drift chambers 133
C Q and t measurement 137
D Track reconstruction 141
E Breit frame of reference 145
F Fits to mass distributions 149
G Resumen del trabajo de tesis 167
Bibliography 173
Chapter 1
Theoretical framework
The ep HERA collider at DESY enables through deep inelastic scattering (DIS)
events the study of the proton composition and the test of the Standard Model
and other aspects of Quantum Chromo Dynamics. The kinematic variables for the
description of the events are presented in this chapter, as well as the theoretical
framework of the simulation programs for DIS processes. The Lund fragmentation
model of hadronization describing the mechanism of hadron creation, an essential
part of the Monte Carlo programs, is presented.
1.1 Deep inelastic scattering
In 1911, Rutherford unexpectedly discovered the subatomic structure using the
scattering technique. An analogue of such a technique is used today in high energy
particle physics to study the substructure of hadrons. For DIS at HERA, the hadron
is a proton studied by the scattering of an electron beam off it.
The Deep Inelastic Scattering process at HERA consists in the interaction
of incoming electrons1 with incoming protons through the exchange of a virtual
boson [4]. The proton breaks up resulting in a final hadronic state system.
1For simplicit, the incoming and scattered electrons are always referred as ’electrons’, althoughthe data studied here were obtained with both electorns and positron beams.
1
2 CHAPTER 1. THEORETICAL FRAMEWORK
The DIS process can be of two types depending on the kind of the exchanged
boson. The neutral current process (NC-DIS), ep → eX, consists in the exchange of
a neutral gauge boson, a photon γ or a Z0 boson, X represents the hadronic final
states. The charged current process (CC-DIS), ep → νeX, is mediated by a charged
gauge boson W±, at the end there are a hadronic state system and a neutrino of the
electron.
Figure 1.1 shows the diagram of a NC-DIS event, the incoming electron e with
four-momentum k interacts with a quark of the incoming proton p which carries a
xP fraction of the four-momentum P of the proton, through the interchange of a
neutral virtual gauge boson (γ or Z0) with four-momentum q. After the interaction,
the scattered electron e′ has final four-momentum k′ and the proton breaks up into
a multiparticle state of hadrons denoted as X. The contribution of the Z0 boson to
the process only becomes significant at very high Q2 values compared to its mass2
squared. The CC-DIS events are not considered in this analysis.
a)
p
P=(Ep,p→
p)
X
qs (xP)q
γ, Z0 (q)
e+
k=(Ee,p→
e)
e+
(k’)
Figure 1.1: Neutral Current Deep Inelastic Scattering diagram, the four-momentumof the incoming electron (k), the scattered electron (k′) and the incoming proton (P )are shown. The transfer gauge boson can be γ or Z0.
The Q2 variable provides the specific wavelength λ = h/√
Q2 that allows to quan-
tify the resolution power of the experiment for the study of the proton components:
2MZ0 = 91.1876 ± 0.0021 GeV [11].
1.1. DEEP INELASTIC SCATTERING 3
if it increases then the resolution also increases.
1.1.1 Kinematics
The kinematics of the DIS process, for a fixed center of mass energy√
s, can be
described by two independent variables commonly chosen from the Lorentz invari-
ant variables: the negative squared of the four-momentum of the virtual exchanged
boson −q2 = Q2, the invariant mass squared of the final hadronic system W 2, the
dimensionless Bjorken scaling variable x and the inelasticity y. x represents the frac-
tion of the proton momentum carried by the struck quark and y corresponds to the
fractional energy transferred from the electron to the hadronic system in the proton
rest frame. The variables can be determined by the expressions: take values in
s = (k + P )2 (1.1)
Q2 = −q2 = −(k − k′)2 (1.2)
W 2 = (p + P )2 (1.3)
x =Q2
2P · q (1.4)
y =P · qP · k (1.5)
Neglecting the mass of the proton, the following relations are satisfied:
s ≈ 4EeEP (1.6)
Q2 ≈ sxy (1.7)
W 2 ≈ Q2
(
1 − x
x
)
(1.8)
where Ee and EP are the energies of the incoming electron and proton, respectively.
The correct reconstruction of DIS kinematics depends on how well the detector mea-
sures the neccessary variables for the calculation. Typically, the variables used for
reconstruction are the energy of the incoming and scattered electron Ee, E ′
e, the
polar angle Θe of the scattered electron, the sum Σ = Eh − pz,h of each hadronic
4 CHAPTER 1. THEORETICAL FRAMEWORK
final particle h and the inclusive angle γ of the hadronic system. There are three
basic methods sensitive to kinematic reconstruction [12]: those based on electron
information only (e electron method), those based on hadronic final measurements
only (Σ sigma method) and those combining electron and hadronic information (DA
double angle method). To know more about the different methods of reconstruction
see appendix A. The method chosen for this analysis is the electron method.
1.2 Theoretical DIS cross section
In the lowest-order perturbation theory for QCD, the DIS cross section can be
expressed in terms of the product of leptonic and hadronic tensors associated with
the coupling of the exchanged bosons at the upper and lower vertices:
d2σ
dxdy=
2πyα2
Q4
∑
j
ηjLµνj W j
µν .
where the summation is over j = γ, Z for NC-DIS, ηj denotes the corresponding
propagators and couplings, Lµνj is the lepton tensor associated with the coupling
of the exchange boson to the leptons and the hadronic tensor W jµν describes the
interaction of the appropiate electroweak currents with the proton.
The part of the lepton tensor is very well understood but the proton structure
functions defined in terms of the hadronic tensor are not. The best attempt of the
complete modeling of DIS event is made by the Monte Carlo simulation programs.
1.3 Event generators: Monte Carlo programs
The Monte Carlo programs (MC) are computational tools for simulation in the
physical and mathematical sciences, business, economy, telecommunications, design,
and even games. They are very useful and successful methods due to their ability for
modeling systems with a large number of degrees of freedom, many-body problems
and/or systems under complicated conditions.
1.3. EVENT GENERATORS: MONTE CARLO PROGRAMS 5
The applications to high energy physics are related to the design of detectors, ac-
celerators and detectors performance, difficult QCD calculations by the evaluation of
difficult integrals and sample random variables governed by complicated probability
density functions.
In MC programs for DIS particle physics, the hadronic tensor part of the cross
section is considered as a convolution of matrix elements ME, parton density func-
tions PDFs and fragmentation functions Dfrag. The separation of matrix elements
(the interaction of the parton with the boson) and PDFs (the partonic structure of
the proton) is given by the factorization scale µF as shown in Figure 1.2. The mean-
ing of µF can be understood roughtly as: if the emission with transverse momenta is
below µF they are accounted within the PDF, if it is higher than µF are included in
the interaction. In inclusive DIS, the default choice for the scales is usually µF = Q2.
K0s
K0s
K*+
F
Figure 1.2: The factorization scheme of a DIS event showing the perturbative crosssection eγ∗, the non-perturbative parton density function (PDF).
PDFs are non-perturbative objects which can not be computed within pQCD,
but the evolution of PDFs as they move in phase space can be computed perturba-
tively. Several groups have proposed fits for the PDFs based on different theoretical
6 CHAPTER 1. THEORETICAL FRAMEWORK
assumptions, the two most famous approaches are the DGLAP [13] (Dokshitzer, Gri-
bov, Liatov, Altarelli, Parisi) and the BFKL [14] (Balitsky, Fadin, Kuraev, Lipatov)
evolution equations.
The MC event generators involve several stages, the generation of an event starts
with the random generation of the kinematics and partonic channels of whatever
hard scattering process (the ME) the user has requested. This is then followed by the
parton cascade (CDM and MEPS as chosen in the MCs simulated for this analysis,
see section 1.3.1) down to a scale ∼ 1 GeV that separates the perturbative and non-
perturbative part of the simulation. These cascades are governed by a model of the
evolution equations previously mentioned. Once the partonic configuration has been
generated, the fragmentation process (where the parton fragmentation functions take
place) starts to model the hadronization of the final state system. The Lund string
model has been chosen for the MCs used in this analysis, the description can be
found in the subsection 1.3.2.
1.3.1 Colour dipole model and parton showers
As mention above, two different parton cascade approaches are applied for the
two DIS MCs used in this thesis: the colour dipole mode (CDM) and the parton
showers (MEPS).
The CDM model describes the parton radiation in terms of a colour field gener-
ated by a chain of radiating colour dipoles extending between a pair of colour charges.
A gluon is emitted from a colour dipole forming two independent colour dipoles as
shown in Figure 1.3 a). Further gluons can be radiated, leading to a chain of colour
dipoles, where one gluon connects two dipoles, and one dipole connects two gluons.
The CDM evolving parton cascade has no strong ordering in the transverse momenta
kT of the emitted gluons.
On the other hand, the MEPS model considers that a parton of the proton can
initiate a parton shower by radiating gluons, which become increasingly space-like
(m2 < 0) after each branching, see Figure 1.3 b). After the exchanged electroweak
1.3. EVENT GENERATORS: MONTE CARLO PROGRAMS 7
K0s
K0s
K*+
K0s
K0s
K*+
Figure 1.3: The Django and Rapgap MCs scheme used in this thesis. It is possibleto observe the MC treatment of the DIS events: the matrix elements, marked σ,the parton density funcion PDF and the parton cascade simulated according to a)the colour dipole model and b) the parton shower, and the hadronization processmodeled with the string fragmentation model.
a) b)
boson is absorbed, the struck quark becomes on-shell (has a time-like virtuality
m2 > 0). In the latter case a final state shower will result, with both the virtuality
of the struck quark and the off-shell mass of the radiated gluon decreasing after each
successive branching. Any time-like parton produced in an initial shower will have
a similar evolution.
The parton shower is based on DGLAP equations with strong ordering in the
transverse momenta kT of the emitted gluons.
1.3.2 Fragmentation and hadronization
The hadronization process is a long-distance transition from the free coloured
quarks at parton level to the colour neutral final states or hadrons, involving only
small momentum transfers. The idea is based on the independent splitting or frag-
mentation of each parton, gluon or quark from the parton cascade or the hard process,
which then mix (hadronize) to create the final baryons and mesons.
8 CHAPTER 1. THEORETICAL FRAMEWORK
The fragmentation process evolves perturbatively, so the fragmentation functions
can be determined describing the production of hadrons h from a quark q at a given x-
Bjorken value and four-momentum transfer squared Q2. However, the hadronization
mechanism can not be treated perturbatively so detailed phenomenological predic-
tions have been developed. The two commonly used models are the cluster fragmen-
tation and the string fragmentation, both are expected to be universal which means
that should reproduce results from e+e− collisions and ep scattering. For the MCs
generated for this analysis only the string fragmentation model is used, since have
been found that the cluster model does not describe the DIS physics.
q_ q
_
q_
q_
q_
q_
q_
q_
q_
q_
q_
Dis
tanc
e
q
q
q
q
q
q
q
q
q
Time
Mesons
Figure 1.4: The string fragmentation model.
The scheme of hadronization by the Lund string fragmentation model [15] con-
siders the colour field between the partons, quarks and gluons, to be the fragmenting
entity rather than the partons themselves. In it, a produced quark-antiquark can be
viewed as moving apart from their common production vertex in opposite directions,
losing kinetic energy to the colour field, represented by a colour string stretching
between them and providing a linear rise of the potential energy stored in the colour
string due to their separation. When the potential becomes energetically favourable,
the string breaks up into two new qq colour strings forming out of the vacuum (or
1.3. EVENT GENERATORS: MONTE CARLO PROGRAMS 9
colour field). If the invariant mass of either of these two resulting colour strings
is large enough, the breaking continues iteratively, creating more qq pairs, see Fig-
ure 1.4. The gluons are supposed to produce kinks on the string, each initially
carrying localized energy and momentum equal to that of its parent gluon.
In this model, the string break up process proceeds until only on mass-shell
string fragments combined into mesons and baryons remain. The qq pairs are
created according to the probability of a quantum mechanical tunneling process.
The production probability can be estimated from the product of the q and the q
wave functions and the colour field potential [16]. Due to the dependence on the
parton mass and/or the hadron mass, the production of strange and, in particu-
lar, the heavy quark hadrons is suppresed. The relative production is assumed as
u : d : s : c ≈ 1 : 1 : 0.3 : 10−11. The charm and heavier quarks (b and t) are not
expected to be produced in the soft fragmentation, but only in perturbative cascade
branchings g → qq.
The model considers as important free parameters for the production of strange
particles the following relative production probabilities:
• The strangeness suppression factor λs = P (s)/P (q), expresing the ratio pro-
duction probability of strange quark s to light quarks up u and down d.
• The diquark suppression factor λqq = P (qq)/P (q), which gives the production
probability of a light diquark pair P (qq) relative to a light single quark pair
P (q).
• The strange diquark suppression factor λsq = (P (sq)/P (qq))/(P (s)/P (q)) pro-
viding the ratio probability of a diquark pair production containing a strange
quark P (sq) to the diquark pair production P (qq), normalised to the strangeness
suppression factor.
Although in detail, the string motion and fragmentation is more complicated
with the appearance of additional string regions during the time evolution of the
10 CHAPTER 1. THEORETICAL FRAMEWORK
system, the scheme is infrared safe. After the particles have been produced with
the hadronization model, the MC programs use the measured decay channels and
branching ratios to simulate their decays, yielding at the end of the process a list of
stable particles.
1.4 Django and Rapgap Monte Carlo programs
In this analysis, two Monte Carlo generators are considered: Django and Rapgap.
Both MCs simulate lepton-nucleon scattering physics, the difference radicates in the
treatment of the parton cascade process: Django is based on CDM and Rapgap
in MEPS. The hadronization process is chosen to be the Lund string fragmentation
model [15] as implemented in the JETSET program [17], tuned to ALEPH parameter
values [18]: λs = 0.286, λqq = 0.108 and λsq = 0.690.
Two sets of MCs are generated for each Django and Rapgap, one including the
possibility of the initial and final radiation which is called the radiative MC and one
without including this possibility, the so called non-radiative MC.
The radiative events are passed through the GEANT [19] simulation of the H1
apparatus in order to reproduce the detector response (reconstructed MC) whereas
the non-radiative MC are produced only at the parton level. Both are used for data
corrections.
The MC’s for comparison to data are generated without including initial and
final radiation with CTEQ PDF for the three different strangeness values λs =0.22,
λs =0.286 and λs =0.3. And other MC samples are produced with λs =0.286 but
considering as PDFs the CTEQ6L, H12000LO and GRV98.
1.4.1 Django
The Django [20] simulator of ep scattering events assigns the event proper-
ties, as the phase space, the initial conditions and the kinematic cuts with HER-
ACLES [21] [22]. The QCD part is implemented by LEPTO [23] or ARIADNE [24].
1.4. DJANGO AND RAPGAP MONTE CARLO PROGRAMS 11
Django as used for this work uses ARIADNE to generate the cascade of partons and
is based on the colour dipole model CDM.
Different PDFs can be used with the MCs. For this MC, the used PDFs are
CTEQ6LO [25], GRV98 [26], and H12000LO [5]. The renormalisation and factoriza-
tion scale are placed to µR = µF = Q2.
In total, there are four simulated radiative samples of events with Django, each
corresponding to the data periods where HERA ran either with electrons or positrons.
From the Django samples, one corresponds to the 2004e+p period, has 7 millons
of events and luminosity value equals to 1535 pb−1; for 0405e−p year there are 14
million events with corresponding luminosity of 3048 pb−1; for 2006e−p the MC has
7 millions of events corresponding to a luminosity value of 1524 pb−1 and the sample
for 0607e+p with 20 millions of events and 4383 pb−1 of luminosity.
The non-radiative files for each year period correspond to samples of 20 mil-
lion of events with luminosity of approx. 6320 pb−1 for the samples with e−p and
approximately 6379 pb−1 for the samples with e+p.
1.4.2 Rapgap
In Rapgap MC [27] the DIS events are simulated by LEPTO. The hard interaction
is taken as the standard model electroweak cross section and the implementation of
QCD parton showers at leading order are based on DGLAP splitting functions in
leading order αs. The matrix elements for leading order αs processes, as BGF and
QCDc, and the QED corrections are included by the interface to HERACLES event
generator.
The same PDFs (CTEQ6LO, GRV98 and H12000LO), normalisation and factor-
ization scales (µR = µF = Q2) as in Django, were used for Rapgap in order to be
congruent in the comparison between both models.
The radiative samples for Rapgap are of 6 millons of events for 2004e+p with
luminosity of 1529 pb−1; for 0405e−p are 12 millions of events with luminosity of
3034 pb−1; the 6 millions of events for the 2006e−p period has luminosity equals
12 CHAPTER 1. THEORETICAL FRAMEWORK
to 1516 pb−1 and for 0607e+p period are 12 millions of events and luminosity of
3056 pb−1.
The non-radiative samples consist of 20 millions of events for each year with
L = 6920 pb−1 for the periods with e−p collisions and L = 6996 pb−1 for those with
e+p.
Chapter 2
Strange mesons
There are several interesting topics in particle physics which are not completely
understood yet. The study of K0S meson production in DIS improves the cur-
rent understanding of the particle creation during hadronization, the mechanism
of strangeness production, QCD aspects related to strange quarks, and allows to
study the resonant production of particles including K0S in their decay modes, like
heavier standard particles or exotic particles like glueballs.
In this chapter, the most relevant properties of the K0S particles, their different
production mechanisms and previous related results obtained in e+e−, heavy ion and
ep collisions are presented. Special emphasis is given to most recent results of the
H1 collaboration K0S production at low Q2 values.
2.1 What is a K0S meson?
As mentioned in the preface, nature is made of strongly interacting particles
called hadrons. There are two kind of hadrons, baryons and mesons. The baryons
are bound states of three quarks, while mesons are bound states of a quark and an
antiquark.
Mesons have also angular momentum J = L+S, where L represents the orbital
angular momentum (L = 0,1,2,...) and the meson spin is denoted by S (S = 0,1).
13
14 CHAPTER 2. STRANGE MESONS
When the meson has L = 0, it is called pseudoscalar or vector depending whether
S = 0 or S = 1, respectively.
If only the three lighter quarks (up u, down d and strange s) of the standard
model are taken into account, something known as SU(3) algebra, there are eight
pseudoscalar and eight vector mesons. Using their properties – the strangeness quan-
tum number S, charge Q, isospin I3 or mass – it is possible to plot the particles in
a coordinate system and obtain geometric figures of remarkable shape, as the octect
of pseudoscalar mesons [11] shown in the Figure 2.1 and listed in Table 2.1.
Figure 2.1: Octect of the pseudoscalar mesons plotted in the axis corresponding tostrangeness quantum number S, charge Q and isospin I3.
An important observation is that K0 can be produced by non-strange particles
together with a hyperon [28], but K0 is only produced in association with a Kaon or
a hyperon:
π+ + p → Λ + K0
S 0 0 − 1 + 1
π+ + p → K+ + K0 + p
S 0 0 + 1 − 1 0
this indicates that K0 and K0 have different strangeness quantum number. Then,
the question is how to establish the presence of these two mesons.
2.1. WHAT IS A K0S MESON? 15
Table 2.1: List of the pseudoscalar and vector mesons with the specification of theirquark content.
Pseudoscalar Vector
Particle symbol Quark content Particle symbol Quark content
π− ud ρ− ud
π0 1/√
2(dd − uu) ρ0 1/√
2(uu − dd)
π+ ud ρ+ ud
K0 ds K∗0 ds
K+ us K∗+ us
K− us K∗− us
K0 ds K∗0 ds
η′ ss φ ss
Although both are usually produced via the strong force, they decay weakly. As
weak interactions do not conserve strangeness, once they are created one can turn
into another. The K0 can turn into a K0 and then turning back to the original K0,
and so on. The Figure 2.2 shows a strange quark in the K0 turning into a down quark
by successively emitting two W-bosons of opposite charge. The down antiquark in
the K0 turns into a strange antiquark by absorbing them.
_
__ _
Figure 2.2: Diagram of the K0 turning into a K0. A strange (down) quark (anti-quark) from the K0 turns into a down (strange) quark (antiquark) by the emissionof two W -bosons of opposite charge.
Experimentally it was found that a K0 produced by strong interactions decays
16 CHAPTER 2. STRANGE MESONS
with two different lifetimes [28]: K0 → ππ and K0 → πππ, so K0 seems to be two
different particles when studying its weak decays. The same is observed for K0.
This implies that if one has a pure K0 state at t = 0, at any later time t one will
have a superposition of both K0 and K0 (equation 2.1). It is known that particles
decaying by weak interactions are eigenstates of charged parity (CP), expressed as
the equation 2.2.
|K(t) > = α(t) |K0 > + β(t) |K0 >, (2.1)
CP |K0 > = |K0 > . (2.2)
Since K0 and K0 are not CP eigenstates, there must be linear combinations:
|K0S > =
1√2
(
|K0 > + |K0 >)
CP = +1, (2.3)
|K0L > =
1√2
(
|K0 > − |K0 >)
CP = −1. (2.4)
These two different modes of decay were observed by Leon Lederman and his
coworkers in 1956, establishing the existence of the two weak eigenstates called K0S
as referred in equation 2.3 and K0L as referred in equation 2.4. Later, James Cronin
and Val Fitch in 1964 (Nobel Prize in 1980) showed that a small CP symmetry
violation exists, but the states already assumed are still a very good approximation.
Since the mass of K0L is just a little larger than the sum of the masses of three
pions, this decay proceeds very slowly, about 600 times slower than the decay of K0S
into two pions.
The main properties of the K0S are I(JP ) = 1
2(0−), the mass value of 497.648 ± 0.022
MeV and the lifetime value τ = 0.8953 x 10−10 ± 0.0005 s or cτ = 2.6786 cm [11].
The K0S mesons decay by three different general modes: hadronic, with photons or
lepton anti-lepton ll, and semileptonic. The hadronic modes containing the most
frequent decay channels are listed in Table 2.2.
2.2. PRODUCTION OF K0S 17
Table 2.2: The K0S most frequent hadronic decay channels and their branching ratio
values [11].
K0S Decay channel Branching ratio
π0π0 30.69 ± 0.05 (%)
π+π− 69.20 ± 0.05 (%)
π+π−π0 3.5+1.1−0.9 x 10−7
2.2 Production of K0S
The strange quark s is not so heavy as the bottom (mb = 4.2 +0.17−0.07 GeV), charm
(mc = 1.27 0.07−0.11 GeV) or top quarks (mt = 171.2 ± 1.1 ± 1.2 GeV) but it is also not
light as up (mu = 2.55 +0.75−1.05 MeV) or down (md = 5.04 +0.96
−1.54 MeV) quarks. It has a
mass value of 105+25−35 MeV [11] what allows its creation in ep collisions at HERA.
There are different mechanisms of strange particle production, which are illus-
trated schematically in Figure 2.3, the hard interaction or QPM process, the boson
gluon fusion process (BGF), heavy decays and hadronization processes.
The hard interaction or QPM process occurs when the photon of the DIS
event interacts directly with a s quark belonging to the quarks of the proton sea.
This process involves a large momentum transfer, Figure 2.3 a).
The strange production through BFG process consists of the photon inter-
acting with a gluon emitted by the proton, which splits into a ss quark pair, see
Figure 2.3 b). As the gluon density of the proton increases at small Bjorken scaling
variable x, the BFG becomes more important at low x values.
The Figure 2.3 c) shows the heavy decay process . It is similar to the BFG
process but in this case the gluon splits into heavy quarks (c and b); then they decay
into s quarks. Due to the small probability to find c and b quarks in the proton sea,
this is the main mechanism of strangeness production by heavy quarks. At low Q2
values this process is highly suppressed due to the masses of the heavy quarks, but
18 CHAPTER 2. STRANGE MESONS
−
−
−
*
−
−
−
−
Figure 2.3: The four different mechanisms of strange particle production: a) hardinteraction or QPM process, b) boson gluon fusion (BGF), c) heavy quarks decaysand d) hadronization.
a) b)
c) d)
2.3. WHY STRANGENESS STUDIES ARE IMPORTANT? 19
at very high Q2 where the quark masses are not relevant with respect to the process
scales, this process can contribute significantly.
The hadronization process is due to the colour field fragmentation as showed
in Figure 2.3 d). This is the only process which can not be treated perturbatively,
so phenomenological models are needed for its description, such as the LUND string
model. Furthermore, this process provides the largest contribution of strangeness
production over most of the phase space.
2.3 Why strangeness studies are important?
The study of strangeness has been done since the discovery of the first two mesons,
the pion and the kaon, in cosmic rays in 1947 which marked the birth of this subject
on particle physics.
It is interesting because the strange flavour does not exist in ordinary matter, it
appears at colliding machines when the center of mass energy of the reaction is much
larger than the strange hadron masses. The strange mesons and baryons produced
are also not present at the beginning of the collision, they should be cooked in the
reaction in some way, therefore the study of strangeness production provide essential
information about the physical environment created in the collisions.
The strange particle properties make them also interesting, they are all unstable
particles living very short time before decaying into stable particles. The decay
channels and production rates are of considerable interests because they should reflect
the dynamics of the strong interaction.
Since the dynamics of flavour production in colour confinement processes is one
of the big open questions in particle physics, the production of strange hadrons in
high energy reactions provides an extremely valuable study, so the mechanism of
strangeness production has attracted considerable attention, both in perturbative
and non-perturbative regimes. The study of the hadronization process of strange
particle production (an other particles in general) bring us towards a deeper under-
20 CHAPTER 2. STRANGE MESONS
standing of the strong forces responsible of the confinement.
The rate of strange quark production as compared to production rates for light up
or down quarks depends on the energy density in the colour field providing therefore
a measurement of the energy density and the string constant, in other words, the
typical scales of space, time and momentum transfer involved in the confinement
process.
The phonomenologycal models can also be tested by the comparison to strangeness
results from data, and the optimization of their parameters can be performed. This
is very important since due to our limited knowledge some tests rely strongly on
phenomenological models only.
So far, the Lund string model which provides a rather convincing phenomenology
of hadron production in general, and of strange particle production in particular, uses
the strange to light flavours ratio as a natural explanation calling it, the strangeness
suppression factor λs (see also subsection 1.3.2).
Studies of the strangeness production cross section in different regions of the
phase space have been compared to simulation based on the Lund string model, but
certainly no unique λs describes the data perfectly. What has been found is that a
λs value between 0.2 - 0.3 gives a surprisingly good description, not only of the inclu-
sive strange-particle production, but also of correlations between strange particles,
being the only models of baryon production which have survived the experimental
tests including as well the diquark strangeness factors to assume occasional diquark-
antidiquark pair production in the confinement process to explain the formations of
baryons.
The studies of different ratios providing rather direct measurement of λs, λqq
and/or λsq, as the strange to non-strange ratio: K0S /π, Λ/p, strange to non-strange
charmed mesons and strange to non-strange bottom mesons can also provide good
information but no experimental data is available for all of them.
The same suppression factor is expected to describe both the meson and the
baryon sector, however a perfect determination of λs requires knowledge of the cross
2.3. WHY STRANGENESS STUDIES ARE IMPORTANT? 21
sections and determination of all resonances feeding into stable hadrons which is very
difficult and is not yet fully complete.
The availability of data from different collision types is an advantage for the
strangeness production studies and MC tests due to the differences in the physics
escenarios, but also the compatibility among them in some regions. At the end the
comparisons can test the strangeness universality if all methods yield the same λs.
The particle production in pp collisions at a given√
spp compared to e+e− anni-
hilation at√
s =√
spp/2 have not shown drastic differences in the strange-particle
production rates.
The e+e− annihilation advantage is the detection of the baryon polarization be-
cause the configuration of the colour field is much better known, providing a further
excellent test of string models. Baryon production is best studied in processes with-
out incident baryons, such as this case, since the strange diquark is hence more
strongly suppressed than a strange quark.
The heavy ion collisions also play important roles in many aspects, for instance an
enhancement of the strange particle production in nucleus-nucleus collisions relative
to proton-proton reactions have been established, finding that it depends on the
strangeness content of the particle type, that is the reason of investigations of the
energy and system size dependence of strangeness production. The enhancement was
one of the first suggested signatures for quark gluon plasma QGP formation [29].
Another important point that makes the strange particle analysis interesting
is the search for exotic states as pentaquarks (states with more quarks than the
conventional qqq and qq states) and glueballs (e.g. looking for glueball decaying to
K0SK0
S states).
The particle data group [11] lists a number of unestablished resonances, such
as Θ+ state whose signal has been reported in previous experimental studies [30]
looking for decaying modes including K0S particles. In the same aspect some other
particles for instance D0, Λc and K∗ also have K0S mesons in their decay modes, so
a good selection of the K0S mesons can help to the reconstruction and study of these
22 CHAPTER 2. STRANGE MESONS
heavy particles.
Other possible studies include the strangeness content of the pomeron in diffrac-
tive DIS and the determination of the strange structure function F2(s).
2.4 Previous strangeness production studies
Several studies have been done since many years ago in the strangeness field
looking for mesons, baryons, resonances and even exotic signals. Not only at HERA
ep experiments, but also in pp, heavy ions and e+e− collisions at either linear or ring
colliders at different center of mass energies and regions of phase space.
2.4.1 At e+e− colliders
The DELPHI detector at LEP presented results on inclusive production rates
per hadronic Z decay of Σ− = 0.081 ± 0.010 and Λ(1520) = 0.029 ± 0.007. The
total production rates of vector, tensor and scalar mesons and of baryons follow
phenomenological laws related to the spin, isospin, strangeness and mass of the
particles. This statement was confirmed by other LEP experiments (ALEPH, L3 and
OPAL). In the same study, the ratio Λ(1520)/Λ production increases with increasing
scaled momentum xp. A similar behaviour was found for the ratio of tensor to
vector meson production, f2(1270)/ρ0 but no increase was seen for f0(980)/ρ0 and
a±
0 (980)/ρ± [31]. The strange pentaquark search was performed by the DELPHI
collaboration. None of the states that were searched for was found. Upper limits
were established at 95% CL on the average production rates of such particles and
their charge-conjugate states per hadronic decay.
The π0, η, K0S and charged particle multiplicities were determined for quark and
gluons jets by OPAL collaboration. The multiplicity enhancement in gluon jets was
found to be independent of the studied particle species. The measurement of charged
particle multiplicity in strange flavoured Z0 decays gave < ns >= 20.02 ± 0.13(stat.)
+0.39−0.37 (syst.), while the strangeness factor λs determined was 0.422 ± 0.049 (stat.) ±
2.4. PREVIOUS STRANGENESS PRODUCTION STUDIES 23
0.059 (syst.) [32].
The L3 collaboration measurement of the Λ and Σ0 cross sections at center of
mass energies from 91 GeV to 218 GeV by the processes γγ → ΛΛ and γγ →Σ0Σ
0were extracted as function of the center of mass energy and compared with
CLEO collaboration results, as well to quark-diquark model and three quark model
predictions [33]. Other analysis provided the average number of < NΣ+> + <
NΣ+>= 0.114 ± 0.011 (stat.) ± 0.009 (syst.) and < NΣ0
> + < NΣ0>= 0.095
± 0.015 (stat.) ± 0.013 (syst.) finding that JETSET, HERWIG and ARIADNE
predictions subestimated the measurements [34].
The measurement of inclusive production of the Λ, Ξ− and Ξ∗(1530) baryons in
two-photon collision with the L3 detector were described by PYTHIA and PHO-
JET Monte Carlo programs, the comparison to e+e− annihilation processes provides
evidence for the universality of fragmentation function in both reactions; while the
search for inclusive production of the pentaquark Θ+(1540)→ pK0S showed no sig-
nal [35].
The CLAS collaboration at Jefferson laboratory presented a work with main
goal of measuring observables related to the propagation of a quark struck by the
virtual photon from DIS through cold nuclear matter and compared with quark
propagation through hot QCD matter, or quark gluon plasma (QGP) formed in
relativistic heavy ion collisions at RHIC. That work presented for the first time
results for K0S hadronization plotting the multiplicity ratios of K0
S over DIS events
versus the energy fraction z [36].
2.4.2 At pp and heavy ions collisions
The KAOS collaboration with CC and AuAu collisions at 1-2 GeV where the
kaon emission is a rare process, reported studies of K+ and K− particle production,
showing a dependence on the mass number A of the colliding system, as well as
differences between the K+ and K− cross sections σ per A5/3. The same conclusion
was made for the same particle at different kinetic energies for three different systems
24 CHAPTER 2. STRANGE MESONS
and various beam energies [37].
The FOPI detector studying nuclear matter at high temperatures/high density in
the heavy ion collider GSI in SIS have studied Λp, Λ, K0, φ, Σ∗(1385) and K∗(892).
The inclusive K0 cross section results as function of the target nucleus A after using
π− beam against target nuclei C, Al, Cu, Sn, and Pb, showed an increase at higher
A values [38] and confirming the KAOS collaboration results.
The HADES collaboration also made measurements of strangeness (K+,K−, Λ,
ρ, K0S and Ξ particles) in Ar+KCl system at 1.756A GeV. The results of measured
yields and slopes of the transverse mass of kaons and Λ agrees with KAOS and
FOPI studies [39]. An effective temperature of the kinetic freeze-out of TEff =
92.0 ± 0.5 ± 4.1 MeV [40] is achieved for the K0S .
The CERES studied the K0S yield at midrapidity dN/dy and transverse momen-
tum distributions in central PbAu collisions at top SPS energy [41]. The results were
compared to NA49 [42] and NA57 [43] measurements. An agreement with NA57 K0S
was found in the overlapping rapidity bins within errors.
The PHENIX (pp) [44] and the STAR (AuAu) [45] collaborations at RHIC with√
200 AGeV center of mass energy have measured the ratio of K/π giving a value
between 0.1 - 0.5 and showing very similar results at low pT although a slight hint of
strangeness enhancement (around 20%) is indicated in nucleus collision relative to
pp collisions. The same is expected at LHC [46].
The NA49 collaboration at SPS have also identified K∗(892), K±, ρ, Ξ and Ω
particles [47] and measured the K∗/K± ratio as function of the average number of
wounded nucleons Nw and the resonance lifetime cτ ; while another paper from the
STAR collaboration colliding CuCu and AuAu at√
s =62 GeV, presented the mid-
rapidity dN/dy for K0S , Λ, Ξ and Ω particles and also mid-pT results of the Λ/K0
s
ratio, concluding that the centrality dependance of dN/dy per < Npart > has similar
trends to a parametrisation on the fraction of participants that undergo multiple
collisions. The ratio RAA = (dNAA/dy)/(dNpp/dy) for K0S showed to be greater than
the same ratio for π, providing evidence for parton flavour conversions in heavy-ion
2.4. PREVIOUS STRANGENESS PRODUCTION STUDIES 25
collisions [48].
Other studies with pp collisions have tried to determine the total cross section of
still scarce reactions as pp → nK+Σ+, pp → nK+Σ0 and pp → nK+Λ [49] including
contributions from previously ignored ∆∗(1620) and N∗(1535) resonances. They
shown that these resonances play dominant roles for strangeness production in pp
collisions.
At this section one also ask about the new LHC age, although it consists of
four experiments only ALICE has planes of strangeness studies (in part because
the detector design allows it), a lot of prediction was done concluding the easy
and clear identification of K0S, Λ, Ξ, Ω particles and some resonances [50] but no
measurement are public until today. It is, however, natural to expect that in the
high energy-density phase (quark gluon plasma, QGP) up, down and strange quarks
have similar populations and play equivalent roles. RICH results didn’t confirm that
but it could becomes a good approximation at LHC energies at QGP. Maybe the
expected enhancement of strange anti-baryon production, as proposed by Muller and
Rafelski [29] will be observed.
Can we expect that more final-state strange particles are produced with larger
transverse momenta and pQCD is going to provide more precise predictions?. The
role of strangeness will change at the LHC energies? Do the s quark behave as light
u and d quarks and does charm appear as the first massive flavour?. These and other
questions can find answer in the following few years, being a good reason to continue
with strangeness studies.
2.4.3 At ep colliders
The HERA experiments, HERMES, HERA-B, ZEUS and H1, have also done
measurements of several strange particles, mainly of K0S meson, Λ, Λ baryons, K0
s K0s
and baryonic resonance production.
The fixed target HERA-B experiment measured the cross section rates of K0S , Λ
and Λ [51], K∗0, K∗0
and ρ mesons using C, Ti and W as target materials showing
26 CHAPTER 2. STRANGE MESONS
a power law dependence with the atomic mass of the target. And also reporting a
smaller production of K∗ and K∗0
compared with K+ and K− [52].
The HERMES detector showed that s quarks of Λ, Λ originate predominantly
from s pair production from γ [53].
The Zeus experiment have made a high statistics study of the K0s K
0s system us-
ing the full HERA II data set in the phase space pT (K0s ) ≥ 0.25 GeV and |η| ≤ 1.6.
A number of 672418 K0s K
0s pairs coming mainly from photoproduction were identi-
fied, reporting an observation of states at 1537 MeV and 1726 MeV consistent with
f ′
2(1525) and close to f0(1710), also an enhancement near 1300 MeV which may arise
from the production of f2(1270) and/or a02(1320) [54]. Agreement with the measure-
ments done by L3 [55] and TASSO [56] collaborations at γγ → K0s K
0s was found.
The H1 collaboration have not confirmed these results since no paper or thesis of
these measurements exist until now.
The pentaquark searches at Zeus have looked for baryonic states decaying to
K0S p and K0
S p [57]; e.g., the pentaquark Θ+(uudds) (reported for fixed-target experi-
ments [30]). They find a peak with 221±48 events at 1521.5 ± 1.5(stat.)+2.8−1.7(syst.) MeV
for Q2 ≃ 20 GeV2 providing further evidence for the existence of a narrow baryon
resonance consistent with the predicted Θ+ pentaquark state. Another study at
Q2 >1 GeV2 for Ξ−π−, Ξ−π+ decay channels [58] by ZEUS also gives a clear signal
for Ξ0(1530) → Ξ−π+, but no other signal at higher masses (Ξ−−
3/2 and Ξ+3/2) was
observed. The H1 studies of these resonances are presented in the subsection 2.5.1.
Concerning measurements of the K0S and Λ production, baryon-antibaryon asym-
metry, baryon to meson ratio and strange to light hadrons ratio: The results of
ZEUS in the phase spaces corresponding to photoproduction (Q2 ≃ 0) and DIS
(2< Q2 <25 GeV2 and 25 GeV2 < Q2) collected at√
s = 319 GeV compared to
different ARIADNE and PYTHIA MC models [59] conclude that the DIS results are
reproduced by ARIADNE with λs = 0.22 in gross features, while PYTHIA describes
the cross section as functions of pT and η but doesn’t for x dependence. No Λ - Λ
asymmetry is found. The strange to light quarks ratio is in agreement with e+e−
2.5. PREVIOUS H1 RESULTS OF STRANGENESS AT LOW Q2 27
results but the baryon to meson ratio is larger that e+e− measurements.
The H1 experiment has very nice and recent results of the K0S and Λ production
rates at DIS low Q2 which can be found at references [60], [61] and [62]. The last
published results are discussed extensively in the subsection 2.5.3. The first mea-
surement of the K∗(892) vector by the H1 collaboration at low Q2 is presented in
the subsection 2.5.2.
2.5 Previous H1 results of strangeness at low Q2
The most important studies carried out by the H1 experiment involving the identi-
fication of K0S meson or other strange particles are the search of predicted resonances
as Θ+ → K0S p± and Ξ0(1530) → Ξ−π+, the identification of K∗(892) meson and the
analysis of K0S meson and Λ baryon. All of them through the analysis of data at low
Q2.
2.5.1 Search of resonances
Figure 2.4: Invariant mass spectra of a) K0S candidates reconstructed by the decay
mode π+π− and b) Θ+ candidates decaying to K0S p±, no signal is observed in the
mass range of 1.48 to 1.7 GeV.
b)
28 CHAPTER 2. STRANGE MESONS
A search of the hypothetical baryon Θ+ in the decay channels K0S p± as ob-
served by several fixed-target experiments is done at H1, in the phase space 5<
Q2 <100 GeV2 and 0.1< y <0.6. The data were taken during the years 1996-2000
(HERA I1) with a luminosity of 74 pb−1.
The K0S is reconstructed by looking for π± tracks coming from a secondary vertex
in the central part of the detector. The invariant mass distribution fitted to two
Gaussian functions is showed in Figure 2.4 a). A number of 133,000 K0S candidates
are obtained after subtracting the background.
The combination of the K0S candidate with the proton candidates gives the recon-
struction of Θ. The detailed procedure is explain in [63]. The mass range considered
for the search is 1.48 to 1.7 GeV since the reported masses are between 1520 and
1540 MeV. No signal for the resonance Θ+ production is observed in the studied
decay modes as shown in the mass distribution spectra in Figure 2.4 b) where the
corresponding upper limits are also shown.
The analysis was repeated at large Q2 and low proton momentum region in which
ZEUS collaboration made its observation but no evidence was found.
The analysis of baryonic resonances and their antiparticles X−− and X0 in the
mass range 1600 to 2300 MeV is also carried out with the H1 detector. The search
is perfomed in the region defined by 2< Q2 <100 GeV2 and 0.05< y <0.7 using data
taken in 1996-1997 and 1999-2000 with L = 100.5 pb−1. The particle decay modes
are X−− → Ξ−π− → [Λπ−]π− → [(pπ−)π−]π− and X0 → Ξ−π+ → [Λπ−]π+ →[(pπ−)π−]π+.
The identification of these particles is done first by looking for the Λ (Λ) baryon
by their p (p) and π− (π+) daugther signals, second it is made a combination of the Λ
candidate with negatively charged track assumed to be a pion and third, the X−−/0
candidates are formed by combining each of these Ξ− candidates with an additional
pion track; for extended explanation of the reconstruction, see references [64] or [61].
In Figure 2.5 one can see the resulting invariant mass spectra for the neutral
1The description of the HERA I and HERA II data can be found in the chapter 3.
2.5. PREVIOUS H1 RESULTS OF STRANGENESS AT LOW Q2 29
Figure 2.5: Invariant mass distribution of the combinations a) Ξ−π+, b) Ξ+π−, c)Ξ−π− and d) Ξ+π+ with the fit to signal and background. A clear signal of theΞ0(1530) baryon is observed for the neutral combinations in the mass range of 1600to 2300 MeV.
a) b)
c) d)
30 CHAPTER 2. STRANGE MESONS
Ξ−π+ and Ξ−π+, and the doubly charged combinations Ξ−π− and Ξ+π+. In the
neutral particle distributions, a peak is observed corresponding to the established
Ξ0(1530) state. A fit using a Gaussian function for the signal and p1(M − mΞ −mπ)p2 ∗ (p3 +p4M +p5M
2) for the background is applied to the mass spectra yielding
a total of 171 ± 26(stat) Ξ0(1530) baryons in the mass range of 1600-2300 MeV. In
the other hand, for the doubly charged combinations no signal is found.
The results showed compatibility with ZEUS measurement at 2< Q2 <100 GeV2
looking for the same decay modes.
2.5.2 Analysis of K∗(892) meson production
The H1 collaboration has made important progress in the K∗(892) vector meson
cross section measurement both in the laboratory and in the hadronic center of
mass system (γ∗p) frames. The meson was studied looking for the decay channel
K∗(892) → K0s π
± → (π+π−)π± with BR = 23.06% in the data period 2005-2007
with a corresponding accumulated luminosity of 302 pb−1. The events where selected
in the phase space defined by 5< Q2 <100 GeV2, 0.1< y <0.6, -1.5< η(K∗) <1.5
and pT (K∗) > 1 GeV. The detailed selection criteria of the kinematics, the electron,
the tracks, the K0S and the K∗ can be found in reference [65].
The number of K∗(892) are extracted from a fit to the invariant mass of the
Breit Wigner function for the signal description and the p1(m0 − (mK0s +mπ
)p2) ∗Exp(p3m + p4m
2 + p5m3) function for the background. At the end, 80000 K∗±
candidates are identified after the background subtraction and used for the cross
section determination:
σvis = 7.36 ± 0.087(stat.) ± 0.88(syst.) nb. (2.5)
The differential cross section measurement of the K∗(892) in the laboratory and
γ∗p frames are compared to the Monte Carlo simulation programs Django and Rap-
gap, both simulated with matrix elements plus colour dipole model (CDM) and par-
ton showers (MEPS) respectively convoluted with CTEQ6L parton density function
2.5. PREVIOUS H1 RESULTS OF STRANGENESS AT LOW Q2 31
[GeV]T
p1 10
[pb/
GeV
]T
/dp
σd
1
10
210
310
410
510 H1 Data (Prel.)Djangoudcbs
X)±*
eK→ cross section in DIS (ep ±*
Inclusive K
H1 PreliminaryHERA II
5η
-1 0 1
[nb
]η
/dσd
0
1
2
3
4
5H1 Data (Prel.)Djangoudcbs
X)±*
eK→ cross section in DIS (ep ±*
Inclusive K
H1 PreliminaryHERA II
]2 [GeV2Q10 210
]2 [p
b/G
eV2
/dQ
σd
1
10
210
310
410 H1 Data (Prel.)Djangoudcbs
X)±*
eK→ cross section in DIS (ep ±*
Inclusive K
H1 PreliminaryHERA II
[GeV] pγW100 150 200 250
[pb/
GeV
] pγ
/dW
σd
50
100
H1 Data (Prel.)Djangoudcbs
X)±*
eK→ cross section in DIS (ep ±*
Inclusive K
H1 PreliminaryHERA II
Fx0 0.2 0.4 0.6 0.8 1
[pb]
F/d
xσd
210
310
410
510 H1 Data (Prel.)Djangoudcbs
X)±*
eK→ cross section in DIS (ep ±*
Inclusive K
H1 PreliminaryHERA II
]2 [GeV*2TP
0 20 40 60 80 100
]2 [p
b/G
eV*2 T
/dP
σd
-210
-110
1
10
210
310
410 H1 Data (Prel.)Djangoudcbs
X)±*
eK→ cross section in DIS (ep ±*
Inclusive K
H1 PreliminaryHERA II
Figure 2.6: The K∗ production cross section as functions of transverse momentumpT , pseudorapidity η and photon virtuality Q2 laboratory variables and center ofmass energy Wγp, x-Feynmann xF and transverse momentum squared P ∗2
T in thehadronic center of mass system frame. The Django model describes the data ingeneral features but fails to describe the shape of the cross section as function of η.The contribution of quark flavours are presented in order to study the productionmechanism of strange particles.
32 CHAPTER 2. STRANGE MESONS
(PDF) and interfased to Lund string fragmentation model with strangeness suppre-
sion factors set to ALEPH collaboration tunning. Both, Django and Rapgap models,
describe the data very well in overall features but fail to describe in detail the shape
of η production. The plots of the measurements are presented in Figure 2.6 where
the contribution of the quark flavours to the production studied with Django are
displayed.
The contribution of different flavours to the cross section can provide clues to
the strange particle production mechanisms. It is observed that K∗ coming from ud
quarks are mainly from fragmentation; those coming from cb quarks belong mostly
to heavy hadron decays (heavy quarks created by BGF) and give the second highest
contribution; while the K∗ from s quark (mainly due to the hard subprocess) cor-
respond to only the 20% of the total cross section prominently at high values of xF
and p∗T . It was observed that the xF variable provides good sentitivity to the flavour
composition studies.
2.5.3 K0S and Λ studies at low Q2
The H1 collaboration has recently published [66] the measurement of the K0s ,
Λ and Λ cross sections together with the ratios of baryon to meson and meson to
charged particles using DIS events at the phase space defined by 2 < Q2 < 100 GeV2,
0.5 < pT < 3.5 GeV, -1.3 < η < 1.3 using HERA I data with L = 50 pb−1. The
decay channels used for the identifications are K0S → π−π+ with BR ≃ 69.2% and
Λ → pπ with BR ≃ 63.9%.
The measurements are presented in the laboratory frame as a function of Q2, η
and pT and in the Breit frame (appendix E) in the current and target hemispheres
as a function of the momentum fraction xBFp and the K0
S transverse momentum
pBFT . The results were compared to Django (CDM) and Rapgap (MEPS) models
with λs = 0.2, 0.286 and 0.3 for CTEQ6L, H12000LO and GRV94 parton density
functions.
The 213,000 K0S candidates taken from the fit to the invariant mass distribution,
2.5. PREVIOUS H1 RESULTS OF STRANGENESS AT LOW Q2 33
) [GeV]-π +πM(0.4 0.5 0.6
En
trie
s p
er
2M
eV
0
5000
10000
15000
H1
+π -π → s0K
H1 Data
Figure 2.7: The K0S invariant mass distribution from data with statistical uncertainty
denoted with the error bars for each point.
showed in Figure 2.7, are used for the measurement of the inclusive K0S cross section
in the visible range, giving:
σvis = 21.28 ± 0.09(stat.)+1.19−1.23(syst.) nb.
In analogy, the inclusive cross section of both the 22000 Λ and 20000 Λ identified
is measured as σvis = 7.88 ± 0.10(stat.)0.450.47(syst.) nb.
Figures 2.8 and 2.9 show the differential cross section of the K0S mesons as a
function of laboratory and Breit frame variables, respectively. The MC over data
ratio are plotted in the bottom part of each distribution. It shows the comparisons
to CDM and MEPS. It seems that CDM with λs = 0.3 makes a good description of
the differential cross section as a function of Q2, x, η and pT , but finds difficulties
to describe the shape of η and low pT . Whereas the Breit frame calculations agree
with CDM model taking a strangeness factor λs = 0.3.
Similar plots for Λ were obtained and can be seen in references [66] and [67],
CDM with λs = 0.3 behaves more like data in this case but one should not forget that
sensitivity to λqq and λsq is expected. The Λ asymmetries, AΛ = (σΛ−σΛ)/(σΛ+σΛ),
34 CHAPTER 2. STRANGE MESONS
]2 [n
b/G
eV2
X)/d
Qs0
e K
→(e
p σd
1
2
3
4
5
6
7 H1 H1 Data
=0.3)sλCDM (
=0.22)sλCDM (
=0.3)sλMEPS (
=0.22)sλMEPS (
]2 [GeV2Q10 210
Theo
ry /
Dat
a
0.81
1.2
X)/d
x [n
b]s0
e K
→(e
p σd
310
410
510 H1 H1 Data
=0.3)sλCDM (
=0.22)sλCDM (
=0.3)sλMEPS (
=0.22)sλMEPS (
x
-410 -310 -210
Theo
ry /
Dat
a
0.81
1.2
[nb/
GeV
]T
X)/d
ps0
e K
→(e
p σd
20
40H1 H1 Data
=0.3)sλCDM (
=0.22)sλCDM (
=0.3)sλMEPS (
=0.22)sλMEPS (
[GeV]T
p0.5 1 1.5 2 2.5 3 3.5Th
eory
/ D
ata
1
1.5
[nb]
η X
)/ds0
e K
→(e
p σd
2
4
6
8
10 H1
H1 Data
=0.3)sλCDM (
=0.22)sλCDM (
=0.3)sλMEPS (
=0.22)sλMEPS (
η-1 -0.5 0 0.5 1Th
eory
/ D
ata
1
1.5
Figure 2.8: The differential production cross sections for K0S in the laboratory frame
as a function of the four-momentum of the virtual photon Q2, Bjorken scaling variablex, K0
S transverse momentum pT and K0S pseudorapidity η. The theory/data ratios
on the bottom show the comparison to the model predictions. Inner (outer) errorbars for statistical (total) uncertainties.
2.5. PREVIOUS H1 RESULTS OF STRANGENESS AT LOW Q2 35
[nb/
GeV
]Br
eit
T X
)/dp
s0 e
K→
(ep
σd
5
10
15
20
25 H1
target region
H1 Data
=0.3)sλCDM (
=0.22)sλCDM (
=0.3)sλMEPS (
=0.22)sλMEPS (
[GeV]BreitT
p0.5 1 1.5 2 2.5 3 3.5 4Th
eory
/ D
ata
1
1.5
[nb]
Brei
tp
X)/d
xs0
e K
→(e
p σd
1
2
3
4
5
6
7 H1
target region
H1 Data
=0.3)sλCDM (
=0.22)sλCDM (
=0.3)sλMEPS (
=0.22)sλMEPS (
Breitpx
0 5 10 15 20Theo
ry /
Dat
a1
1.5
[nb/
GeV
]Br
eit
T X
)/dp
s0 e
K→
(ep
σd
1
2
H1
current region
H1 Data
=0.3)sλCDM (
=0.22)sλCDM (
=0.3)sλMEPS (
=0.22)sλMEPS (
[GeV]BreitT
p0 0.5 1 1.5 2 2.5 3Th
eory
/ D
ata
0.81
1.2
[nb]
Brei
tp
X)/d
xs0
e K
→(e
p σd
2
4 H1
current region
H1 Data
=0.3)sλCDM (
=0.22)sλCDM (
=0.3)sλMEPS (
=0.22)sλMEPS (
Breitpx
0 0.2 0.4 0.6 0.8 1Theo
ry /
Dat
a
0.81
1.2
Figure 2.9: The differential K0S production cross sections in the Breit frame as a
function of pBCT and xBC
p in the target and current hemisphere. The theory/dataratios on the bottom show the comparison to the different model predictions. Inner(outer) error bars for statistical (total) uncertainties
36 CHAPTER 2. STRANGE MESONS
measured in the laboratory and the Breit frames are consistent with zero showing no
evidence of baryon number transferred from the proton beam to the Λ final state.
The meson to charged particles ratio with an averaged measurement of:
σvis(ep → eK0SX)
σvis(ep → eh±X)= 0.0645 ± 0.0002(stat.)+0.0019
−0.0020(syst.)
was calculated differentially as shown in Figure 2.10 for the laboratory frame as
function of Q2, x, η and pT . The parameter λs is expected to be less model dependent
here. The ratio strongly rises with increasing pT but remains approximately constant
as a function of all the other variables. The models describe reasonably well the ratio
but none is able to describe the shape, especially of η and low pT .
The measured baryon to meson ratio average is
ep → eΛX
ep → eK0SX
= 0.372 ± 0.005(stat.)+0.011−0.012(syst.). (2.6)
The CDM model agrees with data but not completely for the differential measure-
ment in the laboratory frame, no model dependence was found in the Breit frame
since no sensitivity to λs is expected but λqq and λsq can contribute.
The comparison between three different proton PDFs: CTEQ6L, GRV-94 (LO)
and H1 2000 LO, with λs = 0.286 does not show any dependence.
2.5. PREVIOUS H1 RESULTS OF STRANGENESS AT LOW Q2 37
e h
X)
→(e
pσ
X)/d
s0 e
K→
(ep
σd
0.04
0.06
0.08
0.1
0.12
H1H1 Data
=0.3)sλCDM (
=0.22)sλCDM (
=0.3)sλMEPS (
=0.22)sλMEPS (
]2 [GeV2Q10 210
Theo
ry /
Dat
a
0.81
1.2
e h
X)
→(e
pσ
X)/d
s0 e
K→
(ep
σd
0.04
0.06
0.08
0.1
0.12
H1H1 Data
=0.3)sλCDM (
=0.22)sλCDM (
=0.3)sλMEPS (
=0.22)sλMEPS (
x-410 -310
Theo
ry /
Dat
a0.8
1
1.2
0.5 1 1.5 2 2.5 3 3.5
e’ h
X)
→(e
pσ
X)/d
s0 e
’ K→
(ep
σd
0.04
0.06
0.08
0.1
0.12
H1
H1 Data=0.3)sλCDM (
=0.22)sλCDM (
=0.3)sλMEPS (
=0.22)sλMEPS (
[GeV]T
p0.5 1 1.5 2 2.5 3 3.5
Theo
ry /
Dat
a
0.81
1.2-1 -0.5 0 0.5 1
e h
X)
→(e
pσ
X)/d
s0 e
K→
(ep
σd
0.04
0.06
0.08
0.1
0.12
H1H1 Data
=0.3)sλCDM (
=0.22)sλCDM (
=0.3)sλMEPS (
=0.22)sλMEPS (
η-1 -0.5 0 0.5 1
Theo
ry /
Dat
a
0.81
1.2
Figure 2.10: The differential K0S mesons to charged particles cross sections ratio
as a function of the four-momentum of the virtual photon Q2, the Bjorken scalingvariable x, the transverse momentum pT and the pseudorapidity η in the laboratoryframe. The theory/data ratios on the bottom show the comparison to the modelpredictions. Inner (outer) error bars for statistical (total) uncertainties
38 CHAPTER 2. STRANGE MESONS
Chapter 3
HERA and the H1 Detector
The electron-proton collider HERA, located at DESY in Hamburg, Germany, of-
fers the opportunity to study the structure of the proton. HERA consists of four
different experiments spaced evenly along its circumference. One of those experi-
ments, the H1 detector, provided the data analysed in this work. H1 is composed
of several kind of detectors, fixed in a whole unit, designed to measure the particles
properties.
A brief introduction to the HERA machine and the H1 detector components
relevant for the studies presented on this thesis can be found here.
3.1 The HERA collider
The electron-hadron accelerator ring, HERA1, was built at the German electron
synchrotron laboratory, DESY2, in Hamburg, Germany. It consists of two indepen-
dent rings working as accelerators and storing proton and electrons with a center of
mass energy of 319 GeV.
In Figure 3.1 a schematic picture of HERA collider and the pre-accelerator PE-
1Hadronen Elektronen Ring Anlage2Deustches Elektronen SYnchrotron
39
40 CHAPTER 3. HERA AND THE H1 DETECTOR
TRA3 can be found. This pre-accelerator is located at the south-west and it is
amplified in Figure 3.1 b). The performance of the accelerator begins with injection
of protons4 with an energy of 50 MeV from the linear accelerator, H−-linac, to the
DESY III ring, where they are accumulated and accelerated until having 70 bunches
with 7.5 GeV. Then, one by one are sent to the PETRA ring to be accelerated up to
40 GeV, to finally be transferred to the HERA ring. HERA operates with 180 circu-
lating bunches of protons, every one of them consisting of approximately 1010-1011
protons, separated in time by 96 ns and accelerated to an energy of 920 GeV.
Hall North
H1
Hall East
HERMES
Hall South
ZEUS
HERA
HERAhall west
PETRA
cryogenichall
Hall West
HERA-B
magnettest-hall
DESY II/IIIPIA
e -linac+
e -linac-
-H -linac
NWN NO
O
SOSW
W
proton bypass
p
e
ep
VolksparkStadion
360m
360m
R=7
97m
e
p
Trabrennbahn
Figure 3.1: a) The HERA accelerator and b) the PETRA pre-accelerator circumfer-ences. The four experiments around HERA: HERA-B, H1, HERMES and ZEUS areindicated in a) together with the traveling direction of the electron e and proton pbeams.
a) b)
The electrons (or positrons) acceleration begins at the e− (e+)-linac accelerator,
the electrons are injected from there to the DESY II ring, where they are accelerated
from 450 MeV to 7 GeV. After the storage of 70 bunches is completed, they start
to be sent to PETRA for their acceleration up to 14 GeV. At the end, 180 bunches
3Positron Elektron Tandem Ring Anlage4The protons are taken from hydrogen ions
3.1. THE HERA COLLIDER 41
of electrons are injected to HERA until they get an energy of 27.5 GeV, separated
by the same time interval as proton bunches. Sometimes, some bunches, called pilot
bunches, are left empty to be used for the background estimation, of protons colliding
with the beam pipe or residual gas.
The proton bunches lifetime easily exceeds 24 h, but the lifetime of the electron
bunches is limited to about 6 h (the lifetime for positrons is approximately a factor
of 2 higher). Both electrons and positrons are more difficult to keep circulating due
to the synchrotron radiation.
The HERA accelerator ring has a circumference of 6.3 km where superconduct-
ing dipole and focusing quadrupole magnets are distributed to guide the particles
trajectories and to keep the bunches positionally stables. Between the quadrupoles,
∼12 m of free space is available for a detector. The beams pass inside a 190 mm
inner diameter beam pipe with a wall of 150 µm Aluminium on the inside backed by
2 mm carbon fiber. The beam pipe is cooled with nitrogen gas and kept in vacuum
conditions. It crosses the detector in its center at a height of 5.9 m above the floor
level at an inclination of 5.88 mrad.
Around HERA, four experiments are located: HERMES, HERA-B, ZEUS and
H1. Their locations are graphically shown in Figure 3.1 a). The electrons and
protons, traveling to the right and left hand sides respectively, are made to collide
head on (as in H1 and ZEUS detectors) or against a target (as in HERMES and
HERA-B detectors) every 96 ns or 10.4 MHz. HERMES, HEra MEasurement of Spin,
is dedicated to spin studies of the proton, HERA-B is interested in CP violations in
B0 − B0 systems and, ZEUS and H1 study the proton structure.
An important characteristic of any accelerator operation is the produced lumi-
nosity which gives directly the number of events per second for a cross section of
1 cm2 (units of cm−2s−1). The instantaneous luminosity L, can be calculated with
the revolution frequency f of the bunches, the number of protons Np and electrons
42 CHAPTER 3. HERA AND THE H1 DETECTOR
Ne per bunch and the beam radii σx and σy of the bunches at the crossing point:
L =f ∗ Ne ∗ Np
2π ∗√
2σx ∗√
2σy
, (3.1)
due to the uncertainty in the beam collimation the luminosity is measured as ex-
plained in the subsection 3.2.3.
The luminosity is also related to the effective cross section σ as: dN/dt = Lσ.
The accumulated luminosity at a period T of time is denoted as:
L =
∫
T
Ldt (3.2)
day
Prod
uced
by H
ERA
[pb-1
]
0 100 200 3000
100
200 2002200320042005200620072007 low-E run2007 mid-E run
Figure 3.2: Accumulated luminosity by HERA II collider in pb−1 vs number of daysfor six years of operation. In 2007 two periods of several months were dedicated tothe operation of the machine at low and middle energies.
The HERA operation time is divided in two periods called HERA I and HERA II.
HERA I corresponds to data taken from 1992 to 2000 while HERA II goes from 2002
to 2007. The separation responds to the improvements made to the accelerator in
3.2. THE H1 DETECTOR 43
2001. Several super-conducting quadrupole magnets where installed, improving the
focusing of the beams and consequently increasing the luminosity by a factor of 4
to 5. In Figure 3.2 is possible to see the produced luminosity by HERA in pb−1 per
year. The HERA accelerator ended its performance in summer 2007.
3.2 The H1 detector
The H1 experiment [68] is located in the northern side of the HERA ring, at 20 m
underground. The detector measures 12 x 10 x 15 m3 and its weight is 2,800 tons. The
coordinate system of H1 is right-handed with the origin settled up on the interaction
vertex (also called nominal point), the x axis points to the center of HERA, y pointing
up and the z axis defined by the incoming proton beam direction (from right to left
hand side in Figure 3.3). In polar coordinates, the azimuthal angle φ rests in the xy
plane being φ = 0 over the x axis while the polar angle θ is zero on the positive z
axis. The pseudorapidity is defined as η = −ln [tan(θ/2)].
Figure 3.3 presents a longitudinal cut of the H1 detector with the protons and
electrons coming into the detector from the right and left hand side, respectively.
The H1 detector is composed by several kind of sub-detectors in order to measure
the energy, momentum and charge of the particles produced during and after the
ep collisions. The difference of energy between electrons and protons makes that
most of the particles are scattered in the outcoming proton direction or the so called
forward region. This is the reason why the H1 detector is considerably more massive
and highly segmented in that direction.
The detector is arranged as follows: immediately outward from the interaction
vertex is the tracking system, consisting of the Central Silicon Tracker (CST), a
central (CJC, COZ, CIZ, COP and CIP) and a Forward Tracking System (FTS)
used for the trajectory particle reconstruction. Two calorimeters surrounding the
trackers are the liquid argon calorimeter (LAr Cal) in the central and forward region,
and the scintillator spaghetti calorimeter (SpaCal) in the backward region, both
44 CHAPTER 3. HERA AND THE H1 DETECTOR
Figure 3.3: Cut along the z beam axis of the H1 detector. The components ofthe tracker, calorimeter and muon systems are indicated. The separation in cen-tral, forward at the left hand side and backward to the right hand side can be alsoschematically seen.
3.2. THE H1 DETECTOR 45
calorimeters have electromagnetic and hadronic sections ideal to measure the energy
of the particles. Housing all these systems is a superconducting solenoidal cylindrical
magnet with a diameter of 6 m and a length of 5.75 m which provides a homogeneous
magnetic field of 1.16 T parallel to the z axis. This magnetic field makes that charged
particles produced in the collision move in an helical trajectory. The projection of
this trajectory in the xy plane yields a circle with radius r = 1/pt where pt is
the transverse momentum of the particle. The iron return yoke of the magnet is
laminated and filled with limited streamer tubes.
The small fraction of hadronic energy leaking out the calorimeter and the muon
tracks are measured by the central muon identification system (CMS) placed af-
ter the solenoid coil. Stiff muon tracks in the forward direction are analysed in a
supplementary toroidal magnet sandwiched between drift chambers. See Figure 3.3.
An electron tagger located at z = -33 m from the interaction point in coincidence
with a corresponding photon detector at z = -103 m upstream (not shown in Fig-
ure 3.3) detect the tag electrons and photons produced with very small scattering
angle and monitor the luminosity by the Bethe-Heitler process.
The H1 detector, as well as the HERA accelerator, was updated substantially
during the time changing from HERA I to HERA II to cope with the new challenges
at HERA II. The innermost detector regions saw major modifications to accommo-
date the superconducting quadrupoles of HERA II. The new silicon detector system
(Forward Silicon Tracker) completely surrounds the interaction region to significantly
improve vertexing and tracking in conjuntion with the upgraded inner tracking sys-
tem (new Forward Tracker). Combined with upgrades in the trigger (new Time Of
Flight System, new multiwire proportional chamber CIP2k replacing the CIP and
CIZ to overcome the increased non-ep background, an upgraded neural net event
trigger for the second level, a new processing farm for the third level and a new Fast
Track Trigger at the very first level) and data acquisition system (DAQ) to make
best use of the luminosity increase in all physics areas. As well as, the installation
of a new superconducting magnet G0 and GG (see Figure 3.3) to obtain a better
46 CHAPTER 3. HERA AND THE H1 DETECTOR
longitudinal polarisation of the electron beam at the interaction point.
Days of running
H1 I
nte
gra
ted
Lu
min
osi
ty /
pb
-1
Status: 1-July-2007
0 500 1000 15000
100
200
300
400electronspositronslow E
HERA-1
HERA-2
day
Acc
umul
ated
by
H1
[pb
-1]
0 100 200 3000
40
80
120
1602002200320042005200620072007 low-E run2007 mid-E run
Figure 3.4: Accumulated luminosity in pb−1 of the H1 detector a) during the HERA I(1992-2000) and HERA II (2002-2007) data taking, indication of the periods withthe machine operating with electrons and positrons are plotted in blue and red, b)the HERA II accumulated luminosity, as function of the number of days, separatedby years.
a) b)
The H1 accumulated luminosity is plotted in the Figure 3.4 a), where can be
seen the comparison between the collected luminosity during HERA I and HERA II
periods, with HERA operating electrons and positrons alternatively. A clear increase
in the accelerator performance can be observed. The plot in Figure 3.4 b) shows the
HERA II period luminosity separated year by year since 2002 to 2007.
This study is done with the data taken from 2004 to 2007 where the integrated
luminosity has a value of ∼ 340 pb−1.
The H1 phase space is pretty wide in x-Bjorken and virtuality Q2 as can be seen
in Figure 3.5, where the comparison to different experiments is presented. The range
of Q2 considered for this analysis lies in the regime of the LHC experiments, ATLAS
3.2. THE H1 DETECTOR 47
Table 3.1: The HERA ep collider characteristics.
HERA I HERA II
e− p e− p
Energy 27.6GeV 920 GeV 27.6 GeV 920 GeV
Total current 52 mA 109 mA 45 mA 110 mA
Number of available bunches 180 180 180 180
Number of bunches in collision 174 174 174 174
Number of particles per buch 3.5 x 1010 7.3 x 1010 4.2 x 1010 10 x 1010
Transverse cross section per buchσx x σy (µm x µm) 192 x 50 189 x 50 112 x 30 112 x 30
Length of the bunch 10 mm 191 mm 10 mm 191 mm
Luminosity 6.5 x 10−3 (nb−1s−1) 17.2 x 10−3 (nb−1s−1)
6.5 x 1030 (cm−2s−1) 17.2 x 1030 (cm−2s−1)
and CMS.
In the next sections a brief description of the most important subdetectors for
this analysis can be found. For more information about the H1 detector, see the
Table 3.1 or consult the reference [69].
3.2.1 Tracker system
The tracker system consists of drift and multiwire proportional chambers detec-
tors, see appendix B, for triggering and the identification of particles by the mea-
surement of their charges, momentum and the reconstruction of their trajectories,
with resolutions of σp/p2 ≈ 3 x 10−3 GeV−1 and σθ ≈1 mrad. The tracking chambers
are built to interfer as little as possible with the passing track.
This system is the main detector at H1, designed for the reconstruction of jets
with high particle densities. Each component of the tracking system was built and
48 CHAPTER 3. HERA AND THE H1 DETECTOR
Figure 3.5: Phase space of different experiments presented in x-Bjorken vs. Q2. TheH1 detector has pretty wide range, so that the Q2 considered for this analysis lies inpart of the regime from ATLAS and CMS experiments.
tested separately, then assembled and locked to one mechanical unit to provide pre-
cise alignment relative to outside support, but with electrostatic shielding and inde-
pendent gas volume. A schematic picture of the tracking detectors can be found in
Figures 3.6 and 3.7.
The tracker system is divided in the central (CTD), the forward (FTD) tracker
detectors and the backward proportional chamber (BPC).
The CTD is covered by the central (CST), the forward (FST) and the backward
silicon tracker (BST), the central jet chamber (CJC), the central inner (CIZ) and
central outer z-chamber (COZ), and the central inner (CIP) and central outer (COP)
multiwire proportional chambers.
The CJC is based on two large concentric drift chambers, CJC1 and CJC2, de-
signed for transverse track momentum determination by the signals recorded, in
addition, the specific energy loss dE/dx can be used to improve particle identifica-
3.2. THE H1 DETECTOR 49 @@@@@@@@@@@@ÀÀÀÀÀÀÀÀÀÀÀÀ@@@@@@@@@ÀÀÀÀÀÀÀÀÀ@@@@@@@@@ÀÀÀÀÀÀÀÀÀ @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQ¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQ¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢@@@@@@@@@@@@@@@@ÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀ@@@@@@@@@@@@ÀÀÀÀÀÀÀÀÀÀÀÀ @@@@@@@@@@@@@@@ÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀ@@@@@@@@@ÀÀÀÀÀÀÀÀÀ@@@@@@@@@ÀÀÀÀÀÀÀÀÀ @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQ¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQ¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢¢@@@@@@@@@@@@ÀÀÀÀÀÀÀÀÀÀÀÀ@@@@@@@@@@@@ÀÀÀÀÀÀÀÀÀÀÀÀ013 2 -1 -2 m
0
1
-1
Forward TrackDetector (FTD)
Central Track Detector(CTD)
Central Jet Chamber (CJC)
CJC2
CJC1
COZ COP CIZ CIP
Silicon Tracker
cableselectronics
BDC elm hadrSpaCal
cable distri-bution area
(CDA)
transitionradiators
planars
radials MWPCsCST BST
Figure 3.6: Longitudinal view of the forward and central tracker systems. The CST,CJC, COZ, CIZ, COP and CIP detector locations are shown.
tion. The measurement is complemented by the two thin z drift chambers, CIZ and
COZ, which give better accuracy by measuring the z coordinate of the tracks.
The FTD, electrically isolated from the CTD, has three supermodules covering
a polar angle range of 5 < θ < 25. Each supermodule consists of planar drift
chambers orientated in different wire geometries, a multiwire proportional chamber
(FWPC), a passive transition radiator and a radial drift chamber, all them with
wires strung perpendicular to the beam direction, Figure 3.6. This tracker allows
accuracy in θ, rφ measurements and fast triggering.
The CIP, COP and the FWPC, are used to trigger on tracks coming from a
nominal interaction vertex, providing the first level (L1) trigger decision which is
also used to distinguish between successive beam crossings.
The following subsections will refer in detail the detector components of the
central tracker system.
50 CHAPTER 3. HERA AND THE H1 DETECTOR
Figure 3.7: Transversal view of the central tracker system (CTD). The main detec-tors, CST, CJC1, CJC2, CIP2k, COZ and CIP are indicated together with theirradial distances.
3.2.1.1 Central silicon tracker
The central silicon tracker [70], CST, is the nearest detector surrounding the
beam pipe. It was installed in 1997 but updated during the time changing from
HERA I to HERA II. The BST and FST were installed later to complement the
device performance. Its main use is to improve the CJC reconstruction of tracks
relating them to the interaction vertex.
The silicon trackers consist of two radial cylindrical layers of silicon strip detec-
tors, the inner layer with 12 ladders and the outer layer with 20 sensor ladders (each
containing 6 sensors). The CST covers an acceptance of 30 < Θ < 150. Its intrinsic
resolution is σz = 22 µm and σrφ = 12 µm.
3.2.1.2 Central jet chambers
The inner CJC1 and outer CJC2 jet chambers [71] measure the trajectories of
charged particles5, both having a longitude of 2.5 m parallel to the z axis. The CJC1,
5See appendix B for an explanation of the drift chambers performance.
3.2. THE H1 DETECTOR 51
with an inner (outer) radius of 20.3 cm (45.1 cm), has 720 sense wires distributed in
30 azimuthal cells. On the other hand, the CJC2 has 32 sense wires in each of its 60
cells and its inner (outer) radius is 53 cm (84.4 cm). All cells are tilted by about 30
in radial direction, in order that also the tracks with high momentum (low curvature)
can be reconstructed, see Figure 3.7. In fact, the separation of tracks coming from
different bunch crossings is possible to an accuracy of σ ∼ 0.5 ns.
Each cell is composed by three planes of wires, the cathode wires planes marking
the limits of the cell and the anode sense wires plane lying in between. All wires
parallel to the z beam line axis. The diameters of the wires limits the surface field
to ≤ 2 KV/mm.
The jet chambers are closed and filled in the first phase with a gas mixture of
Ar/CO2/CH4 by 89.5/9.5/1.0 %, and Ar/C2H6+H2O by (50/50) + 0.5 % during
the second phase. In this condition, when a charged particle passes through the jet
chambers, the electrons will drift to a velocity of 50 mm/µs−1 towards the anode wires
to induce the current signal which allows the measurement of the hit position in the
xy plane with a resolution of σrφ = 170 µm. Then, comparing the collected charge
at both ends on the wire, the z position can be determined with a precision of σz =
2.2 cm. For a better explanation of the way of charge Q and time t measurements,
read appendix C.
3.2.1.3 Central z chambers
The z central inner CIZ and outer COZ drift chambers measure the z-coordinate
and complement the CJC for the track reconstruction. They are also used for the
trigger of straight tracks pointing to the interaction region.
The CIZ chamber is located between the CST and CJC1, just after the CIP while
COZ is found between the CJC chambers. See figures 3.6 and 3.7. They cover polar
angles of 16 < θ < 169 and 25 < θ < 156, respectively.
The CIZ chamber is a regular polygon with a length of 2.467 m and thickness of
26.5 mm, it is composed by 15 independent ring cells with 4 sense and 3 potential
52 CHAPTER 3. HERA AND THE H1 DETECTOR
wires each of them. The gas mixture inside is Ar/C2H6 + H2O at a proportion of
(70/30) + 0.2 allowing a drift velocity of 52 mm/µs and measurement resolutions of
σrφ = 28 mm and σz = 26 µm.
The COZ polygonal chamber is 2.59 m long and 25 mm width, has 24 cells (or
rings), each cell containing 4 sense and 6 potential wires. It has a gas mixture of
Ar/C2H6 + C3H7OH by (48/52) + 1 %, so the drift velocity is 48.5 mm/µs with
accuracy of σrφ = 58 mm and σz = 2.0 µm.
The wires are all tilted by 45 with respect to the normal to the chamber axis.
The first backward nine cells of CIZ are backward tilted but the other six in the
forward direction are tilted forward.
3.2.1.4 Central proportional chambers
There are two multiwire proportional chambers6 (MWPC’s) in the H1 detector:
the central inner (CIP) and the central outer (COP). During HERA II period, the
CIP chamber, together with CIZ, were replaced by a high granularity central inner
proportional chamber (CIP2k) [72] to increase the non-ep background rejection and
to deliver a precise information about the event timing (t0).
The CIP2k chamber has an inner (outer) radius of 15 cm (20 cm) and an active
length of 2.2 m. It is located between the CST and the CJC1. It consists of five
cylindrical detector layers segmented into 16 azimuthal sectors with cathode pad
readout about 2 cm along the z axis. Due to the very fast response to ionizing
particles (depending on the chamber gas and the field strength) this chamber is used
to provide a precise information about the event timing t0 (the typical intrinsic time
resolution is 10 ns) to suppress background events.
The COP detector is located between the CJC1 and CJC2 (Figure 3.6). It is used
in parallel to the CIP2k trigger to suppress tracks with a low momentum transfer
(pt cut) and to the z-vertex trigger to reconstruct the exact vertex in a z region of
± 43.9 cm around the nominal interaction point (σz ≈ 5.5 cm).
6See appendix B for an explanation of the multiwire proportional chambers performance.
3.2. THE H1 DETECTOR 53
3.2.2 Calorimeters
The calorimeters of the H1 detector were designed to identify and provide a precise
measurement of charged and neutral particles, specially the electron parameters of
the DIS events in a wide range of solid angle, as well as jets with high particle
densities. This kind of detector have the purpose of measuring the energy of the
particles by their total or partial absorption.
According to the material of construction they can provide signal such as ion-
ization, as the liquid argon calorimeter in H1, or scintillated light, as the SpaCal
detector.
3.2.2.1 Liquid argon calorimeter
The liquid argon calorimeter [73] (LAr) surrounds the system of tracker detectors
but it is still inside the superconducting coil. It has 1.5 m of thickness active diameter
and measures 7 m of longitude, covering a polar angle range of 4 ≤ θ ≤154 and
4π coverage in φ. The calorimeter is complemented in the forward region (between
the beam pipe and the liquid argon cryostat) by the PLUG, the Spacal and the tail-
catcher system (TC) in the backward direction, to cover the region were hadronic
particles can be leaking out of the detector.
The LAr is segmented in eight wheels each of them divided in φ into eight identical
units in the xy plane. The first two wheels starting from forward region, are two half
rings assembled. The Figure 3.8 presents longitudinal and transversal views of the
LAr calorimeter.
The LAr has a fine granularity for e/π separation (electromagnetic and hadronic
showers) and energy flow measurements as well as homogeneity of response. Each
wheel is divided in an electromagnetic (EM) and a hadronic section (HAD), see
Figure 3.8. The octants are segmented in 45000 cells, where 30000 belong to the EM
and the rest to the HAD part.
A EM cell consists of two lead absorber plates of 2.4 mm interleaved with LAr ac-
tive material interspaces of 2.35 mm. Over each face of the absorber, next to the LAr,
54 CHAPTER 3. HERA AND THE H1 DETECTOR
Figure 3.8: a) Longitudinal views of the LAr Calorimeter with the eight wheels di-vided in electromagnetic and hadronic sections. b) Transversal cut of the calorimetershowing one wheel where the separation between electromagnetic and hadronic sec-tions are also indicated, the inclination of the 8 units is visible.
a)
b)
3.2. THE H1 DETECTOR 55
there are circuit planes impressed in G10 (a composite made of glass fiber and epoxy
resin) which have the copper lecture modules (the pads). The electrons produced in
the liquid argon are collected at these plates. Since there is no charge multiplica-
tion, the collected charge is quite small, and the detector requires a preamplifier and
associated electronics for each channel. The chamber must operate at liquid argon
temperatures (80K) and thus requires a cryogenic system (circulation of helium gas).
The hadronic cells has a similar EM structure, an absorber material made of
16 mm (19 mm) stainless steel with sheets connected to high voltage and a double
gap of 2.4 mm liquid argon. The double gap is separated by the G10 plate which
contains the lecture pads.
The liquid argon was chosen because its easy calibration, good stability and
homogeneity in the response. Although the detector is relatively slow, it is stable, is
not adversely affected by the presence of a magnetic field, and is easily segmented.
The detector has uniform sensitivity, and it is possible to make a highly accurate
charge calibration.
The radiation length of the electromagnetic part is about 20 X0 in the central
region and 30 X0 in the forward while it is about 5 interaction lengths λ in the central
and 8 λ in the forward area for the hadronic part.
The energy resolution for EM and HAD showers are:
σEME
E=
11%√
E[GeV ]⊕ 1%
σHADE
E=
50%√
E[GeV ]⊕ 2%
3.2.2.2 Spaghetti calorimeter (SPACAL)
The spaghetti calorimeter (SpaCal) consists of scintillating fibers embedded in a
lead absorber, parallel to the z-axis. As the LAr, the SpaCal also has electromagnetic
(EM) and hadronic (HAD) sections. The angular range covered is 155 < θ < 177.
The SpaCal has 1192 channels which are read out with a time resolution of 1 ns.
56 CHAPTER 3. HERA AND THE H1 DETECTOR
The molecules, excited by the particles passing through, emit scintillation light
which travels by the fibers to the photomultiplier tubes to be converted in electrical
signals. The SpaCal is used to measure the scattered electron at low Q2 and to
contribute to the reconstruction of hadronic final states.
The EM (HAD) corresponds to 27.8 X0 (2 λ). The EM and HAD energy resolu-
tion are:
σEME
E=
7%√
E[GeV ]⊕ 1%
σHADE
E=
56%√
E[GeV ]⊕ 7%
3.2.3 Luminosity system
The H1 luminosity system [74] main task is the relative measurement of the
luminosity as seen by the main detector. The measurement is based in the Bethe-
Heitler [75] process, ep → epγ, determined by the electron tagger (ET), photon
detector (PD) and Cherenkov counter (VC) detectors located close to the beamline
but far away from the interaction point (ET at z =-33.4 m and PD at z =-102.9 m) to
cover the small angles of the electrons and photons traveling in the primary electron
beam direction. The VC detector and a Pb filter 2X0 protect the PD from the high
synchrotron radiation flux.
Figure 3.9: Detection of the Bethe-Heitler event (ep → epγ) by the electron tagger(ET), photon detector (PD) and Cherenkov counter (VC).
The ET (PD) detects the scattered electrons (the photons) at approx. 0 - 5
(0 - 0.45) mrad as shown in Figure 3.9. The event rate R′, corrected of background
3.2. THE H1 DETECTOR 57
(mainly from electrons bremsstrahlung), is used for the luminosity determination:
L =R′
σvis
, (3.3)
where σvis is the visible part of the Bethe-Heitler cross section (with acceptance and
trigger efficiency included).
3.2.4 Trigger system
The H1 trigger system has the function of separating out the ep events containing
interesting physics from the background sources in the total 10.4 MHz input rate,
while keeping a minimum dead-time.
This system is divided into four levels, called L1 - L4, to facilitate the making of
decision as more H1 detector components combines their information. The events
fulfilling all level requirements are written to tape for permanent storage. The final
rate for storage is limited to 10 Hz. See Figure 3.10.
The first trigger level L1 provides a decision for each bunch crossing. The full
system run deadtime free at 10.4 MHz and is phase locked to the RF signal of HERA.
The decision delay is 2.3 µs and must reduce the event rate to 1 kHz.
The L1 must provide a sophisticated identification of the characteristics of an
event. It widely uses the track origin information, that uniquely distinguishes ep
interactions from the beam gas background, and for the ep events, where the vertex
information may not be the best requirement, the hadronic final state topology. So,
at first level only the MWPC and LAr calorimeter data are correlated in such a way.
The L1 output are called trigger elements (TE) which are sent to the central
trigger control (CTC) to be combined with other subtriggers.
The intermediate levels L2 and L3 are called synchronous, because they operate
during primary dead time of the readout. They are based on the same information
prepared by the L1 trigger.
The level 2 decision is made evaluating a large number of subsystems signal
correlation in detail. Its time decision is only 20 µs but is able to reduce the event
58 CHAPTER 3. HERA AND THE H1 DETECTOR
L1
µ
L3L2 L4
s
farmprocessor
processorfarmlogic
circuit
neuronalnetwork
topolog.trigger
full eventreconst.
~100 msµ22 sµs2.3 ~100
detector1 kHz~10 MHz
data
clear pipelines & restart
L1
subdetector
trigger data
L2 reject L3 reject
pipelines pipelines
stop read−out continuedata pipelines
keep keep keepL2 L3
L4
L4reject
read−out
max
50 Hz
maxmax
Dead timefree
Deadtime asynchronous phase
keep
write
10 Hz
on
ta
pe
reje
ct
200 Hz
Figure 3.10: The H1 trigger system consisting in four levels (L1 - L4). The eventsfulfilling all level requirements are written to tape for permanent storage.
rate to 200 Hz. L2 consists of two independent systems, the neural net trigger
(NNT) and the topological trigger (TT) trained with ep and background events and
a geometry of the detector in the θ and φ space samples.
In parallel, a flexible third level has 100 µs to take a decision using software
algorithms running on a microprocessor. It can potentially refine the trigger giving
a 50 Hz rate event at the end. In case of a rejection, the readout operations are
aborted and the experiment is alive again after a few µs.
The L4 filter farm is an asynchronous software integrated into the central data
acquisition system. It is divided into several logical modules to make a quick deci-
sion of the events (100 ms). If the event passes the selection criteria, it is written
to POTs (production output tape), in a rate of approx. 5 Hz, together with the
detectors information and an online calculation of the trajectory, energy signature
and momentum of all particles of the event, which is used for an event classification.
A small fraction of about ∼ 1% of the rejected events is kept for monitoring
purposes.
Chapter 4
Selection of DIS events and K0
Scandidates
The selection of the DIS event sample requires several steps, which focus in
cleaning the sample by reducing the contamination of the events of interest. The first
selection is independent of the analyser, hence this stage is called online selection,
and consists in the action of the trigger as described in section 3.2.4. Next, the offline
selection is carried out by many steps as the analyser decides depending in the aim
of study or the cleanliness wished for.
In the first section of this chapter a clear description of the online selection can
be found. The offline part is also described in detailed in the following sections,
starting with the selection of events containing the information of the needed de-
tectors, the commonly called run sample selection. Then, general cuts and the DIS
event selection are presented, finishing with the K0S candidates reconstruction. As
it was already pointed out, the K0S travel some distance before decaying to π+π−,
in the corresponding section it is explained how the V 0 (the vertex of decaying) is
reconstructed and the K0S identified from their daughters signature.
Several control plots of the used variables are going to be presented with the
comparison to the Django and Rapgap models.
59
60 CHAPTER 4. SELECTION OF DIS EVENTS AND K0S CANDIDATES
4.1 Trigger
The online selection consists of the subtrigger elements only. The subtrigger
chosen for this work corresponds to the level L1, the so called S67, which is defined
as:
S67 ≡ LAr && T0 && V ET
where LAr means the condition of the LAr calorimeter, T0 the timing condition,
VET the veto condition and the symbol && meaning the logical condition ’AND’.
99.9542 99.7864 95.217 99.9484 99.9565 100 99.6829 99.88 99.9678 96.5123 100 99.8834 100 99.7713 99.8298 99.976999.9877 99.9233 93.8361 99.9137 99.9442 99.871 99.901 99.9365 99.9519 99.9129 99.8842 99.9279 99.8989 99.9847 99.7917 99.979299.8758 99.9155 99.8903 99.8989 99.9411 99.9647 99.8834 99.7892 99.6705 98.961 98.2197 99.8992 99.8189 90.4458 98.9704 99.956199.9177 99.9069 97.3444 99.9366 99.982 99.9632 99.9745 99.9528 97.6126 99.9832 96.1395 99.8892 99.9571 97.7898 96.8944 99.988399.8932 99.9855 99.8168 96.8607 99.9526 99.9118 99.9664 99.9946 99.9736 99.9761 99.949 98.467 99.9369 99.9507 96.1926 99.944299.9563 99.9894 99.8406 99.97 100 99.9279 99.9522 99.9653 99.9386 99.8617 99.9626 99.974 98.7527 99.9681 94.5946 99.896199.9655 99.9393 99.5625 99.9399 99.9473 99.8996 97.2664 99.9141 98.8621 99.7811 99.8864 99.9666 96.4055 99.8805 97.4561 99.804699.9059 99.8264 99.1855 99.902 99.9299 99.9291 100 99.9656 79.8381 99.8441 99.5997 99.9857 98.0585 99.916 99.7256 98.711399.8913 99.9252 98.1199 99.9108 99.9373 99.9737 100 99.9564 97.5504 99.83 99.6129 99.9328 97.7725 99.9368 98.5646 95.796299.9195 99.984 99.9661 99.9755 99.9525 99.9356 93.8665 99.9742 99.9005 99.9797 99.9125 99.9129 83.0226 99.8959 81.333 77.714399.9675 99.9213 99.9705 99.9383 99.9875 99.9195 100 99.7448 99.9003 99.9705 99.8874 99.9005 68.7215 100 84.065 33.416899.8213 99.9052 99.9827 99.879 99.9839 99.9168 98.8292 98.6421 99.7893 99.8576 99.6564 99.9082 77.7557 99.9613 83.0409 63.8415
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(cm
)im
pZ
-200
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EPlus04 Fiducial Volume CutsEPlus04 Fiducial Volume Cuts
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(cm
)im
pZ
-200
-150
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EMinus05 Fiducial Volume CutsEMinus05 Fiducial Volume Cuts
99.9135 100 99.9683 99.955 99.9104 99.9852 99.9283 99.9526 99.9634 99.9868 99.9529 99.9243 100 100 99.9818 99.968999.9532 99.9944 99.9134 99.9727 99.9612 99.9425 99.991 99.9433 99.9515 99.9744 99.9932 99.966 99.9562 99.9845 99.8948 99.988899.8988 99.8838 99.8352 99.943 99.9407 99.9562 99.964 99.5948 99.5846 99.5414 99.943 99.9256 99.9342 90.6717 99.7529 99.975499.9435 99.943 99.9523 98.0071 99.9032 99.9632 99.9954 99.9681 99.977 99.9653 99.9721 99.993 99.9718 97.8791 99.9363 99.993399.9891 99.9374 99.931 99.9774 99.9794 99.9765 99.9824 99.9466 99.9484 99.9954 99.9776 99.964 99.9812 99.9506 99.9759 99.978299.9856 99.9464 99.956 99.9946 99.9699 99.9804 99.9863 99.9629 99.9465 99.9871 99.9704 99.9507 99.9851 99.973 99.9914 99.961399.992 99.9616 99.7287 99.9075 99.9558 99.9524 99.4407 98.5649 99.5836 99.8536 99.5649 99.9225 98.8752 99.9001 99.9269 99.925
99.9899 99.9634 99.6095 99.9748 99.9827 99.9776 98.6385 99.9401 90.0458 99.9728 99.6332 99.9593 97.8934 99.9803 99.8981 98.824599.9758 99.9723 99.1891 99.9877 99.9947 98.8886 97.4827 99.9573 89.9419 99.8246 97.8783 99.9494 97.9139 99.9023 99.9797 99.942698.9025 99.9881 99.896 99.9493 99.9693 99.9526 98.2085 99.9923 99.9221 99.9687 98.9331 99.9605 80.195 99.963 89.7151 86.798399.9593 99.9723 99.9859 99.9907 99.982 99.9887 97.5504 99.9478 99.9852 99.9696 99.9536 99.9509 65.2515 99.9569 71.5956 86.737998.743 98.7526 98.8145 99.9108 99.9519 99.9663 97.8599 99.9772 98.0022 99.8725 99.1854 99.8824 75.0172 99.0575 75.089 84.2327
100 99.9648 75.8107 99.7868 99.5806 99.9376 99.9935 98.8414 99.8475 99.9709 99.8247 100 99.3471 99.9583 94.7108 10098.1583 99.9519 63.1097 99.9881 99.9534 99.9808 99.9262 99.9116 100 99.3604 99.9534 99.9754 100 99.9798 90.9176 99.787697.6596 100 85.6835 100 100 100 99.9557 99.9882 99.9234 100 99.901 99.7984 99.3993 99.9827 87.6642 99.751863.4146 99.949 100 100 99.7605 100 100 99.9706 99.9584 99.9328 100 99.916 99.9446 100 86.1397 10089.8649 99.9675 98.0476 100 99.9267 100 99.9812 100 100 99.9405 99.8746 99.9488 100 99.8046 81.3139 10087.2093 100 98.3457 99.9108 100 100 99.9471 100 99.9043 99.9343 100 100 99.696 100 96.9697 97.8085
100 100 100 100 98.9037 100 99.9405 100 100 100 99.9343 100 99.4652 100 98.4899 100100 100 99.84 100 100 100 100 100 100 100 100 100 100 100 100 98.2456100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100100 99.654 100 100 100 100 100 100 100 100 100 100 100 100 100 100100 100 100 100 100 100 100 100 100 100 100 100 100 100 99.6094 100100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100100 100 100 100 100 100 100 100 76.1905 100 100 100 100 100 100 100
98.4375 100 100 100 100 100 100 100 96 100 100 100 100 100 100 100100 100 100 100 100 100 100 100 100 100 100 100 100 100 100
)° (φ-150 -100 -50 0 50 100 150
(cm
)im
pZ
-200
-150
-100
-50
0
50
100
EMinus06 Fiducial Volume CutsEMinus06 Fiducial Volume Cuts
99.9782 99.9786 99.9854 99.9935 99.9807 99.9714 99.9622 99.9924 99.9845 100 99.9867 99.994 99.9904 99.9931 99.9284 99.975299.9955 99.9931 99.991 99.9906 100 99.9784 99.9412 99.9946 99.9832 99.9889 99.9979 99.9963 99.9962 99.995 100 99.967299.931 99.9807 98.6527 99.9931 98.7205 99.9847 99.9485 99.918 99.744 99.7332 99.9849 99.9781 99.9791 94.9018 99.8322 99.9703
99.9835 99.9945 99.9835 99.9892 99.9592 99.9966 99.9973 99.9898 99.9912 99.9906 99.9921 99.9834 99.9903 98.6865 99.9871 99.991899.9942 99.9775 98.7433 99.9901 99.9928 99.9739 99.9924 99.9842 99.9918 99.9892 99.9986 99.9928 99.9878 99.9867 99.99 99.990999.9958 99.9796 99.9824 99.9746 99.9957 99.9837 99.9921 99.996 99.9891 99.9952 99.9958 99.9961 99.9948 99.9772 99.9821 99.992799.9882 99.9913 99.929 99.9219 99.9956 99.9947 98.1516 99.9942 99.4314 99.0741 99.8767 99.9892 99.7845 99.9849 99.9714 99.961999.9903 99.9802 99.8536 99.189 99.9946 99.9982 97.3529 99.9621 93.4035 99.9396 99.8022 99.9919 99.6762 99.9796 99.9183 99.985899.9488 99.9963 99.5141 99.9981 99.9859 99.9853 100 99.9741 97.1647 99.9506 99.6879 99.9839 98.8471 99.964 99.9882 99.9999.9678 99.9928 99.9654 99.9565 99.9926 99.9935 100 99.9928 99.9829 99.9863 99.9493 99.9978 76.7002 99.9888 82.6118 73.1786
100 99.9926 99.9785 99.966 99.9936 99.996 100 99.9648 99.9956 99.9819 99.9074 100 58.2329 99.9929 82.1026 62.253299.8789 99.9763 100 99.9844 99.9598 100 100 98.9197 99.9835 99.4383 99.3758 99.9522 77.4827 99.9756 76.4192 63.229898.2369 100 82.4654 98.8987 99.9274 100 100 99.8779 99.9942 99.9664 100 99.9482 98.432 99.9749 67.6367 99.9175
100 99.9843 58.7025 99.9595 99.9699 100 99.9762 99.9868 100 99.9724 99.9767 99.5003 99.0731 99.9838 70.5262 99.758396.0687 100 85.0295 100 99.9858 100 100 99.9672 99.9131 99.9675 99.2159 99.2128 100 100 79.7101 99.878854.4085 99.9824 100 99.9646 99.9328 100 99.9698 100 99.9806 99.9904 99.9726 100 99.9794 99.9806 78.4 10032.4622 100 99.0823 99.984 100 99.977 99.9706 100 100 99.9713 100 100 100 100 65.407 10080.3377 99.9763 100 100 99.9388 100 100 100 99.9802 100 100 100 100 99.9519 93.6684 90.3061
100 100 100 100 100 99.9657 100 100 100 100 99.9692 100 99.7074 99.8462 100 98.1667100 100 100 100 100 100 100 100 100 100 99.6047 100 100 100 99.6094 98.0769100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 99.4898100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100100 100 100 100 100 100 100 100 97.7778 100 100 100 100 100 100 100100 100 100 100 100 100 100 100 88.8889 100 100 100 100 100 100 100100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100
)° (φ-150 -100 -50 0 50 100 150
(cm
)im
pZ
-200
-150
-100
-50
0
50
100
EPlus06 Fiducial Volume CutsEPlus06 Fiducial Volume Cuts
Figure 4.1: Trigger efficiency plots as functions of azimutal angle φ and z impactposition of the electron in the LAr calorimeter for 2004e+p, 0405e−p, 2006e−p and0607e+p periods. The enclosed areas correspond to the fidutial volume cuts negletedfrom the entire data (in red) and for some periods (in blue).
The LAr efficiency (εLAr) is measured with the events firing the S67 after removing
the subtrigger and fidutial volume cuts1. This can be determined thanks to the
1Cells switched off because high noise, damage or malfunctioning hardware.
4.2. DATA QUALITY CONSTRAINS 61
independence between the electron fired and the hadronic final states fired, so one
can be used to monitor the other one. The LAr efficiency becomes close to 100 % as
can be seen in the Figure 4.1 for the four periods (plots made by Maxime Gouzevitch),
where the efficiency value of each cell is depicted as function of φe angle and zimpact
position of the electron. The enclosed areas correspond to the fidutial volume cuts
(rejected cells) negleted from the entire data (in red) and for some periods (in blue).
The T0 efficiency εT0 is determined in a similar way as the εLAr using the inde-
pendent LAr calorimeter and the CIP2k detector as monitors. As it uses the LAr,
the fidutial cuts are also applied here. A 100 % efficiency is obtained.
The veto efficiency εveto is calculated by the contributions of the time of flight
(ToF), CIP2k and MUON detectors. It is found a εveto = 98.83 ± 0.42 for e− and
εveto = 99.13 ± 0.24 for e+.
When the AND condition is made, the efficiency εS67 is found to be ∼ 99 %.
For an extended explanation of the trigger efficiency determination see the sec-
tions 2.6, 2.7 and 6.2 of reference [76].
4.2 Data quality constrains
The first steps of the offline selection consists in the choice of the recorded events
containing all the data information needed for the study of this thesis. The run
sample selection also provides the luminosity value which is subsequently used in the
cross section determination.
The cuts belonging to the general event selection constrains are explain now and
listed in the first column of Table 4.2.
4.2.1 Run sample selection
The data recorded at the H1 tapes are separated in runs, which are basically
events occurring in a time interval and containing very similar operating detector
and accelerator conditions. They are classified as good, medium or poor depending
62 CHAPTER 4. SELECTION OF DIS EVENTS AND K0S CANDIDATES
on the turn on subdetectors, the operating status and the quality of the lepton and
proton beams.
The run selection is a filter to obtain a sub-set of events where the detector
components relevant to this analysis are switched on and working properly. The
components required for K0S studies are CJC1, CJC2, CIP, LAR, SPACAL, TOF,
LUMI and VETO, with the additional condition of the trigger S67 and a primary
vertex range of ± 35.0 cm.
Table 4.1 lists the data periods considered here, the type of lepton, the run
ranges and the luminosity corresponding to the periods. It is important to remark
that not all runs of each year were used, some of them were rejected because of
detector malfunction, powerglitch, high voltage problem, noise or low yield, etcetera;
however the luminosity values presented are corrected for the rejected events. A total
luminosity of 339.6 pb−1 is obtained for the HERA II data.
Table 4.1: Run selection sample and corresponding luminosity value.
Year Collision Part. First Run Last Run L [pb−1]
2004 e+p 367284 392213 49.02
2004 e−p 398286 398679 0.160
2005 e−p 399629 436893 99.90
2006 e−p 444307 466997 56.87
2006 e+p 468531 492541 87.70
2007 e+p 492559 500611 45.92
Total 339.6
4.2.2 Vertex cuts
The ep collision should occur at the idealized primary interaction vertex (xvtx, yvtx,zvtx) =
(0, 0, 0), however there are technical difficulties to achieve this properly, specially at
the z axis, then a range of several centimeters around this nominal vertex should be
4.2. DATA QUALITY CONSTRAINS 63
considered. A typical range of |zvtx| < 35 cm is acceptable specially to reject contam-
ination of either the interactions of the particles from the beam with the residual gas
in the beampipe or the interactions between the electrons and the proton satellites2.
The distributions are shown in Figure 5.1 a) and Figure 5.4 a) for the DIS and the
K0S samples, respectively.
In addition, it is required that the vertex be central. This means that the vertex is
found by the central tracker chambers which provides high precision and reconstruc-
tion of the parameters compared with those reconstructed by the forward trackers.
4.2.3 DIS kinematic range
The kinematic variables referred here were already introduced in the subsec-
tion 1.1.1. The values of the photon virtuality Q2, inelasticity ye and x-Bjorken were
determined by the e method and eΣ method, as explained in appendix A, finding
at the end the same results within the systematic errors. The e method has been
chosen for the reconstruction of event kinematics in this work.
This analysis is focused at high Q2, meaning Q2 greater than 145 GeV2. This cut
ensures that the scattered electron is measured in the LAr calorimeter. An upper
cut, Q2 < 20000 GeV2, is also applied as precaution due to the limited phase space
at HERA. The Q2 distributions are shown in logarithm scale in Figure 5.1 b) for the
DIS sample and Figure 5.4 b) for the K0S sample.
The ye cut in the range 0.2 < ye < 0.6 is done to avoid the fake electrons and for
to be in a safety range of resolution of the e method, see Figures 5.1 c) and 5.4 c)
for the corresponding DIS and K0S sample distributions. There is not explicit cut
applied to x but due to its relation with the other kinematic variables it is affected,
see the distribution for DIS events in Figure 5.1 d).
2Small bunches delayed with respect to the main bunch.
64 CHAPTER 4. SELECTION OF DIS EVENTS AND K0S CANDIDATES
4.3 Selection of DIS events
The next step consists in the DIS event selection, based on the identification of the
scattered electron e′. The criteria list in this case was chosen because high efficiency
of detection, resolution, geometrical acceptance of the detectors, physical rules of
conservation or because rejection of others kind of processes that are considered as
background in this analysis. The applied cuts have already been widely studied and
tested for other analysers and they are settle as the best for DIS events selection.
All these cuts are listed in the second column of the Table 4.2.
4.3.1 Scattered electron energy
According to the four-momentum Q2 of photon participating in the interactions
at HERA, e′ can be detected by the LAr or the SpaCal calorimeter. For this thesis,
the chosen phase space dictates that the electron must be identified by the LAr
Calorimeter.
The electron energy restriction is done to avoid the fake electrons (typically
hadronic clusters from photoproduction events) or the non well identified electrons,
but also to take advantage of the LAr efficiency which is close to 100% at E ′
e >11 GeV
(the distribution is presented in Figure 5.2 a)). The clear recognizion of the elec-
tron is possible because the position, shape and size of the cluster left by its energy
deposition in the LAr is very well known.
4.3.2 Scattered electron polar angle and zimpact coordinate
The limits on the polar angle θe and the impact coordinate in the z axis of the
electron zimpact are based on geometrical acceptance of the H1 LAr Cal detector.
The polar angle is defined as the angle between the incident proton beam direction
and the line given by the primary interaction vertex and the center of the energy
cluster in the LAr. The chosen range is 10 < θe < 150 (see its distribution in
Figure 5.2 b)).
4.4. RECONSTRUCTION OF K0S CANDIDATES 65
The z coordinate of the electron impact is chosen to be zimpact > −180 cm (Fig-
ure 5.2 c)) to ensure that the electron falls on the acceptance of the LAr calorimeter.
4.3.3 Four-momentum conservation
By conservation of energy and momentum, the value of the total E − pZ mea-
sured in H1 should be twice the energy of the incoming electron, that means 2∗27.5
GeV≃55 GeV, but several effects can affect this, for instance if the electron was not
detected in the LAr calorimeter, if there were initial or final state radiation so the
energy of the electrons is reduced or if photoproduction events occurred. Mainly due
to these possibilities the constrain 35 < E − pZ < 70 GeV is made, as shown in
Figure 5.1 e).
4.4 Reconstruction of K0S candidates
Once the DIS sample is available, one goes ahead with the particle identification
of interest, in this case the K0S meson. As the K0
S is a neutral particle, it only can be
detected through its daughter particles. As was listed in Table 2.2, this meson have
several decay channels but the one chosen for this analysis is the more frequent and
the one with only charged particles, K0S → π+π−; see Figure 4.6.
A general explanation of how to deal with the reconstruction of the K0S candidates
is the following:
1) Look for central tracks with opposite charge which satisfy the selection criteria
mentioned in section 4.4.1.
2) As the K0S has a relatively large lifetime it travels some distance before decay-
ing. The decay occurs at a vertex, displaced from the primary vertex, known as
secondary vertex V 0. The selected tracks in 1) are assumed to be the daughters
of a neutral particle and are associated to the V 0.
66 CHAPTER 4. SELECTION OF DIS EVENTS AND K0S CANDIDATES
3) The last step consists in a series of cuts applied to the identified neutral particle
to decide if it can be considered as a candidate to K0S .
The summary of all the cuts applied to the tracks and the K0S candidate can be
found in the two last columns of the Table 4.2.
4.4.1 Track cuts
In H1, the tracks can be reconstructed by only central trackers, only forward
trackers or by the combination of both, but the best quality of reconstruction comes
from the central trackers. That is the reason why these are chosen here.
Reconstructed tracks with a starting radius less than 30 cm are chosen (see Fig-
ure 5.3 a)). This condition implies tracks whose beginning is located inside the CJC1
detector avoiding in this way the consideration of pieces of trajectories produced by
the interaction with the material between the CJC1 and CJC2.
A combination of the track segments of the CJC1 and CJC2 chambers provides
a better reconstructed track, then a cut to the length of the transverse projection of
the tracks is applied with the restriction of radial length > 10 cm to get a track of
good reconstruction quality, Figure 5.3 b).
It is known from previous studies that the reconstruction of the tracks get worse
at very low transverse momentum values because of the multiple interactions with
the material of the detector and the curling of the trajectory, therefore a cut of
pt > 0.12 GeV is applied to each track to have a good identification and to avoid
background of wrong tracks. The distribution is presented in Figure 5.3 c) for the
π− of the K0S.
The cut dca(π+)∗dca(π−) < 0, where dca means the distance of closest approach
to the origin of the interaction as explained in appendix D, is done to ensure that
a pair of selected opposite charged tracks share the same V 0; but also to test the
charge of the considered particles, because due to the magnetic field the tracks with
opposite charges should bend in different directions giving a negative value of their
dca product.
4.4. RECONSTRUCTION OF K0S CANDIDATES 67
The so called significance |dca′|/σdca′ , the ratio of the absolute value of the dca′
(the distance of closest approach of the track in the rφ plane to the primary vertex)
and its error σdca′ is chosen to be greater than 3; this constrain helps to reject
tracks coming from the primary vertex. Studies made by D. Pitzl and A. Falkiewicks
showed that more statistic and better signal to background ratio is obtained with
the application of this cut complemented with the dca(π+) ∗ dca(π−) < 0 constrain.
The distribution of significance for the π− from the K0S can be seen in Figure 5.3 d).
Table 4.2: Summary of the selection criteria.
Event selection Electron cuts Tracks cuts K0S cuts
central vertex Trigger 67 Central tracks > 1 Number of K0S >0
|zvtx| <35 cm Ee > 11GeV Different charges Daughters = 2
145< Q2 < 20000GeV2 10 < θe <150 Start radius < 30cm Decay length >2cm
0.2< Ye <0.6 zimpact >-180cm Radial length > 10cm |η| <1.5
35< E − pz < 70GeV pt > 0.12GeV pt >0.3GeV
Fiducial cuts dca(π+) ∗ dca(π−) <0 M(pπ−) >1.125GeV
|dca′|/σdca′ >3 M(e−e+) >0.05GeV
Fit χ2 <5.4
| cos(θ⋆)| < 0.95
4.4.2 Cuts to the K0S candidates
Until here, the selection criteria provides the two candidates to πs tracks and the
V 0 position. If the number of found V 0’s is different of zero. Then, one can follow
with the next conditions.
The phase space of this analysis is characterized by the Q2 and ye kinematic
ranges but also by the transfer momentum pt(K0S) and the pseudorapidity |η(K0
S)|limits of the K0
S :
0.3 GeV < pt(K0S) |η(K0
S)| < 1.5
68 CHAPTER 4. SELECTION OF DIS EVENTS AND K0S CANDIDATES
The pt(K0S) cut is chosen to have good acceptance and good efficiency on the
reconstruction of the V 0 from the pions tracks, while the η(K0S) cut is used to ensure
that the K0S is contained within the geometrical acceptance of the central detectors.
Positive (negative) values of η corresponds to the forward (backward) region of the
H1 detector, so it can be traduced to θ cuts, see Figure 5.4 d) and e).
The distance in the rφ plane between the primary vertex and the secondary vertex
V 0, known as the radial decay length, is chosen to be DL > 2 cm (Figure 5.4 f)),
mainly due to the efficiency of V 0 reconstruction and the boost of the K0S lifetime to
the laboratory frame.
Another cut applied to the vertex finding is the χ2 quantity which expresses the
quality of the fit of the two daughter particles to the secondary vertex. A value of
χ2 < 5.4 is considered as good enough since the distribution decays exponentially
and start to be almost flat from approx. χ2 = 3, as shown in Figure 5.5 a). A value
of 5.4 allows to have a little bit more statistic.
The angle between the positive track in the rest frame of the K0S and the direc-
tion of the K0S in the laboratory frame is the so called θ∗ angle. A requirement of
|cos θ∗| < 0.95 is applied to the selection in order to avoid background from photon
conversion (γ → e+e−) and ensure that the K0S candidate comes from the primary
vertex. Figure 5.5 b) shows the distribution of this variable.
The way to improve the rejection of neutral particles faking the K0S reconstruc-
tion, for instance the photon conversion, Λ0 and Λ0 particles, between others, is
calculating the invariant mass and making some cuts to it.
The invariant mass M can be calculated under the hypothesis of the π mass for
both negative and positive tracks3 by the formula:
M(π+, π−) =√
(Eπ+ + Eπ−)2 − (pπ+ + pπ−)2 (4.1)
where pπi is the momentum vector, Eπi =√
p2πi + m2
π the energy, mπ the pion
mass [11] of the pion i = + or i = −.
3From the track reconstruction is possible to extract the momentum vector but not the mass ofthe particle. The four-momentum can only be obtained by assuming a mass value.
4.4. RECONSTRUCTION OF K0S CANDIDATES 69
d
V0
pprel
1 d2
p1,L
2,L
prel
TT
K0s π
Λ p πΛ p π_ _
0 10.69
+
PT
rel [GeV]
α−1
0.104
0.206
+ −
π−
−0.69
Figure 4.2: a) Definition of longitudinal pL and the relative transverse prelT momentum
variables. b) The armenteros plot where half ellipses with its center lying at α axisbelong to V 0 particles. The value of the centers gives the difference between themasses of the daughters.
a) b)
The Λ0 and Λ0 contributions are eliminated by requiring M(pπ) > 1.125 GeV,
assuming the π− and p masses for the invariant mass calculation when the search is
for Λ0, or the π+ and p masses for Λ0 [11]. The track with the highest momentum is
considered to be the p or p according to the charge of the track.
In the same way, the photon conversion contribution is avoided by M(e+e−) >
0.05 GeV. The masses considered here are those of the electron e− and positron
e+ [11].
The values of the last two cuts were obtained using the Armenteros-Podolsk-
Thompson plots [77], which plot the α vs. prelT variables to describe the kinematic of
a body decaying to two daughters d1 and d2. α is defined as:
α =pd1
L − pd2
L
pd1
L + pd2
L
where pdi
L is the longitudinal momentum measured in the laboratory frame of the
daughters with respect to the flight direction of the mother particle; prelT is the
value of the relative transverse momentum of the daughters, see Figure 4.2 a). The
condition prelT (d1) = prel
T (d2) is imposed by momentum conservation.
70 CHAPTER 4. SELECTION OF DIS EVENTS AND K0S CANDIDATES
Figure 4.3: Armenteros plots from all HERA II data.
) [GeV]-π +πM (0.3 0.4 0.5 0.6 0.7
Ent
ries
/ 3 M
eV
0
1000
2000
3000
4000
5000
-π +π → s0K
1194±) = 38154 s0 N(K
H1 Preliminary
Figure 4.4: Invariant mass distribution of the K0S candidates reconstructed from the
decay channel π+π−. The corresponding fits to describe signal and background areshown in red and blue lines respectively, while the total fit is plotted with the greenline.
4.4. RECONSTRUCTION OF K0S CANDIDATES 71
A typical Armenteros plot is shown in Figure 4.2 b) where half ellipses with
its center lying on α axis belong to V 0 particles. The value of the centers gives
the difference between the masses of the daughters. The band structure is due
to momentum conservation of the different V 0 decays, while the band widths are
determined by the widths of the V 0s combined with the detector resolution. The
bands of Λ0 and Λ0 are lower than the K0S band. The reason is that the sum of the
pion and proton masses is only 38 MeV smaller than the Λ0 mass, while the sum
of the two pions is ∼219 MeV below the K0S mass. Due to the finite resolution the
measured distributions are smeared out. However, the separation of K0S and Λ0 still
can be seen. In Figure 4.3, the Armenteros plot from HERA II data is presented,
the rejection of Λ0 particles has already be done.
) [GeV]-π +πMass(0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
En
trie
s/
1 M
eV
-210
-110
1
10
210
310
Decays0K DecayΛ
Other Decay Pair Prod→ γ
Secundary Inter.Other vertex
Django HERA II
comes from:-π +π
) [GeV]-π +πMass(0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
En
trie
s/
1 M
eV
-210
-110
1
10
210
310
Decays0K DecayΛ
Other Decay Pair Prod→ γ
Secundary Inter.Other vertex
Rapgap HERA II
comes from:-π +π
Figure 4.5: Invariant mass distribution of the K0S for Django and Rapgap models.
The study of the remaining contamination shows some contribution of Λ decays,other particles decaying to two charged daughters, photon conversion, interactionswith the dead material of the detector and events coming from other vertex.
After applying all mentioned cuts, the mass distribution of the K0S candidates is
plotted and shown in Figure 4.4. A clear peak is obtained concluding that most of
the background has been rejected. However, using Monte Carlo models, a study of
72 CHAPTER 4. SELECTION OF DIS EVENTS AND K0S CANDIDATES
the remaining contamination can be done showing that still some few events of Λ
decays, other particles decaying to two charged daughters, photon conversion (γ →pair production), secondary interactions (interactions with the dead material of the
detector) and events coming from other vertex are part of the sample, in Figure 4.5
Django and Rapgap models results are presented, similar predictions are obtained.
Figure 4.6: Seagull and sailor decay topologies identified by the sign of the crossproduct of the three-momentum of the pions, (~pπ+ x ~pπ−)z > 0 for seagull and(~pπ+ x ~pπ−)z < 0 for sailor.
a) b)
The invariant mass distribution shown in Figure 4.4 contains in fact two different
track combinations of curvatures or decay topologies, the outward-curved or seagull
and the inward-curve or sailor topologies both depicted in Figure 4.6. The separation
of these can be done by the cross product of the three-momentum of the pions, the
seagull decay topology is defined as (~pπ+ x ~pπ−)z > 0, whereas the sailor decay
topology corresponds to (~pπ+ x ~pπ−)z < 0. The K0S mass distributions for each
topology are presented in Figure 4.7.
4.5 Event yield
The event yield Y is defined as the ratio of the number of events in the sample
(N) and the integrated luminosity as measured in section 3.2.3, corresponding to the
4.6. SIGNAL EXTRACTION 73
-) [GeV]π +πM (0.3 0.4 0.5 0.6 0.7
Ent
ries
/ 3 M
eV
0
200
400
600
800
1000
1200
1400
1600
1800
2000 -π +π → s0K
0.000122±Mass = 0.497388
0.000146± = 0.010593σ
723±) = 18285 s0 N(K
S/B = 5.610861
Seagull
) [GeV]-π +πM (0.3 0.4 0.5 0.6 0.7
Ent
ries
/ 3 M
eV
0
500
1000
1500
2000
2500
-π +π → s0K
0.000088±Mass = 0.496719
0.000113± = 0.007467σ
936±) = 20042 s0 N(K
S/B = 3.946869
Sailor
Figure 4.7: Invariant mass distribution of the seagull and sailor topologies showing9% higher contribution from sailor compared with seagull.
a) b)
selected run period, then Y = N/L.
An abnormal low or high yield may indicate a period where the detector efficiency
or measured integrated luminosity is not well understood. In Figure 4.8 the yield
plots as a function of the run number, also separated by year periods, are presented
for the DIS sample and K0S sample, respectively. It is in general stable. The small
changes have been observed in other analysis and have been attributed to biases in
the integrated luminosity measurement (acceptance of the photon tagger).
4.6 Signal extraction
To know the number of K0S candidates is necessary to make a fit to the invariant
mass distribution. Figure 4.4 shows the total fit ftot(mπ+,π−) as a green line, which is
in fact a sum of two functions, one to describe the signal fsig(mπ+,π−) showed with a
red line in the Figure and one describing the background fbgrd(mπ+,π−) in blue line:
ftot(mπ+,π−) = fsig(mπ+,π−) + fbgrd(mπ+,π−).
The function chosen for the signal is the t-student distribution:
fsig(xm(π+,π−)) =N Γ((ν + 1)/2)√
νπ Γ(ν/2)(1 +
t2
ν)−(ν+1)/2,
74 CHAPTER 4. SELECTION OF DIS EVENTS AND K0S CANDIDATES
Run Number380 400 420 440 460 480 500
310×
Yie
ld (
Eve
nts/
1 pb
)
0.8
1
1.2
1.4
1.6
1.8
2
2.2
2.4 +Data 04 e-Data 0405 e
-Data 06 e+Data 06 e+Data 07 e
DIS sample
Run Number380 400 420 440 460 480 500
310×
Yie
ld (
Eve
nts/
1 pb
)
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35+Data 04 e
-Data 0405 e-Data 06 e+Data 06 e+Data 07 e
Candidatess0K
Figure 4.8: Yield plots as a function of run number for a) the DIS sample and b) theK0
S sample. The 2004e+p period in blue, 0405e−p in magenta, 2006e−p in yellow,2006e+p in green and 2007e+p period in red.
a)
b)
4.6. SIGNAL EXTRACTION 75
t =xm(π+,π−) − µK0
s
σ,
where the normalization N , the mean value of the mass µK0s, the standard deviation
σ and the number of degrees of freedom ν are free parameters. The variable xm(π+,π−)
runs over the complete x axis range of the invariant mass distribution.
The t-student, as many other functions, is very useful to estimate population
values from the data samples, specially when the media and standard deviation are
not known. Some advantages are its continuity and symmetry with respect to the
average but one should pay special attention to the parameters and the χ2 values to
be sure that the fit is valid. In this case for instance, one should look at ν > 1, µK0s
close to the value provided by PDG [11], small σ and χ2 normalized to the degrees
of freedom (NDF) as close to 1 as can be possible.
This function was also chosen because of its bell shape a little bit lower and wider
than the normal standard distribution; as well due to its approximation to the Breit-
Wigner function when ν = 1; also because if ν has a high value (approx. ν > 200)
the distribution is more like a normal standard distribution; and because it behaves
as Gaussian when ν → ∞.
The best function for the background was found to be:
fbgrd(xm(π+,π−)) = p0(xm − 0.344)p1 ∗ Exp(p2xm + p3x2m + p4x
3m)
where pi are the free parameters. This choice gives a good description of the back-
ground shape which goes to zero at the value 0.344 GeV, due to a cut in the relative
transverse momentum of the pion (prelT ) of 100 MeV which traslates to a minimum
mass of 2√
m2 + (0.10)2 = 0.344.
The number of K0S candidates are taken from the integral of the signal func-
tion. The fit to the invariant K0S mass for all HERA II data, Figure 4.4, gives
38154 ± 1194 K0S candidates with a estimated mass in the peak of 496.97 MeV and
low σ (8.85x10−3). The ratio signal over background S/B in the range [0.45 GeV,
0.55 GeV] is 4.5.
76 CHAPTER 4. SELECTION OF DIS EVENTS AND K0S CANDIDATES
4.7 Selection of charged particles
The charged particles (h±) sample is needed for the determination of the K0s /h
±
cross section ratio. They are selected in the same phase space as the K0S, 145 < Q2 <
20000 GeV2 and 0.2 < y < 0.6, together with additional conditions to ensure the
good quality of the tracks.
The tracks are detected by the CTD specially by the CJC chambers. The char-
acteristics to fulfill are:
• The track of the scattered electron is not considered in the sample.
• The cosine of the angles between the momemtum of the scattered electron and
the track of the charged particle must be less than 0.99 to reject tracks close
to the scattered electron.
• All tracks must be associated to the primary vertex such that the distance of
closest approach of the track in the rφ plane to the primary vertex is chosen
to be |dca′| < 2.0 cm.
• The minimum radial length of the reconstructed track must be greater than 10
cm.
• The tracks must have the first hit in the CJC1, then the start radius is chosen
to be less than 30 cm.
• The tranverse momentum required to be larger than pT > 0.3 GeV for good
efficiency of the track reconstruction and compatibility with the phase space
of the K0S sample.
• The psedorapidity range being between -1.5 < η < 1.5 as the K0S sample which
means that the tracks are in the central region of the detector.
After the selection a sample consisting of 2,615,100 charged particles is obtained,
mainly populated by charged pions.
Chapter 5
The measurement of the crosssection
As mentioned previously, the goal of this thesis is the measurement of the K0S
particle production. In this chapter is explained how the total production cross
section is determined and the way to calculate differential cross section as a function
of one or more variables; also a series of important issues of data correction that one
should not forget to take into account during the calculations.
The measurement from data is never an exact value. It is always accompanied of
additional quantities which represents the statistical and the systematic uncertain-
ties; this last one consisting on several sources which are explained in the last part
of this chapter.
5.1 Determination of the cross section
The interaction between two particles is generally described in terms of the cross
section. This quantity essentially gives a measure of the probability for a reaction to
occur and may be calculated if the form of the basic interaction between the particles
is known.
Two methods are commonly used to directly measure total cross sections. The
77
78 CHAPTER 5. THE MEASUREMENT OF THE CROSS SECTION
first method is the transmission experiment where one measures the intensity of
particles before and after the target and infers the total cross section from the relation
I = I0exp(−NσT ), where I(I0) is the transmitted (incident) intensity and N is the
number of target nuclei per cm2. This method is frequently employed at fixed target
accelerators. In the second method one attempts to record every interaction that
takes place, this requires a detector with ∼ 4π acceptance. This method is often
used for colliding beam experiments, like at HERA. The total cross section is given
by σT = N/L where N is the measured total interaction rate and L is the measured
incident luminosity.
The total K0S cross section in the visible phase space defined by:
145 < Q2 < 20000 GeV2, 0.2 < ye < 0.6,
−1.5 < η(K0s ) < 1.5, 0.3 GeV < pT (K0
s ), (5.1)
is measured using the relation:
σvis(ep → e′K0s X) =
NdataK0
s
ε · BR(K0s → π+π−) · L (5.2)
where NdataK0
sis the number of K0
S mesons gotten from the fit to the invariant mass
distribution of data, as described in the section 4.6; ε the efficiency of detection with
the QED corrections included; BR the branching ratio of the K0S decaying to two
pions and L the accumulated luminosity.
The differential cross section in terms of a variable ℘ is calculated by:
dσvis(ep → e′K0s X)
d℘=
NdataK0
s
∆℘ · ε · BR(K0s → π+π−) · L (5.3)
where ∆℘ will take values of the different intervals of ℘, the so called bins. NdataK0
s
and ε should be now calculated for each bin. The values for NdataK0
swere obtained
after fitting the mass distribution for each bin, as shown from Figure F.1 to F.16
in appendix G for the bins of laboratory and Breit frame1 variables refered in the
1Description of the Breit frame in the appendix E.
5.1. DETERMINATION OF THE CROSS SECTION 79
Table 5.1. The same will be applied when double differential cross section as a
function of ℘ and 0 are required, the values needed for the measurement of the cross
sections should correspond to those bins of ∆℘ and ∆0.
5.1.1 Binning scheme
For the calculation of the differential cross section of the K0S belonging to the
final sample, one must split in different intervals the variable range. The size of the
intervals, known as bins, are chosen depending on the statistical data sample as fine
as one could, but ensuring that they are wide enough to get a good fit to the invariant
mass distribution of each bin, so it can occur that some bins are larger that others.
The bin width is also checked to be at least twice its resolution. A good binning
choice can help to limit the statistical error on the differential cross section.
Here, the data sample was binned as a function of the kinematic variables Q2, x
and the K0S variables η and pt in laboratory frame and also as a function of xCBF
p ,
xTBFp , pCBF
T and pTBFT in the Breit frame using the bin boundaries listed in Table 5.1
and bounded by the corresponding phase space cuts.
Table 5.1: The bin boundaries list.Q2[GeV 2] x η PT [GeV] XCBF
p XTBFp PBF
t [GeV ]
145,167 0.0,0.004 -1.5,-0.5 0.3,0.8 0.0,0.07 0.0,0.07 0.0,0.35
167,200 0.004,0.008 -0.5, 0.0 0.8,1.1 0.07,0.13 0.07,0.13 0.35,0.6
200,280 0.008,0.017 0.0, 0.45 1.1,1.55 0.13,0.2 0.13,0.2 0.6,1.0
280,500 0.017,0.2 0.45, 0.95 1.55,2.23 0.2,0.33 0.2,0.33 1.0,1.8
500,1000 0.95, 1.5 2.23,3.5 0.33,1.0 0.33,1.0 1.8,14
1000,5000 3.5,14 1.0,2.0
However, the binning used for the differential cross section is acceptable only if it
also satisfies other detector requirements (the efficiency ε, stability S, purity P and
acceptance A) as described in the following section.
80 CHAPTER 5. THE MEASUREMENT OF THE CROSS SECTION
5.2 The correction of data
For the cross section extraction, the data is submitted to corrections because of
loses of the K0S from the sample or the inclusion of fake K0
S in the sample, both
possibilities can occur due to the incapability of the detectors to capture all the
particles produced (geometrical and electronic acceptance), the limitations in the
track reconstruction due to the selection criteria, fluctuations in the physical variables
determination due to finite resolution, the possible rejection of particles of our interest
during the signal extraction, etc.
The corrections are done using Monte Carlo simulations. There are three different
kinds of MCs mentioned in section 1.4, the generated MCs and the reconstructed
MC. The generated are the radiative MC and the non-radiative MC, based in the
simulations of the HERA collision. The first one takes into account QED radiative
effects. The reconstructed MC has the consideration not only of the HERA collider
but also the H1 detector conditions of operation. The reconstructed particles pass
by the same selection criteria and cross section extraction as data.
5.2.1 Control plots
A comparison between the data and the reconstructed Monte Carlo is done for
the complete event sample. The kinematic, DIS, tracks, K0S and other detector vari-
ables are compared in order to know the quantitative agreement between the data
and simulation. Those plots, called control plots, were done and checked for each
year period, as well for all HERA II data sample as shown in Figures 5.1, 5.3 and 5.4
where the data are compared to the Django and Rapgap models with normalization
to the number of events. It can be concluded that the simulations of the two models
describe reasonably well the distribution of several variables from data (the back-
ground as well). Then, the detector response to expected physics is well understood
and represented by efficiency reweights and detector simulation.
5.2
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trie
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e)
Figu
re5.1:
Con
trolplots
ofa)
the
zvertex
distrib
ution
ofth
ein
teraction,
b)
the
logarithm
ofth
ephoton
virtu
alitylog(Q
2),c)
the
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teC
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ectively.
82C
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5.
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ME
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[GeV]eE0 10 20 30 40 50 60 70
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trie
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e)
Figu
re5.2:
Con
trolplots
ofa)
the
energy
Ee ,
b)
the
polar
angle
θe ,
c)th
ez-im
pact
coord
inate,
d)
the
azimuth
alan
gleφ
ean
de)
the
energy
calculated
with
the
dou
ble
angle
meth
od
ofth
escattered
electron.
The
data
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asblack
dots
while
Djan
goan
dR
apgap
Mon
teC
arloare
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and
blu
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ectively.
5.2
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FD
ATA
83
[cm]πStart Radius 10 15 20 25 30 35
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200
300
400
500
600
700
800 f)
Figu
re5.3:
Con
trolplots
correspon
din
gto
the
negative
pion
dau
gther
π−
ofth
eK
0S
candid
ate,a)
the
startrad
ius
and
b)
the
radial
length
ofth
etrack
,c)
the
transverse
mom
entu
mof
the
pion
pT
π ,d)
the
signifi
cance
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the
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ution
ηπ
and
f)th
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gleφ
π .Sim
ilardistrib
ution
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found
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pion
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The
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while
Djan
goan
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apgap
Mon
teC
arloare
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ectively.
84C
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TH
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ION
[cm]vtxZ-40 -30 -20 -10 0 10 20 30 40
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0.80.9
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trie
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2000HERAII DataDjangoRapgap
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trie
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f)
Figu
re5.4:
Con
trolplots
correspon
ging
toth
eK
0Ssam
ple,
a)th
ez
vertexposition
ofth
eK
0Sorigin
,b)
the
logarithm
ofth
ephoton
virtu
alitylog(Q
2),c)
the
inelasticity
ofth
escattered
electrony
e ,d)
the
transverse
mom
entu
mp
T,
e)th
epseu
dorap
itydistrib
ution
and
f)th
erad
ialdecay
length
ofth
eK
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did
ates.T
he
data
areplotted
asblack
dots
while
Djan
goan
dR
apgap
Mon
teC
arloare
inred
and
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eresp
ectively.
5.2
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85
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HERAII DataDjangoRapgap
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0.80.9
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trie
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-)π+,π (φ-3 -2 -1 0 1 2 3
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trie
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ts
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1600c)
Figu
re5.5:
Con
trolplots
correspon
ging
toth
eK
0Ssam
ple,
a)th
eχ
2distrib
ution
,b)
the
cos(θ∗)
and
c)th
eazim
uth
alan
gleof
the
K0S
candid
ates.T
he
data
areplotted
asblack
dots
while
Djan
goan
dR
apgap
Mon
teC
arloare
inred
and
blu
eresp
ectively.
86C
HA
PT
ER
5.
TH
EM
EA
SU
RE
ME
NT
OF
TH
EC
RO
SS
SE
CT
ION
Start Radius (charged part)10 15 20 25 30 35
MC
/Da
ta
0.80.9
11.11.21.310 15 20 25 30 35
210
310
410
510
610
710
HeraII DataDjangoRapgap
a)
radial length (charged part) [cm]0 10 20 30 40 50 60 70
MC
/Da
ta
0.80.9
11.11.21.30 10 20 30 40 50 60 70
-110
1
10
210
310
410
510
610 b)
Track multiplicity0 5 10 15 20 25 30 35 40
MC
/Da
ta
0.80.9
11.11.21.30 5 10 15 20 25 30 35 400
50
100
150
200
250
310×
c)
(charged part)η-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
MC
/Da
ta
0.90.95
11.05
1.11.15-2 -1.5 -1 -0.5 0 0.5 1 1.5 20
20
40
60
80
100
1203
10×
d)
(charged part)φ-3 -2 -1 0 1 2 3
MC
/Da
ta
0.90.95
11.05
1.11.15 -3 -2 -1 0 1 2 30
20
40
60
80
100
1203
10×
e)
(charged part) [GeV]t
p0 2 4 6 8 10 12 14
MC
/Da
ta
0.80.9
11.11.21.30 2 4 6 8 10 12 14
310
410
510
610 f)
Figu
re5.6:
Con
trolplots
correspon
ging
toth
eselected
charged
particles,
a)th
estart
radiu
san
db)
the
radial
length
ofth
etrack
s,c)
the
trackm
ultip
licity,d)
the
pseu
do-
rapity
distrib
ution
η,e)
the
azimuth
alan
gleφ
and
f)th
etran
sversem
omen
tum
ofth
etrack
sp
Tπ .
The
data
areplotted
asblack
dots
while
Djan
goan
dR
apgap
Mon
teC
arloare
inred
and
blu
eresp
ectively.
5.2. THE CORRECTION OF DATA 87
5.2.2 Reweighting procedure
As mentioned in the previous subsection and also to have reliability of the gener-
ated Monte Carlo data to be used further on, it is important that the Monte Carlo
models describes well the data distributions. Sometimes the first comparison shows
that the MC does not agree with data, in that case (if the differences are not too
large) a satisfactory description can be achieved by applying a reweighting procedure
to the MC.
One takes a measured distribution in data and the corresponding in Monte Carlo
to determine the event weight. In this thesis a reweighting of the observable (E −pz)HFS of the hadronic final states was done. The first step is to get the ratio of the
MC over the data distribution, secondly the event weight is calculated fitting the
ratio to a function F((E − pz)HFS) of an appropriate shape. The fit function used
here is the polynomio:
F(§) = p0 + p1x + p2x2.
The procedure is done for each year period independently, so the weights are not
the same. Besides an improvement of the data description by MC in the reweighted
distributions, which is of course expected, other distributions are also positively
affected. A spoiling of the description of other distributions has not been observed.
There are cases where the MC reweighting of one observable is not enough, then
the procedure can be done using another observables and, under the assumption
that these quantities are uncorrelated, the total event weight is given by the product
of single weights Wtot(obs1, obs2, obs3) = W (obs1)W (obs2)W (obs3). This assumption
seems to be approximately correct, since usually already after the first iteration a
quite reasonable data description is achieved.
Altogether with (E − pz)HFS reweighted other default H1 weights are applied in
this analysis: zvtx, trigger and PDF. Whereas the first two are related to the detector
simulation, the remaining is directly sensitive to the physics implemented in the MC
model.
88 CHAPTER 5. THE MEASUREMENT OF THE CROSS SECTION
5.2.3 Purity and Stability
Other detector effects can be studied using both reconstructed and generated MC
simulations, as the migrations effects (the purity P , stability S and resolution σres)
described in this subsection, which corrects the reconstruction or generation of events
in wrong bins. The migrations effects are quantifed by the purity P and stability S;
which can be defined as the ratio of K0S generated and reconstructed in a given bin
over the K0S reconstructed for P (generated for S) in the same bin, respectively:
P =N stay
i
N reci
, S =N stay
i
N geni − N lost
i
,
where the following combinations were taken into account:
• N stayi : the number of events reconstructed (passing the selection) and generated
in the same given bin i, Figure 5.7 a).
• N smear−outi : the number of events generated in the given bin i but reconstructed
in the bin j. Figure 5.7 b).
• N smear−ini : the number of events reconstructed in the bin i but generated from
the bin j. Figure 5.7 c).
• N losti : the number of events generated in the given bin i but do not recon-
structed because did not pass the selection. Figure 5.7 d).
• N reci = N stay
i + N smear−ini , the number of events reconstructed in the bin i.
• N geni = N stay
i + N smear−outi + N lost
i , the number of events generated in the bin
i.
As their name indicates, they say how much pure and stable the K0S sample
is. The unity is never completely reached, nevertheless is expected that the large
fraction of events belongs to the bin where they are measured in. For this thesis the
purity and stability values calculated for Q2, x, η(K0s ) and pT (K0
s ) are presented in
5.2. THE CORRECTION OF DATA 89
a) Stay
c) Smear−in d) Lost
b) Smear−out
i jout
Rec
Gen
i jout
Rec
Gen
i jout
Rec
Gen
i jout
Rec
Gen
Figure 5.7: Schematic view of migrations possibilities: stay, smear-out, smear-in andlost.
a) b)
c) d)
90 CHAPTER 5. THE MEASUREMENT OF THE CROSS SECTION
Figure 5.8 in the laboratory frame, while the corresponding plots for xBFp and pBF
T in
the current and the target hemispheres of the Breit frame are shown in Figure 5.9.
The Figures correspond to Django MC; Rapgap gives similar values as shown in
Table 5.2 for bins of x.
Table 5.2: Purity and Stability values in bins of x estimated from Django and Rapgapmodels.
Purity Stability
Django Rapgap Django Rapgap
x - Bin 1 86.95 86.62 82.37 82.56
x - Bin 2 88.32 88.13 87.67 87.74
x - Bin 3 86.21 86.47 87.94 87.80
x - Bin 4 91.49 91.92 94.08 94.20
The purity and stability are greater than 80% as functions of Q2, x and η(K0s ). A
rise is observed as Q2 goes higher, the same can be said for x, while η(K0s ) is almost
flat from the second bin. The purity as function of pt(K0s ) improves a little bit from
∼ 74% to around 82%, then decreases again but not less than 70%; the stability, on
the contrary, starts around 80% then decreases to 76%, at high pT bins the values
incresases until ∼83%. In the Breit frame, the purity and stability as function of
xBFp are around 80% for both regions, although flatter for the current hemisphere;
however as function of pBFT the values oscilate between 60% to 80%.
5.2.4 Efficiencies
The efficiency of reconstruction ε appearing in the equation 5.2 and 5.3 is in fact
a combination of two efficiencies ε = εnon−raddet · εtrigger, the non-radiative detector
efficiency εnon−raddet and the trigger efficiency εtrigger. However the efficiency of the S67
trigger used in this analysis at high Q2 as explained in section 4.1 is ∼100%, so it is
taken as 100% and an error of 1% is included in the systematic uncertainties, then
5.2. THE CORRECTION OF DATA 91
[GeV]2Q310
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
Purity
StabilityHERA II
Candidatess0K
X-310 -210 -110
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
Purity
Stability
HERA II Candidatess
0K
η-1.5 -1 -0.5 0 0.5 1 1.50.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
Purity
Stability
HERA II Candidatess
0K
[GeV]TP1 10
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
Purity
Stability
HERA II Candidatess
0K
Figure 5.8: The K0S purity (in black) and stability (in green) as a function of Q2, x,
η and pT in the laboratory frame.
CurrentpX
-210 -110 10
0.2
0.4
0.6
0.8
1
1.2
Purity
Stability
HERA II Breit Frames
0K
TargetpX
-210 -110 10
0.2
0.4
0.6
0.8
1
1.2
Purity
Stability
HERA II Breit Frames
0K
[GeV]CurrentTP
-110 1 100
0.2
0.4
0.6
0.8
1
1.2
Purity
Stability
HERA II Breit Frames
0K
[GeV]TargetTP
-110 1 100
0.2
0.4
0.6
0.8
1
1.2
Purity
Stability
HERA II Breit Frames
0K
Figure 5.9: The K0S purity (in black) and stability (in green) as a function of xp and
pT in the current and the target hemispheres of the Breit frame.
92 CHAPTER 5. THE MEASUREMENT OF THE CROSS SECTION
the efficiency becomes ε = εnon−raddet . The εnon−rad
det is defined as the ratio between the
number of K0S taken from the signal extraction of the reconstructed Monte Carlo
sample and the number of K0S from the generated MC, both in the same phase space
and satisfying the complete selection criteria listed in Table 4.2:
εnon−raddet = εrad
det ∗ (1 + δQED) =N rec(K0
s )
N genrad (K0
s )∗ (1 + δQED), (5.4)
here N genrad (K0
s ) indicates that this number was taken from the MCs including QED
initial and final state radiation, then could be that wrongly reconstructed (falling in
a different bin) K0S exists due to the change in the four-momentum of the scattered
electron. The way to correct for these QED events is introducing in QED correction
factor (1 + δQED) defined as:
1 + δQED =N rad
gen
Nnon−radgen
· Lnon−rad
Lrad, (5.5)
where, Lnon−rad and Lrad denotes the luminosity of the generated radiative and non-
radiative samples.
The QED corrections for bins of Q2, x, η(K0S) and pT (K0
S) in the laboratory
frame are shown in Figure 5.10 for K0S and 5.11 for charged particles using Django
and Rapgap models, the QED correction average is found around 5.5% with a flat
behaviour in terms of Q2, x and pT (K0S) while η(K0
S) presents a QED correction
increasing in the forward direction.
The plots of QED corrections for K0S in the Breit frame variables are shown in
Figure 5.12, the xCBFp and pCBF
T in the current region presents lower QED corrections
compared to the same variables in the target region. At high values of both variables
(xp and pT ) at target region a difference in the models corrections is observed.
The plots of the efficiency of reconstruction εnon−raddet are shown in Figures 5.13,
5.14 and 5.15 for the same variables as QED corrections, the average efficiency used
for the total inclusive cross section determination is ∼ 30.55 % but it varies from
bin to bin. As functions of x and η it behaves very stable but for Q2 and pT (K0S)
goes from ∼ 20% in the first bins to around 40% (a little bit higher for pT ) in their
5.2. THE CORRECTION OF DATA 93
]2 [GeV2Q310
Gen
Rad
/Gen
Non
Rad
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4Django CDM
Rapgap MEPS
X-310 -210 -110
Gen
Rad
/Gen
Non
Rad
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4Django CDM
Rapgap MEPS
η-1.5 -1 -0.5 0 0.5 1 1.5
Gen
Rad
/Gen
Non
Rad
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4Django CDM
Rapgap MEPS
[GeV]TP1 10
Gen
Rad
/Gen
Non
Rad
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4Django CDM
Rapgap MEPS
Figure 5.10: QED corrections of K0S as a function of Q2, x, η and pT in the laboratory
frame. The Django MC presented in red and the Rapgap MC in blue.
]2 [GeV2Q310
Gen
Rad
/Gen
Non
Rad
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
Django CDM
Rapgap MEPS
X-310 -210 -110
Gen
Rad
/Gen
Non
Rad
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
Django CDM
Rapgap MEPS
η-1.5 -1 -0.5 0 0.5 1 1.5
Gen
Rad
/Gen
Non
Rad
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
Django CDM
Rapgap MEPS
[GeV]T
p1 10
Gen
Rad
/Gen
Non
Rad
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
Django CDM
Rapgap MEPS
Figure 5.11: QED corrections of charged particles as a function of Q2, x, η and pT
in the laboratory frame. The Django MC presented in red and the Rapgap MC inblue.
94 CHAPTER 5. THE MEASUREMENT OF THE CROSS SECTION
CBFpX
0 0.2 0.4 0.6 0.8 1
Gen
Rad
/Gen
Non
Rad
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4Django CDM
Rapgap MEPS
TBFpX
0 0.5 1 1.5 2
Gen
Rad
/Gen
Non
Rad
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
Django CDM
Rapgap MEPS
[GeV]CBFTP
-110 1 10
Gen
Rad
/Gen
Non
Rad
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4Django CDM
Rapgap MEPS
[GeV]TBFTP
-110 1 10
Gen
Rad
/Gen
Non
Rad
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
Django CDM
Rapgap MEPS
Figure 5.12: QED corrections of K0S as a function of xp and pT in the current and
the target hemispheres of the Breit frame. The Django MC presented in red and theRapgap MC in blue.
]2 [GeV2Q
310
ε
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7Django CDM
Rapgap MEPS
X-310 -210 -110
ε
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7Django CDM
Rapgap MEPS
η-1.5 -1 -0.5 0 0.5 1 1.5
ε
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7Django CDM
Rapgap MEPS
[GeV]TP1 10
ε
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7Django CDM
Rapgap MEPS
Figure 5.13: Efficiencies of K0S as a function of Q2, x, η and pT in the laboratory
frame. The Django MC presented in red and the Rapgap MC in blue.
5.3. THE SYSTEMATIC UNCERTAINTIES 95
middle range, going down again to around 32% at the highest bins. This shows an
up and down behavior which is also observed in the Breit frame variables where the
difference in the models at high values in the target regions still remains.
]2 [GeV2Q310
Cha
rged
Par
t.ε
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3Django CDM
Rapgap MEPS
x-310 -210 -110
Cha
rged
Par
t.ε
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3Django CDM
Rapgap MEPS
η-1.5 -1 -0.5 0 0.5 1 1.5
Cha
rged
Par
t.ε
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
Django CDM
Rapgap MEPS
[GeV]T
p1 10
Cha
rged
Par
t.ε
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3Django CDM
Rapgap MEPS
Figure 5.14: Efficiencies of charged particles as functions of Q2, x, η and pT in thelaboratory frame. The Django MC presented in red and the Rapgap MC in blue.
5.2.5 Resolution
The resolution of a variable X is defined as the width of the distribution:
σres = Xrec − Xgen
where Xrec and Xgen denotes the reconstructed and the generated value of the variable
X, respectively. The resolutions are shown in Figures 5.16 and 5.17.
5.3 The systematic uncertainties
The accuracy of the cross section measurement is altered by several sources of
uncertainty which change the determined value by a ∆σ. The study of these changes
96 CHAPTER 5. THE MEASUREMENT OF THE CROSS SECTION
CBFpX
-210 -110 1
ε
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7Django CDM
Rapgap MEPS
TBFpX
-210 -110 1
ε
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7Django CDM
Rapgap MEPS
[GeV]CBFTP
-110 1 10
ε
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7Django CDM
Rapgap MEPS
[GeV]TBFTP
-110 1 10
ε
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7Django CDM
Rapgap MEPS
Figure 5.15: Efficiencies of K0S as functions of xp and pT in the current and the target
hemispheres of the Breit frame. The Django MC presented in red and the RapgapMC in blue.
2log Q2.2 2.4 2.6 2.8 3 3.2 3.4 3.6
rec
2 -
log
Qge
n2
log
Q
-0.04-0.03-0.02-0.01
00.01
0.020.030.04
genlog x
-2.5 -2 -1.5 -1 -0.5
rec
- lo
g x
gen
log
x
-0.04-0.03
-0.02-0.01
0
0.010.020.03
0.04
η-1.5 -1 -0.5 0 0.5 1 1.5
rec
η -
gen
η
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
[GeV]T
p1 10
T re
c -p
T ge
np
-1
-0.5
0
0.5
1
Figure 5.16: Resolutions as functions of Q2, x, η and pT variables in the laboratoryframe. The Django MC presented in red and the Rapgap MC in blue.
5.3. THE SYSTEMATIC UNCERTAINTIES 97
CBFpx
-210 -110 1
CBF
p ge
n -
xC
BFp
gen
x
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
TBFpx
-210 -110 1
TBF
p re
c -
xTB
Fp
gen
x
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
[GeV]CBFT
p
-110 1 10
[GeV
]C
BFT
rec
-pC
BFT
gen
p
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
[GeV]TBFT
p
-110 1 10 [G
eV]
TBF
T re
c -
pTB
FT
gen
p-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
Figure 5.17: Resolutions as functions of xCBFp , xTBF
p , pCBFT and pTBF
T variables inthe Breit frame. The Django MC presented in red and the Rapgap MC in blue.
is done varying each possible uncertain quantity under investigation by some reason-
able deviation in both sides, upward and downward, then all the analysis procedure
is repeated and the corresponding cross section is calculated again under the same
selection criteria in order to know the sensitivity of the applied cuts. Depending on
the kind of source the uncertainty is calculated using data and MC models or MCs
only.
The sources can be classified as reconstruction uncertainties if the source comes
from or depends on the reconstruction of the electron and hadronic final states parti-
cles (as the energy and the polar angle of the electron), the luminosity measurement,
the V0 finding efficiency and the topology reconstruction; and correction uncertain-
ties if they are applied to simulation models (model dependence), efficiencies (trigger
and track efficiency) or signal extraction.
The total uncertainty consists of the addition in quadrature of the systematic
98 CHAPTER 5. THE MEASUREMENT OF THE CROSS SECTION
and the statistic uncertainties:
∆σtot =
√
σ2stat +
∑
i
σ2i,sys.
where i runs over all sources of systematics uncertainties. When one is dealing with
differential cross section the uncertainties should be calculated for each bin.
The estimation of the systematic uncertainties expectations are detailed sepa-
rately in the following subsections.
5.3.1 Energy and polar angle of the electron
The energy and the polar angle of the scattered electron is used for the estimation
of the kinematic variables Q2, x and y but also for the boost to the Breit frame, so
a variation in the energy range can directly affect the K0S rate production.
The systematic effect due to the energy scale can be studied varying by ± 1%
the reconstructed energy on the LAr calorimeter. The resulting uncertainty for the
inclusive cross section is found to be +1.5 % and -2.9 %, a higher uncertainty when
the energy is down.
For the differential cross section the variation is calculated bin by bin, the un-
certainty plots as functions of variables in the laboratory and the Breit frames are
shown in Figures 5.18 and 5.19. It is observed that the uncertainties when the en-
ergy of the electron is varied up are between 0.2 and 2 % for most of the bins in the
laboratory frame but for the fist bin of Q2 the uncertainty is higher, up to around
8 %; when the energy of the electron is varied down the uncertainties are between 1
and 4 % except for the last two bins in x where the uncertainty goes to 8 %. In the
Breit frame the higher uncertainty appears in the current hemisphere with a higher
value of 7 % when the energy of the electron is varied down.
The resulting uncertainty, due to effects in the polar angle reconstruction of the
LAr Cal, is estimated to be +2.9% and -3.1% by changing the θe′ angle by ± 3 mrad.
Figures 5.20 and 5.21 present the uncertainties bin per bin in the laboratory and
5.3. THE SYSTEMATIC UNCERTAINTIES 99
the Breit frame variables, except for the bins in Q2 all the other plots show more
symmetry when the θe′ angle varies up and down.
]2 [GeV2Q310
[%]
σ) / e
(Eσ ∆
-4
-2
0
2
4
6
8 DownUp
X
-310 -210 -110
[%]
σ) / e
(Eσ ∆
-10
-8
-6
-4
-2
0
2
4
6
8DownUp
η-1.5 -1 -0.5 0 0.5 1 1.5
[%]
σ) / e
(Eσ ∆
-5
-4
-3
-2
-1
0
1
2
3
4 DownUp
[GeV]T
p1 10
[%]
σ) / e
(Eσ ∆-3
-2
-1
0
1
2
3
4DownUp
Figure 5.18: The systematic uncertainties due to the variation on the energy of thescaterred electron Ee′ as functions of the laboratory frame variables.
5.3.2 Luminosity
The uncertainty in the luminosity measurement (subsection 3.2.3) is not the same
for all year periods, for 2004 e+p it is 2.92 %, for 0405 e−p the value is 2.44 % and
2.69 % for the year 2006 e−p while it is 2.28 % for 0607 e+p period. At the end, the
contribution to the total systematic uncertainty for the HERA II data is taken to be
2.6 %.
5.3.3 Topology
The topology error comes from the difference in the seagull and sailor topologies
reconstruction efficiency. The uncertainty is estimated, first taking the ratio of the
K0S number extracted from the fit to the invariant mass distribution of the data and
100 CHAPTER 5. THE MEASUREMENT OF THE CROSS SECTION
CBFpx
-110 1
[%]
σ) / e
(Eσ ∆
-8
-6
-4
-2
0
2
4
6DownUp
TBFpx
-210 -110 1
[%]
σ) / e
(Eσ ∆
-6
-4
-2
0
2
4
6DownUp
[GeV]CBFT
p-110 1 10
[%]
σ) / e
(Eσ ∆
-6
-4
-2
0
2
4 DownUp
[GeV] TBFT
p-110 1 10
[%]
σ) / e
(Eσ ∆
-6
-4
-2
0
2
4
6DownUp
Figure 5.19: The systematic uncertainties due to the variation on the energy of thescattered electron Ee′ as functions of the Breit frame variables.
]2 [GeV2Q310
[%]
σ) / eθ(σ ∆
-12
-10
-8
-6
-4
-2
0
2
4
6
DownUp
x-310 -210 -110
[%]
σ) / eθ(σ ∆
-8
-6
-4
-2
0
2
4
6
8DownUp
η-1.5 -1 -0.5 0 0.5 1 1.5
[%]
σ) / eθ(σ ∆
-5
-4
-3
-2
-1
0
1
2
3
4
5DownUp
[GeV]T
p1 10
[%]
σ) / eθ(σ ∆
-6
-4
-2
0
2
4
6DownUp
Figure 5.20: The systematic uncertainties due to the variation on the polar angle ofthe scattered electron θe′ as functions of the laboratory frame variables.
5.3. THE SYSTEMATIC UNCERTAINTIES 101
CBFpx
-110 1
[%]
σ) / eθ(σ ∆
-6
-4
-2
0
2
4
6DownUp
TBFpx
-210 -110 1
[%]
σ) / eθ(σ ∆
-6
-4
-2
0
2
4
6DownUp
[GeV]CBFT
p-110 1 10
[%]
σ) / eθ(σ ∆
-6
-4
-2
0
2
4
6DownUp
[GeV]TBFT
p-110 1 10
[%]
σ) / eθ(σ ∆
-6
-4
-2
0
2
4
6DownUp
Figure 5.21: The systematic uncertainties due to the variation on the polar angle ofthe scattered electron θe′ as functions of the Breit frame variables.
the model Ri = N idata/N
imodel where i represents the topology types, seagull or sailor.
Then, the double ratio Rdouble = Rsailor/Rseagull leads to a uncertainty contribution.
A value of ± 3.0% is calculated for the visible inclusive cross section of the K0S . This
3 % is applied to all bins in the laboratory and the Breit frames.
5.3.4 Model dependence
The full analysis is corrected using Django MC which uses CDM as parton cas-
cade. To test the effect of the parton evolution scheme on the K0S production, the
analysis is also done using Rapgap with a different parton evolution (MEPS); A con-
tribution of ± 0.05 % to the total uncertainty is gotten by half of the ratio between
the difference in the efficiencies obtained from both models and the efficiency using
Django:
0.5 ∗ εCDM − εMEPS
εCDM.
The variations per bins in the laboratory and the Breit frame variables are seen
102 CHAPTER 5. THE MEASUREMENT OF THE CROSS SECTION
in Figures 5.22 and 5.23, the uncertainties oscillate between 0.1% to 1.2% in the
laboratory but it goes to higher values in the Breit frame, specially in the target
hemisphere where the values are between 0.1% and 3.4%.
]2 [GeV2Q310
[%]
σ(m
odel)
/ σ ∆
-1
-0.5
0
0.5
1
x-310 -210 -110
[%]
σ(m
odel)
/ σ ∆
-3
-2
-1
0
1
2
3
η-1.5 -1 -0.5 0 0.5 1 1.5
[%]
σ(m
odel)
/ σ ∆
-2
-1
0
1
2
3
[GeV]T
p1 10
[%]
σ(m
odel)
/ σ ∆
-3
-2
-1
0
1
2
3
Figure 5.22: The systematic uncertainties due to the variation on the model depen-dence as functions of the laboratory frame variables.
5.3.5 Track efficiency
The track efficiency uncertainty is considered due to the imperfection in the
reconstruction of the tracks that can mainly affect the K0S tag. In H1 detector, there
is no other component besides the central trackers to be used for checking the track
reconstruction efficiency, then a 2 % uncertainty is choosen for each track which is
determined by the tracks curling up at the CJC.
As two tracks compose the K0S, an uncertainty of ± 4 % (the sum of 2 % per track)
is considered for the total uncertainty calculation becoming the dominant systematic
error of the analysis. The same 4% value is applied to all bins in the laboratory and
the Breit frames.
5.3. THE SYSTEMATIC UNCERTAINTIES 103
CBFpx
-110 1
[%]
σ(m
odel)
/ σ ∆
-3
-2
-1
0
1
2
3
TBFpx
-210 -110 1
[%]
σ(m
odel)
/ σ ∆
-2
-1
0
1
2
3
[GeV]CBFT
p-110 1 10
[%]
σ(m
odel)
/ σ ∆
-3
-2
-1
0
1
2
3
[GeV]TBF T
p
-110 1 10
[%]
σ(m
odel)
/ σ ∆
-4
-3
-2
-1
0
1
2
3
Figure 5.23: The systematic uncertainties due to the variation on the model depen-dence as functions of the Breit frame variables.
5.3.6 Trigger efficiency
The uncertainty on the trigger efficiency is chosen to be ± 1 % as mentioned in
the first paragraph of the section 5.2.4, since the efficiency of the S67 trigger used in
this analysis is approximately 100 %. The same percentage is applied to all bins for
the uncertainty trigger contribution.
5.3.7 Signal extraction
The systematic effect of the signal extraction over the number of K0S candidates is
estimated using different procedures for the signal description. In the analysis, the fit
to a polynomial-exponential function for the background and a t-student distribution
for the signal were used, but the alternative way chosen to get the uncertainty here is
the side band subtraction method (SBS). The SBS gets the number of K0S candidates
by counting the number of events contained in the range [0.4 GeV, 0.6 GeV] around
the K0S mass peak from the original histogram of invariant mass distribution (without
104 CHAPTER 5. THE MEASUREMENT OF THE CROSS SECTION
any fit), then the number of background events is taken from the integral to the
background function previously used, in the same range [0.4 GeV, 0.6 GeV]. Then,
NSBSK0
S
= N signal
K0S
(counting the histogram)−N bgrd
K0S
(integral to background function) is
the number of K0S candidates from the SBS method.
The resulting uncertainty is finally gotten from the ratio:
N fit
K0S
− NSBSK0
S
N fit
K0S
,
where N fit
K0S
is the number of K0S from the signal extraction as discussed in section 4.6.
For the total HERA II systematic determination the contribution is ± 2.0 %.
]2 [GeV2Q310
[%]
σ(si
gnal)
/ σ ∆
-1
0
1
2
3
4
5
6
x-310 -210 -110
[%]
σ(si
gnal)
/ σ ∆
-3
-2
-1
0
1
2
3
η-1.5 -1 -0.5 0 0.5 1 1.5
[%]
σ(si
gnal)
/ σ ∆
-3
-2
-1
0
1
2
3
[GeV]T
p1 10
[%]
σ(si
gnal)
/ σ ∆
-3
-2
-1
0
1
2
3
Figure 5.24: The systematic uncertainties due to the variation on the signal extrac-tion as functions of the laboratory frame variables.
The plots of the uncertainty variation due to signal extraction bin by bin are in
Figures 5.24 and 5.25. The oscillation of the values shows the difficulties to obtain
a fit of better quality to the mass invariant distribution, per example the last bin in
Q2 (Figure F.1) and xTBFp (Figure F.6) and the first bin of pTBF
T (Figure F.8).
5.3. THE SYSTEMATIC UNCERTAINTIES 105
CBFpx
-110 1
[%]
σ(si
gnal)
/ σ ∆
-3
-2
-1
0
1
2
3
TBFpx
-210 -110 1
[%]
σ(si
gnal)
/ σ ∆
-18-16-14-12-10-8-6-4-202
[GeV]CBF T
p-110 1 10
[%]
σ(si
gnal)
/ σ ∆
-3
-2
-1
0
1
2
[GeV]TBFT
p-110 1 10
[%]
σ(si
gnal)
/ σ ∆
-12
-10
-8
-6
-4
-2
0
2
Figure 5.25: The systematic uncertainties due to the variation on the signal extrac-tion as functions of the Breit frame variables.
5.3.8 Branching ratio
This uncertainty is taken into account because the branching ratio of the K0S de-
caying to π+π− is not exactly known, the PDG reports a BR = (0.6920 ± 0.0005)% [11],
then ± 0.1% is considered for the contribution to the total uncertainty determina-
tion. As this contribution is very small, it could be neglected. The same uncertainty
values is applied to all bins in the laboratory and the Breit frames.
All sources contributing to the total systematic uncertainty for the measured
inclusive K0S cross section from the HERA II data are listed in Table 5.3; the variation
used for the estimation and the ∆σ obtained are also presented. It is possible to
distinguish that the dominat contributions come from the topology reconstruction,
the Θe′ variation and the track efficiency reconstruction. At the end, a systematic
uncertainty of +6.9 % and -7.4 % is estimated.
106 CHAPTER 5. THE MEASUREMENT OF THE CROSS SECTION
Table 5.3: Summary of systematic uncertainties.
Source Variation ∆σ(K0s )
E ′
e′ 1 % +1.5%/−2.9%
Θe′ ± 3 mrad +2.9%/−3.1%
signal extraction Nfit−NSBS
Nfit ± 2.0%
model dependence 0.5* εCDM−εMEPS
εCDM ± 0.05 %topology rec ± 3.0 %
luminosity ± 2.6 %
track rec 2 % per track ± 4.0 %
branching ratio ± 0.1 %
trigger efficiency ± 1.0 %
total uncertainty +6.9%/−7.4%
The statistical uncertainty is obtained by:
σstat. =
√
(σNK0
s
NK0s
)2
data
+
(σNK0
s
NK0s
)2
rec−MC
(5.6)
where NK0s
is the number of K0S extracted from the fit and σN
K0s
is the statistical
uncertainty from the fit procedure.
As NK0s
= 38154 and σNK0
s= 1194 for data, and NK0
s= 39984 and σN
K0s
= 233
for reconstructed-MC, a total statistical uncertainty of ∼ 3 % is calculated.
Chapter 6
Results and conclusions
The measurements of the inclusive K0S meson cross section as total, differential
and double–differential are presented in this chapter. The cross section ratio of the
K0S over the charged particles, and the density measurements are also calculated and
explained here.
The comparison to Django (CDM) and Rapgap (MEPS) model predictions are
shown in all plots in order to establish if the data favour any model or strangeness
suppresion factor λs value. The Django model is used for the QCD studies varying
the PDF and λs parameters, while Rapgap is chosen for the study of the quark
flavour contribution to the K0S cross section.
6.1 Total K0s cross section
The inclusive K0S production cross section σvis measured in the visible range
defined by the phase space in equation 5.1 is found to be:
σvis = 531 ± 17 (stat)+37−39 (sys) pb, (6.1)
where the efficiency ε ∼ 30.55% with the included QED correction δQED ∼ 5.5% as
determined in the subsection 5.2.4, the BR = 0.692 from the Table 2.2 for the K0S
→ π+π− decay channel, the luminosity value of 339.6 pb−1 as listed in the Table 4.1
107
108 CHAPTER 6. RESULTS AND CONCLUSIONS
and the NK0S
= 38154 as extracted from the fit in Figure 4.4 are used for the cross
section determination with the equation 5.2. The statistical (3 %) and systematic
uncertainties (+6.9 % and -7.4 %) obtained in the subsection 5.3, are calculated from
the application of the corresponding percentage to the cross section.
The predictions of Django and Rapgap Monte Carlo programs with different
strangeness values λs but same CTEQ6L PDF were estimated giving the cross sec-
tions values presented in the Table 6.1. The statistical errors are very small since
the luminosity of the non-radiative MCs used for the predictions (sections 1.4.1 and
1.4.2) is around 74 times larger than the luminosity of data (339.6 pb−1).
Table 6.1: The Monte Carlo cross section predictions for different strangeness sup-presion factors (λs).
λs = 0.22 λs = 0.286 λs = 0.3
Django (CDM) σ = 443 pb σ = 516 pb σ = 518 pb
Rapgap (MEPS) σ = 444 pb σ = 536 pb σ = 519 pb
The Monte Carlo predictions are in good agreement with the measurement within
the uncertainties, specially with λs = 0.286 and λs = 0.3, while the predictions with
λs = 0.22 for both models underestimate the measurement.
The inclusive cross section was calculated year by year to look for stability of the
measurement. In Figure 6.1, the visible cross section σvis measured for all HERA II
data (equation 6.1) is represented with a black dashed line, the statistical uncertainty
forms the shadow rectangle around the σvis value. The measured cross section per
period are depicted as blue points with their respective statistical uncertainty, while
the cross sections obtained with the Django Monte Carlo are plotted with red points.
It is found that the measurements per period are consistent with the cross section
estimated with the full data sample.
The measured ratio of the inclusive cross section of the K0S meson over the charged
6.2. DIFFERENTIAL K0S CROSS SECTION 109
Year2004 2005 2006 2007
Cro
ss S
ectio
n [p
b]
400
450
500
550
600
650 Data HERA IIDataModel CDM
Figure 6.1: Inclusive cross section for the four year periods of HERA II data. Themeasurement (in blue) presented with statistical uncertainty is compared to the pre-diction of the Django model (in red). The measured cross section for the full HERA IIdata is shown in the black line with the shadow being its statistical uncertainty.
particle production:
σvis(ep → eK0SX)
σvis(ep → eh±X)= 0.05867 ± 0.0019 (stat) ± 0.0024 (sys), (6.2)
is in agreement (within the uncertainties) with the prediction of the CDM model:
0.05922. It is also consistent with the results obtained from the analysis at low Q2,
presented in subsection 2.5.
The density ratio gives a measurement of:
σvis(ep → eK0SX)
σvis(ep → eX)= 0.3842 ± 0.0115 (stat) ± 0.0159 (sys), (6.3)
and the prediction of Django gives 0.3988, showing good consistency.
6.2 Differential K0s cross section
The differential cross section in the laboratory frame as functions of the four-
momentum of the virtual photon Q2, the Bjorken scaling variable x, the pseudo-
rapidity η of the K0S, and the transverse momentum pT of the K0
S are shown in
110 CHAPTER 6. RESULTS AND CONCLUSIONS
Figure 6.2, where the cross section graphs are placed in the upper part of each plot,
while the ratio between the models and data for the two strangeness factor (λs = 0.22
and λs = 0.286) for Django and Rapgap are presented in the bottom of each plot in
order to have a better visualization of the comparisons.
The measurement decreases quickly when Q2 and pT take higher values. While
the behaviour as functions of x and η is a small increasing that then falls down.
The data are better described by the models with λs = 0.286 in normalization and
shape, independenly of the MC model, since both Django and Rapgap give similar
descriptions. The models with λs = 0.22 subestimate the measurements in most of
the bins. The results are bin-averaged and no bin-center corrections are applied.
The corresponding differential K0S cross section in the Breit frame as function of
the scaled momentum fraction xBFp and the K0
S transverse momentum pBFT in the
current (CBF) and the target (TBF) hemispheres are shown in Figure 6.3. The
production decreases at high values of the variables. The comparison to Django and
Rapgap Monte Carlo programs shows good description of data by the models with
λs = 0.286 in the current region were the preferred production mechanism is the
hard interaction process, while in the target region the models allow to observe some
sensitivity to the λs factor, as expected due to the domination of the hadronization
process in this hemisphere of the BF. The differential cross sections together with
statistical, systematic uncertainties and the CDM model prediction values can be
found in the Tables 6.2 and 6.3.
6.3 Ratios of the differential cross sections
Due to the cancellation of some uncertainty sources the total uncertainty is re-
duced for the cross section ratios, for instance the K0S cross section over the charged
particle production and the K0S over the DIS cross section ratios. Therefore the ra-
tios are used for looking at global description of all observed cross sections or test
different aspects of the meson production within the fragmentation models. They
6.3. RATIOS OF THE DIFFERENTIAL CROSS SECTIONS 111
]2 [GeV2Q
310
MC
/Da
ta
0.70.80.9
11.11.2
3
]2
[p
b/G
eV
2/d
Qσ
d
-210
-110
1
H1 Data=0.22)sλCDM (
=0.22)sλMEPS (=0.286)sλCDM (
=0.286)sλMEPS (
H1 preliminary
Xs0 e K→ep
x-310 -210 -110
MC
/Da
ta
0.70.80.9
11.11.2
-3
/dx [
pb
]σ
d
210
310
410
510
H1 Data=0.22)sλCDM (
=0.22)sλMEPS (=0.286)sλCDM (
=0.286)sλMEPS (
H1 preliminary
Xs0 e K→ep
η-1.5 -1 -0.5 0 0.5 1 1.5
MC
/Da
ta
0.70.80.9
11.11.2 -1.5 -1 -0.5 0 0.5 1 1.5
[p
b]
η/d
σd
50100150200250300350400450
H1 Data=0.22)sλCDM (
=0.22)sλMEPS (=0.286)sλCDM (
=0.286)sλMEPS (
H1 preliminary
Xs0 e K→ep
[GeV]T
p1 10
MC
/Da
ta
0.70.80.9
11.11.2
[p
b/G
eV
]T
/dp
σd
1
10
210
H1 Data=0.22)sλCDM (
=0.22)sλMEPS (=0.286)sλCDM (
=0.286)sλMEPS (
H1 preliminary Xs
0 e K→ep
Figure 6.2: Cross sections of the K0S meson in the laboratory frame as functions
of the four-momentum of the virtual photon Q2, the Bjorken scaling variable x,the pseudorapidity η of the K0
S, and the transverse momentum pT of the K0S. The
comparisons are clearer in the MC model over data ratio plotted in the bottom ofeach plot. The outer (inner) error bar indicates the total (statistical) uncertainty.
112 CHAPTER 6. RESULTS AND CONCLUSIONS
ep → eK0
sX
Q2 dσ/dQ2 stat. syst. (+) syst. (−) MC Pred
[GeV2] [pb/GeV2]
145 – 167 4.12 0.30 0.45 0.54 3.88
167 – 200 2.67 0.16 0.17 0.18 2.73
200 – 280 1.59 0.10 0.11 0.12 1.54
280 – 500 0.58 0.04 0.04 0.04 0.55
500 – 1000 0.14 0.02 0.008 0.008 0.12
1000 – 5000 0.010 0.002 0.0007 0.0007 0.008
x dσ/dx stat. syst. (+) syst. (−) MC Pred
[pb]
0.0 – 0.004 18595 1180 1860 1674 18087.4
0.004 – 0.008 56023 2631 3361 3361 55195.1
0.008 – 0.017 17479 1205 1398 1923 16217.8
0.017 – 0.20 405 39 28 41 414.853
η dσ/dη stat. syst. (+) syst. (−) MC Pred
[pb]
-1.5 – -0.5 96.6 6.41 6.18 6.7 91.5
-0.5 – 0.0 244.6 21.8 15.7 16.4 215.3
0.0 – 0.45 263.2 23.7 17.9 18.9 245.3
0.45 – 0.95 216.3 14.3 16.4 17.3 215.9
0.95 – 1.5 165.3 11.5 12.9 13.9 178.8
pT dσ/dpT stat. syst. (+) syst. (−) MC Pred
[GeV] [pb/GeV]
0.3 – 0.8 285.0 17.8 19.7 21.1 297.3
0.8 – 1.1 228.8 14.2 15.6 16.7 244.7
1.1 – 1.55 172.9 9.6 11.8 12.6 173.8
1.55 – 2.23 115.6 7.8 7.9 8.4 108.7
2.23 – 3.5 63.0 5.5 4.5 4.8 55.3
3.5 – 14.0 7.18 0.8 0.5 0.55 6.6
Table 6.2: The differential K0s cross section values as functions of Q2, x, η and pT
in the visible kinematic region defined by 145 < Q2 < 20000 GeV2, 0.2 < y < 0.6,-1.5 η(K0
S) 1.5 and pT > 0.3 GeV. The bin ranges, the bin averaged cross sectionvalues, the statistical and the positive and negative systematic uncertainties, as wellas the predictions from Django are listed.
6.3. RATIOS OF THE DIFFERENTIAL CROSS SECTIONS 113
CBFpx
-110 1
MC
/Da
ta
0.60.8
11.21.4
[p
b]
CB
Fp
/dx
σd
10
210
310
410
H1 Data=0.22)sλCDM (
=0.22)sλMEPS (=0.286)sλCDM (
=0.286)sλMEPS (
H1 preliminary
X (Breit Frame)s0 e K→ep
TBFpx
-110 1
MC
/Da
ta
0.60.8
11.21.4
[p
b]
TB
Fp
/dx
σd
10
210
310
410
H1 Data=0.22)sλCDM (
=0.22)sλMEPS (=0.286)sλCDM (
=0.286)sλMEPS (
H1 preliminary
X (Breit Frame)s0 e K→ep
[GeV]CBFT
p
-110 1 10
MC
/Da
ta
0.60.8
11.21.4 -1
[p
b/G
eV
]C
BF
T/d
pσ
d
1
10
210
310
H1 Data=0.22)sλCDM (
=0.22)sλMEPS (=0.286)sλCDM (
=0.286)sλMEPS (
H1 preliminary
X (Breit Frame)s0 e K→ep
[GeV]TBFT
p
-110 1 10
MC
/Da
ta
0.60.8
11.21.4 -1
[p
b/G
eV
]T
BF
T/d
pσ
d
1
10
210
310
H1 Data=0.22)sλCDM (
=0.22)sλMEPS (=0.286)sλCDM (
=0.286)sλMEPS (
H1 preliminary
X (Breit Frame)s0 e K→ep
Figure 6.3: Cross section of the K0S meson in the Breit frame as function of the scaled
momentum fraction and the transverse momentum in the current region (xCBFp and
pCBFT in the left hand side of the figure) and the target region (xTBF
p and pTBFT in
the right hand side). The outer (inner) error bar indicates the total (statistical)uncertainty. More details in caption of Figure 6.2
114 CHAPTER 6. RESULTS AND CONCLUSIONS
ep → eK0
sX
xBreitp current dσ/dxBreit
p stat. syst. (+) syst. (−) MC Pred
[pb]
0.0 – 0.07 859.1 78.8 56.6 64.3 848.4
0.07 – 0.13 1339.5 102.6 90.9 107.0 1202.1
0.13 – 0.2 879.2 84.5 61.5 71.9 805.4
0.2 – 0.33 458.1 38.3 32.0 42.2 385.1
0.33 – 1.0 56.7 5.9 4.5 5.7 45.7
xBreitp target dσ/dxBreit
p stat. syst. (+) syst. (−) MC Pred
[pb]
0.0 – 0.07 557.7 88.4 50.1 46.8 522.5
0.07 – 0.13 859.1 59.0 67.8 63.5 929.7
0.13 – 0.2 625.7 52.6 46.2 44.9 721.6
0.2 – 0.33 356.3 29.7 25.6 23.5 388.2
0.33 – 1.0 72.9 6.7 5.6 5.3 71.3
1.0 – 2.0 3.4 0 0.6 0.6 4.9
pBreitT current dσ/dpBreit
T stat. syst. (+) syst. (−) MC Pred
[GeV] [pb/GeV]
0.0 – 0.35 200.2 19.2 13.6 17.4 190.9
0.35 – 0.6 288.7 26.4 21.0 24.8 258.2
0.6 – 1.0 180.8 11.3 12.3 14.9 159.0
1.0 – 1.8 65.2 6.5 4.6 5.2 58.9
1.8 – 14.0 2.3 0.3 0.15 0.2 2.18
pBreitT target dσ/dpBreit
T stat. syst. (+) syst. (−) MC Pred
[GeV] [pb/GeV]
0.0 – 0.35 86.45 23.9 11.2 12.1 74.1
0.35 – 0.6 191.4 18.9 15.3 14.3 204.5
0.6 – 1.0 150.7 9.6 11.3 10.5 167.4
1.0 – 1.8 67.6 4.7 4.9 4.7 71.5
1.8 – 14.0 3.8 0.5 0.3 0.3 3.7
Table 6.3: The differential K0S cross-section values as functions of pBreit
T and xBreitp
in the current and target hemispheres of the Breit frame. More details in caption ofTable 6.2.
6.3. RATIOS OF THE DIFFERENTIAL CROSS SECTIONS 115
also provide a rather direct constrain of λs, or/and λqq and λsq.
6.3.1 Differential K0S/h± cross section
The K0S/h± cross section, defined as the ratio of the K0
S production over the
charged particle cross section measured in the same phase space as the K0S, were
determined in the laboratory frame as shown in Figure 6.4. The measured production
shows an almost flat ratio as function of Q2; as function of η there is a small falling,
and as function of pT rises at higher values due to the K0S, which takes most of the
momentum than the usually lower massive charged particles.
The shape and normalization of the ratios are reasonably well described by the
CDM and MEPS models with λs = 0.286 for the four plots. The values of the
ratio cross sections, the statistical and systematic uncertainties and the CDM model
predictions for each bin can be found in Table 6.4.
6.3.2 Differential K0s/DIS cross section
The density plots, defined as the ratio between the cross section of the K0S and
the DIS event production in the same kinematic region as the K0S, are measured
differentially as functions of Q2 and x as shown in Figure 6.5. The K0S multiplicity
average lies at ∼ 0.4 independenly of the variables, indicating that the K0S production
fraction with respect to the DIS events is almost equal at any region. The Django
and Rapgap models with λs = 0.286 describe quite well the measurements in Q2 but
they predict a small falling as function of x which is not observed from data. The
cross section values of the ratio with their corresponding statistical and systematic
uncertainties as well as the CDM model predictions bin by bin can be found in
Table 6.5.
116 CHAPTER 6. RESULTS AND CONCLUSIONS
]2 [GeV2Q310
X)
± e
h→
(ep
σ
X)/
ds0
eK
→(e
p
σd
0
0.02
0.04
0.06
0.08
0.1
0.12H1 Data
=0.22)sλCDM (
=0.22)sλMEPS (=0.286)sλCDM (
=0.286)sλMEPS (
H1 preliminary
X ± e h→ X / ep s0 e K→ep
x-310 -210 -110
X)
± e
h→
(ep
σ
X)/
ds0
eK
→(e
p
σd
0
0.02
0.04
0.06
0.08
0.1
0.12H1 Data
=0.22)sλCDM (
=0.22)sλMEPS (=0.286)sλCDM (=0.286)sλMEPS (
H1 preliminary
X ± e h→ X / ep s0 e K→ep
η-1.5 -1 -0.5 0 0.5 1 1.5
X)
± e
h→
(ep
σ
X)/
ds0
eK
→(e
p
σd
0
0.02
0.04
0.06
0.08
0.1
0.12H1 Data
=0.22)sλCDM (=0.22)sλMEPS (
=0.286)sλCDM (=0.286)sλMEPS (
H1 preliminary
X ± e h→ X / ep s0 e K→ep
[GeV]T
p1 10
X)
± e
h→
(ep
σ
X)/
ds0
eK
→(e
p
σd
0
0.02
0.04
0.06
0.08
0.1
0.12H1 Data
=0.22)sλCDM (
=0.22)sλMEPS (
=0.286)sλCDM (
=0.286)sλMEPS (
H1 preliminary
X ± e h→ X / ep s0 e K→ep
Figure 6.4: Ratio between the cross sections of the K0S and the charge particles
in the laboratory frame as functions of Q2, x, η and pT . The outer (inner) errorbar indicates the total (statistical) uncertainty. The CDM and MEPS models withλs = 0.22 and λs = 0.286 are presented for comparison.
6.3. RATIOS OF THE DIFFERENTIAL CROSS SECTIONS 117
R(K0
s/h±)
Q2 R(K0
s /h±) stat. syst. MC Pred
[GeV2]
145 – 167 0.0620 0.00464 0.00240 0.0614
167 – 200 0.0574 0.00353 0.00214 0.0610
200 – 280 0.0601 0.00382 0.00221 0.0604
280 – 500 0.0588 0.00382 0.00214 0.0590
500 – 1000 0.0588 0.00657 0.00219 0.0566
1000 – 5000 0.0585 0.01273 0.00345 0.0522
x R(K0
s /h±) stat. syst. MC Pred
0.0 – 0.004 0.0596 0.00378 0.00229 0.0615
0.004 – 0.008 0.0592 0.00278 0.00216 0.0608
0.008 – 0.017 0.0609 0.00420 0.00236 0.0588
0.017 – 0.20 0.0492 0.00477 0.00185 0.0540
η R(K0
s /h±) stat. syst. MC Pred
-1.5 – -0.5 0.0628 0.00417 0.00237 0.0642
-0.5 – 0.0 0.0619 0.00552 0.00254 0.0590
0.0 – 0.45 0.0585 0.00527 0.00228 0.0574
0.45 – 0.95 0.0560 0.00371 0.00210 0.0574
0.95 – 1.5 0.0537 0.00375 0.00232 0.0593
pT R(K0
s /h±) stat. syst. MC Pred
[GeV]
0.3 – 0.8 0.0357 0.00223 0.00154 0.0392
0.8 – 1.1 0.0553 0.00343 0.00227 0.0607
1.1 – 1.55 0.0673 0.00375 0.00249 0.0696
1.55 – 2.23 0.0794 0.00536 0.00294 0.0777
2.23 – 3.5 0.0906 0.00796 0.00372 0.0849
3.5 – 14.0 0.0880 0.00922 0.00352 0.0884
Table 6.4: The values of the ratio of the differential production cross sections formesons and charged hadrons as functions of Q2, x, pT and η. More details in captionof Table 6.2.
118 CHAPTER 6. RESULTS AND CONCLUSIONS
]2 [GeV2Q310
e X
)→
(ep
σ X
)/s0
e K
→(e
p σ
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
H1 Data=0.22)sλCDM (
=0.22)sλMEPS (
=0.286)sλCDM (
=0.286)sλMEPS (
H1 preliminary
e X → X / ep s0 e K→ep
x-310 -210 -110
e X
)→
(ep
σ X
)/s0
e K
→(e
p σ
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
H1 Data=0.22)sλCDM (
=0.22)sλMEPS (
=0.286)sλCDM (
=0.286)sλMEPS (
H1 preliminary
e X → X / ep s0 e K→ep
Figure 6.5: Density plots in the laboratory frame as functions of Q2 and x. Theouter (inner) error bar indicates the total (statistical) uncertainty. The CDM andMEPS models with λs = 0.22 and λs = 0.286 are presented for comparison.
6.4. DOUBLE DIFFERENTIAL CROSS SECTION 119
R(K0
s/X)
Q2 R(K0
s /X) stat. syst. MC Pred
[GeV2]
145 – 167 0.3801 0.02852 0.01459 0.4001
167 – 200 0.3581 0.02210 0.01332 0.4022
200 – 280 0.3862 0.02460 0.01421 0.4048
280 – 500 0.3943 0.02568 0.01435 0.4045
500 – 1000 0.4102 0.04588 0.01530 0.3947
1000 – 5000 0.4161 0.09060 0.02455 0.3573
x R(K0
s /X) stat. syst. MC Pred
0.0 – 0.004 0.3943 0.02513 0.01510 0.4340
0.004 – 0.008 0.3816 0.01797 0.01393 0.4108
0.008 – 0.017 0.3936 0.02718 0.01527 0.3894
0.017 – 0.20 0.3352 0.03250 0.01257 0.3577
Table 6.5: Values of the differential production cross section ratio of the K0S mesons
and the deep inelastic scattering events as function of Q2 and x in the laboratoryframe. More details in caption of Table 6.2.
6.4 Double differential cross section
The double differential cross section of K0S as functions of Q2 and xCBF
p normalized
to the σvis of the corresponding Q2 range is presented in Figure 6.6 for three different
ranges of Q2 and five bins of xCBFp .
In the Figure is possible to see that the K0S production grows up as the Q2 range
is larger and the increase is more significant at low xCBFp values, which is the same
behavior observed for the fragmentation functions in e+e− annihilation and DIS as
shown in reference [11].
The Django (CDM) model with λs = 0.286 chosen for the comparison describes
quite well the measurements.
6.5 Comparison to QCD models
Thanks to the many parameters found in the models, it is possible to do some
additional studies, mainly changing the most relevant parameter values for the K0S
120 CHAPTER 6. RESULTS AND CONCLUSIONS
CBFpX
-210 -110 1
X)
s0 e
K→
(ep
σ d
DIS
σ1/
-210
-110
1
2H1 Data 145 < Q2 < 200 GeV2H1 Data 200 < Q2 < 500 GeV
2H1 Data 500 < Q2 < 5000 GeV2CDM 145 < Q2 < 200 GeV2CDM 200 < Q2 < 500 GeV
2CDM 500 < Q2 < 5000 GeV
e X→ X / ep s0 e K→ep
Figure 6.6: Double differential cross section in bins of xCBFp in three different ranges
of Q2. The comparison to Django model shows good agreement.
production and comparing the results of the predictions to data. Previously, two
different values of strangeness suppresion factor for Django and Rapgap were pre-
sented, now the parton density function PDF is changed in the Django model with
λs = 0.286.
The study of disentangling the flavour contribution of the K0S production is carried
out using the Rapgap model with λs = 0.286.
6.5.1 Parton distribution functions
In order to test for possible dependencies of the K0S strange meson production on
the proton parton density functions (PDFs), the measured K0S cross sections are com-
pared to the CDM model with λs = 0.286 using three different PDF parametrizations,
CTEQ6L, H12000L0 and GRVL0, as shown in Figure 6.7. The model descriptions
are similar in shape for the three PDFs but in normalization only the CTEQ6L and
H12000LO PDFs agree with data, while GRVLO98 underestimates considerably the
measurements due to the absence of c and b flavour. Then, one could uses GRVLO98
6.6. CONCLUSIONS 121
PDF as an estimation of the contribution of c and b quarks to the total K0S produc-
tion to understand or quantify the mechanisms of production from these quarks.
Similar results are obtained in the Breit frame.
6.5.2 Flavour contribution
The flavour contributions to the K0S cross section are investigated using the Rap-
gap (MEPS) prediction with λs = 0.286. The choice was made because a separation
between the QPM, QCDc and BGF production mechanism are possible with this
model but not with Django (CDM).
Figures 6.8 and 6.9 show the contribution of the different flavours in the labo-
ratory and the Breit frames, respectively. The light ud quarks contribution from
fragmentation mechanism dominates for all variables, then the main contribution
process is due to hadronization. The heavy quark contribution of charm c is highest
that the one of bottom flavour b which goes to zero or close to zero in some bins;
both (c and b) make the second dominat contribution coming mainly from the heavy
decay process. The s contribution remains to be the lowest in all variables but it
becomes more relevant at high values of Q2, x and pT (see the logarithm scale) while
in η is almost constant, here the production processes are the boson gluon fusion and
the QPM hard interaction.
As functions of the Breit frame variables, the s contribution becomes more impor-
tant at high xp and pT values, specially in the current region where the contribution
as function of xCBFp even equals the heavy quark contribution.
The contributions can be approximately quantified as 52% of the K0S coming from
ud, 36% from cb quarks and only a 12% from s quarks.
6.6 Conclusions
The K0S meson production in the phase space defined by 145 < Q2 < 20000 GeV,
0.2 < y < 0.6, -1.5 < η(K0S) < 1.5 and 0.3 GeV < pT (K0
S) presented in this thesis cor-
122 CHAPTER 6. RESULTS AND CONCLUSIONS
]2 [GeV2Q
310
MC
/Da
ta
0.6
0.8
13
]2
[p
b/G
eV
2/d
Qσ
d
-210
-110
1
H1 Data=0.286)λCTEQ6L (=0.286)λGRVL098 (=0.286)λH12000L0 (
Xs0 e K→ep
x-310 -210 -110
MC
/Da
ta
0.6
0.8
1-3
/dx [
pb
]σ
d
210
310
410
510
H1 Data=0.286)λCTEQ6L (=0.286)λGRVL098 (=0.286)λH12000L0 (
Xs0 e K→ep
η-1.5 -1 -0.5 0 0.5 1 1.5
MC
/Da
ta
0.6
0.8
1-1.5 -1 -0.5 0 0.5 1 1.5
[p
b]
η/d
σd
50
100
150
200
250
300
350
400
450H1 Data
=0.286)λCTEQ6L (=0.286)λGRVL098 (=0.286)λH12000L0 (
Xs0 e K→ep
[GeV]T
p1 10
MC
/Da
ta
0.6
0.8
1
[p
b/G
eV
]T
/dp
σd
1
10
210
310
H1 Data=0.286)λCTEQ6L (=0.286)λGRVL098 (=0.286)λH12000L0 (
Xs0 e K→ep
Figure 6.7: Comparison of cross section to three different PDFs: CTEQ6L,GRVLO98 and H12000LO in the laboratory frame as functions of Q2, x, η andpT . No dependence is found between CTEQ6L and H12000LO, the underestimationof GRVLO98 is due to the absence of the charm and beauty quark contribution.
6.6. CONCLUSIONS 123
]2 [GeV2Q310
]2
[p
b/G
eV
2/d
Qσ
d
-310
-210
-110
1
10
H1 Dataudscbudscb
H1 preliminary
Xs0 e K→ep
x-310 -210 -110
/dx [p
b]
σd
210
310
410
510
H1 Dataudscbudscb
H1 preliminary
Xs0 e K→ep
η-1.5 -1 -0.5 0 0.5 1 1.5
[p
b]
η/d
σd
50
100
150
200
250
300
350
400
450H1 Dataudscbudscb
H1 preliminary
Xs0 e K→ep
[GeV]T
p1 10
[p
b/G
eV
]T
/dp
σd
1
10
210
310
H1 Dataudscbudscb
H1 preliminary
Xs0 e K→ep
Figure 6.8: Flavour contribution of the light ud quarks, the strange s quark andthe heavy cb quarks to the K0
S cross section studied with the Rapgap model in thelaboratory frame as functions of Q2, x, η and pT . The outer (inner) error bar indicatesthe total (statistical) uncertainty.
124 CHAPTER 6. RESULTS AND CONCLUSIONS
CBFpx
-310 -210 -110
[p
b]
CB
Fp
/dx
σd
1
10
210
310
H1 Dataudscbudscb
H1 preliminary
X (Breit Frame)s0 e K→ep
TBFpx
-210 -110 1
[p
b]
TB
Fp
/dx
σd
1
10
210
310
H1 Dataudscbudscb
H1 preliminary
X (Breit Frame)s0 e K→ep
[GeV]CBFT
p-110 1 10
[p
b/G
eV
]C
BF
T/d
pσ
d
1
10
210
310
H1 Dataudscbudscb
H1 preliminary
X (Breit Frame)s0 e K→ep
[GeV]TBFT
p-110 1 10
[p
b/G
eV
]T
BF
T/d
pσ
d
1
10
210
310
H1 Dataudscbudscb
H1 preliminary
X (Breit Frame)s0 e K→ep
Figure 6.9: Flavour contribution of the light ud quarks, the strange s quark and theheavy cb quarks to the K0
S cross section studied with Rapgap model in the Breitframe as functions of xCBF
p , xTBFp , pCBF
T and pTBFT . The outer (inner) error bar
indicates the total (statistical) uncertainty.
6.6. CONCLUSIONS 125
responds to the first measurement of the H1 collaboration in the high Q2 range [79].
The production is studied total and differentially in the laboratory and the Breit
frames.
The Django and Rapgap DIS events simulation programs are used with matrix
elements plus colour dipole model and parton showers, respectively. The CTEQ6L
parton distribution function and strangeness suppresion factor λs with ALEPH tun-
ning are taken for corrections. The comparison of Monte Carlo to data shows good
agreement in general features for all variables.
]2 [GeV2Q1 10 210 310 410
]2 [
nb
/Ge
V2
/dQ
σd
-610
-510
-410
-310
-210
-110
1
10 H1 DataDjango CDMRapgap MEPS
Figure 6.10: Cross section production of K0S at low Q2 [66] and high Q2 ranges
compared to the Django and Rapgap simulation programs with λs = 0.3 for low Q2
results and λs = 0.286 for high Q2.
The shape of the differential K0S production in the laboratory and the Breit frames
are similar to those obtained at low Q2 analysis, as discussed in the subsection 2.5.3,
although the data in that case were better described with λs = 0.3.
Figure 6.10 presents the results obtained at low Q2 analysis [66] and the ones
126 CHAPTER 6. RESULTS AND CONCLUSIONS
measured at high Q2 range as done in this thesis (in the same phase space defined
at the low Q2 analysis) and the two Monte Carlo predictions taken into account. It
is possible to see agreement between the measurements and theory. The decreasing
behavior of the K0S production continues from low to high Q2 values due to the 1/Q4
factor in the cross section formula.
The ratio of the K0S over the charged particle productions and the so called den-
sity, the ratio of the K0S over the DIS event cross sections, are measured differentially
in the laboratory frame. They show almost flat behavior indicating the same rate of
production in all regions of the H1 phase space considered here. As function of pt,
there is an increase, which is expected due to the higher mass of the K0S compared
to the charged particles which are mainly pions.
The Django model with λs = 0.286 and CTEQ6L, H12000LO and GRVLO98
parton density functions are used for the study of the PDF dependence, but no
evidence of dependence is found between CTEQ6L and H12000LO PDFs. In other
hand, the GRVLO98 PDF underestimates the results due to the absence of the charm
and beauty quark contributions.
The cross section separated by flavour contributions is studied with the Rapgap
model with λs = 0.286 and CTEQ6L PDF. It is found that the K0S production is
dominated by the hadronization process (ud quarks contribution) but the s quark
contribution becomes more important at high momentum values, which is consistent
with the conclusion of the K∗ analysis, as mentioned in the section 2.5.2.
Further studies will be focus in the production ratio of strange baryons to strange
mesons (Λ/K0S) for a better understanding of the di-quarks pair production in the
Lund string model. The ratio of the production of vector to pseudoscalar mesons
(K∗/K0s ) could provides some information about the relative probabilities for the
corresponding spin states which to be produced on the hadronization process. Studies
of asymmetric quark sea in the proton can be carried out analysing the difference in
the production of charged kaons (as K∗+ and K∗−). As well, as the studies of K0SK0
S
states and resonances which have K0S particles in their decays channels can be done
6.6. CONCLUSIONS 127
to improve the current knowledge of strangeness physics.
128 CHAPTER 6. RESULTS AND CONCLUSIONS
Appendix A
Reconstruction methods
The methods of reconstruction at HERA physics are governed by the two body
elastic collision. The final states can be completely reconstructed using two variables
when the energies of the initial particles are known, the energy of the incident electron
(Ee) and proton (Ep) in the case of H1.
The variables of a DIS event can be determined by two of the following inde-
pendent variables: the energy of the scattered electron (E ′), its polar angle (θe′) or
some quantities reconstructed out of the hadronic final state particles, as the four-
momentum conservation Σh =∑
h(Eh−pz,h) of each particle (h, the total transverse
momentum (pT,h) or the angle of the scattered quark (γ) within QPM:
Σh =∑
h
(Eh − pz,h) , pT,h =
√
(∑
h
px,h)2 + (∑
h
py,h)2, tanγ
2=
Σh
pT,h
.
There are three basic methods of reconstruction, the electron e, the hadron h and
the double angle (DA) methods. However mixtures of them have been created in
order to optimize the calculation of the kinematic variables [80]. A brief description
of the most known methods can be found in the next sections.
A.1 The electron method
As its name indicates, this method uses only the information of the electron, Ee,
E ′
e and θe measured by the electromagnetic section of the calorimeters, to calculate
129
130 APPENDIX A. RECONSTRUCTION METHODS
the kinematic variables, the four-momentum transfer Q2, the inelasticity y and the
Bjorken-x:
Q2 = 4EeE′ecos2 θe
2, ye = 1 − Ee
2E ′e
(1 − cos2 θe
2), xe =
Q2e
sye
.
At high y, where the electron is very well detected by the CTD and the SpaCal,
this method provides a high precision, but at low y it is not due to the 1/y dependence
of the resolution (δy/y). In the case of initial state radiation (ISR) the energy of
the electron is reduced from Ee, thus Q2 and y are overestimated, while x suffers a
degradation.
A.2 The hadron method
This method, also called Jacquet-Blondel method, makes use of Σh and pT,h
for the reconstruction. For this reason, it is mainly used for charged current DIS
events, because the scattered neutrino is undetected and the kinematic variables
determination lies on the hadronic final states measured by the calorimeters:
Q2h =
p2T,h
1 − yh
, yh =Σh
2Ee
, xh =Q2
h
syh
.
The angle γ of the hadronic final states is determined as:
cosγ =Q2
h(1 − yh) − 4E2ey
2h
Q2h(1 − yh) + 4E2
ey2h
.
A.3 The double angle method
The DA method reconstruct the kinematic variables using only the θe and γ
angles. If the energy measured is considered as continuous over the full solid angle,
the event kinematics are independent of any calorimetric energy scale uncertainties:
Q2DA =
4E2esenγ(1 + cosθe)
senγ + senθe − sen(θe + γ), (A.1)
yDA =senθe(1 − cosγ)
senγ + senθe − sen(θe + γ),
A.4. THE SIGMA METHOD 131
xDA =Q2
DA
syDA
.
A.4 The sigma method
The sigma method, Σ, compensates for the cases where missing energy exits
due to ISR. The photon is usually undetected because travels in the same electron
beam direction and escapes out of the beam pipe. What it does is to balance the
missed energy by a factor calculated by conservation of longitudinal momentum of
the hadronic and the detected electron energies. Then, y and Q2Σ are independent of
ISR-QED and the resolution is optimal. The kinematics is formulated like:
Q2Σ =
P 2T,e
1 − yΣ
, yΣ =Σh
Σ, xΣ =
Q2Σ
syΣ
Another good point is that the experimental errors on Σh measurements cancel
between numerator and denominator at high y, where Σh becomes dominant.
A.5 The electron-sigma method
The eΣ method [81] improves the imprecise reconstruction of Q2Σ and xe using
Q2e and xΣ, respectively. In that way, the precision at high y is also improved. Then:
Q2eΣ = Q2
e, yeΣ =Q2
Σ
sxΣ
, xeΣ = xΣ.
For high Q2 the better methods to chose are the e, the DA, and the eΣ. The DA
method has good purity in the full range of x and Q2 but is in general less precise that
the other two, which behave similar at high Q2 and at high and low x. Reference [81]
remarks the weakness of the e method at low y; however the lower limit of y in this
analysis is not so low and the inclusive cross section calculated with e and eΣ gives
the same value, within the systematic errors. The total systematic error for the eΣ
method has a contribution from the determination of the hadronic energy and is of
the same size as the systematic error from the e method. This method has been
chosen for the reconstruction of event kinematics in this work.
132 APPENDIX A. RECONSTRUCTION METHODS
Appendix B
Multiwire proportional and driftchambers
The multiwire proportional chambers (MWPC) were developed by Charpak
and his collaborators at CERN in 1968. It is a particle detector consisting essentially
of a container of gas subjected to an electric field whose operating principle is based in
the collection of electrons and ions left by an incident particle when passing through
the chamber.
A particle passing by a gaseous medium losses energy by elastic scattering, by
excitation and by ionization of the gas atoms. The energy loss of the incident particle
in elastic scattering is generally so small that it does not play a significant role in the
operation of the detector. The excitation process raises the gas atoms or molecules to
an excited energy level which deexcite by photon emission, but the most important
process for the operation is the ionization. This occurs when the energy imparted
to the atoms in the medium exceeds its ionization potential and they liberate one or
more electrons leaving positive ions.
The primary ionization is defined to be the number of ionizing collisions per unit
length suffered by the incident particle. Some of the liberated electrons may still have
sufficient energy to cause more ionization what is called secondary ionization. The
MWPC’s use an electric field in the active region so the charged ionization products
have a net motion in the direction of the field.
133
134 APPENDIX B. MULTIWIRE PROPORTIONAL AND DRIFT CHAMBERS
Figure B.1: a) Typical desing construction and b) electric field configuration of amultiwire proportional chamber.
a) b)
A typical geometry of a MWPC can be seen in Figure B.1a), where a plane of
anodes wires is lying between two cathodes planes. A positive voltage is connected
to the sensing wires while the cathode wires are set to a negative voltage in order
to create an electric field configuration as shown in Figure B.1b). An important
point to take care during the construction is that the wire spacing be very uniform
throughout all the detector because a small displacement of a wire or any irregularity
in their diameters can lead to a large change in the charge provided by the displaced
wire and on adjacent wires.
Due to the voltage applied to the wires, electrostatic forces are present. These
forces can cause a net attraction of the cathode toward the anode plane producing a
curvature in the center varying the gap separation and therefore the gain. Another
effect is the displacement of the wires from the nominal positions if the electrostatic
force on the wires is greater than the tension of the wire.
The filling gas should satisfy the desirable properties, mainly low working voltage,
high gain, good proportionality, high rate capability, long lifetime, high specific ion-
ization, fast recovery and avoid recombination that can damage or contaminate the
chamber electrodes. Usually mixtures of gases are needed to optimize the desirable
features as possible.
When a charged particle passes through the chambers, a primary ionization is
135
produced, the electrons liberated will travel with a known velocity towards the anode
wires inducing secondary collisions or avalanche, which occurs within a few wire
diameters of the anode because of the 1/r electric field dependence. Therefore, the
amount of multiplication is a strong function of the wire diameter. On the other
hand, the wire diameter must not be too small or else it would be incapable of
maintaining the tension necessary to resist the electrostatic forces acting on it.
This avalanche is collected at the chamber electrodes and induces a convenient
current signal along the wires to the external circuit. The output pulse is proportional
to the number of primary ion pairs hence the name of the chamber.
Analysing the detected signal it is possible to reconstruct the trajectory of the
particle using the distribution of sense wires hits and the charge distribution.
Although MWPC have no energy resolution, they are almost 100% efficient for
the detection of single, minimum ionizing particles (MIP), allow a large improvement
in spatial resolution and they also have a good response to many simultaneous tracks
due to the fact that each anode wire is essentially an independent detector.
The drift chambers appear shortly after the MWPC’s. The aspect exploited
by these new chambers is the spatial information obtained by measuring the drift
time of the electrons coming from an ionizing event. For this purpose, a constant
drift velocity is necessary to have a linear relationship between time and distance.
The design is basically the same structure used for a MWPC but in order to get
electric field uniformity, field wires are intercalated between anodes. So, the anode
plane is such that adjacent sense wires are separated by two potential wires. The
field wires are held at a slightly higher potential than the cathode. This configuration
shapes and adjusts the drift field but also does that the chamber volume forms a
Faraday cage screening against external electromagnetic noise.
They are generally easier to operate compared to MWPC’s but much more at-
tention must be given to the field uniformity and is of utmost importance the correct
choice of the fill gas since a precise knowledge of the drift velocity is necessary.
The advantages of the design (besides the already mentioned for the MWPC’s)
136 APPENDIX B. MULTIWIRE PROPORTIONAL AND DRIFT CHAMBERS
are its shorter deadtime and better resolving time, so a drift chamber can be also
used as trigger detector.
Now the trajectory of the particle can be reconstructed using besides the distri-
bution of sense wire hits and the charge distribution, the drift times to the sense
wires. The spatial and time resolutions depend on the anode wire spacing1, and the
uncertainty in the arrival time of a pulse at the logic electronics after the passage of
an ionizing particle.
In several experiments, the location of the MWPCs or drift chambers is in or near
the field of a magnet. In such cases, the path of the drifting electrons and the drift
velocity will be altered by the Lorentz force. So, it is necessary a precise knowledge
of the magnetic field in order to correlate the drift time with position. It may also
be possible to adjust the electric field direction so as to compensate the effects of the
magnetic field.
1It is typically one-half the wire spacing value.
Appendix C
Q and t measurement
All the wires of the CJC, CIZ, and CIP2k (and COP when it was in operation)
are individually read at both ends separately (or combined), the information is used
for the z determination with the help of the signal parameters, the signal time t and
the pulse integral Q.
The analog signal pulse passes through an amplifier connected to the signal wires,
then the amplified signal is carried to the H1 electronic trailer by a coaxial cable
28 m long. There, the signal is digitized by F1001-FADCs1 synchronized to HERA
frequency (104MHz), which means that every 10 ns a digitizations occurs. The
FADC system signals are continuously digitized and stored in the memories. Sixteen
FADC-channels are housed on one F1001-card and up to 16 F1001 cads are housed
in a F1000 crate. In each F1000 front end crate there is a scanner card acting as a
sample controller for the FADCs. Its function is the copy of data from the FADCs,
during this action, the data is compared with programmable thresholds and any
significant transition is recorded in a hit table. The signal pulses gotten in this way
are analysed for the charge and arriving time determination, analysis (Q, t), during
the L4 level of the trigger.
The electrons created by primary ionization in places with approx. the same drift
time arrive all to the signal wire more and less at the same time (the isochrones).
1Fast Analog to Digital Converter.
137
138 APPENDIX C. Q AND T MEASUREMENT
β
wireSignal
Drift way
Drift electrons
Isochrone
Ionizedparticle
A
B
Figure C.1: Isochrones model.
Figure C.1 illustrates it, marked with ’A’. The electrons liberated in ’B’ arrive to the
wire at a different time.
If a charged particles goes through perpendicularly to the drift direction, the
contribution of an isochrone tangent due to the electrons produced by the primary
ionization is maximum. While the β angle (angle between the perpendicular direction
to the drift direction and a trajectory) is larger, less can be depart from a tangential
approximation to an isochrone.
Figure C.2 shows a typical signal pulse after the digitization. The essential infor-
mation for the drift determination comes from those electrons produced in ’A’ which
contribute to the sharp rise of the pulse, while the ones produced in ’B’ arrive later
and belong to the smeared out edge of the pulse. A larger contribution of electrons
from ’B’ mean a flatter pulse.
The (Q, t) analysis consists of several steps. First the FADC data are first lin-
earised, then the pedestal for the signal pulses in the hit memory (threshold) is
determined by the average of the 6 bins before the rise of the signal. The next step
is to put in order both pulses from −z and +z originated by the same primary elec-
trons. If there are two pulses in the same wire close to each other such that they
overlap a standard pulse shape is adjusted to each signal pulses and a substraction
of the pulses is made in both wire ends, improving in this way the resolution of two
139
Signal Amplitud
BA
Integration inteval
Presamples
10% Point
50% Point
Charge
50% line
10% line
Time [10ns]Pedestal
Figure C.2: Example of a pulse signal.
hits.
The method for the arriving time determination is called leading edge algorithm.
For both ends, the 50% point of the signal t50% is determined independenly by a linear
interpolation, which corresponds to the half of the maximum value of the signal smax.
In the same way, it is determined the maximum slope between two digitalizations in
the rise signal region. The line defined is used for the t10% determination in which
a pulse signal of 10% of the maximum amplitud (determined by t50% and smax) is
reached. The time t10% is interpreted as the arriving time of the signal.
The determination of the charges Qz+ and Qz− is gotten by the integration of the
signal pulse. The optimal integral interval must be chosen not too short or an error
in the charge determination will be made, but not too large since the small statistic
induces variations in the pulse fall. The chosen mode consists in an interval of 80
FACD digitizations (80 ns) departing from the t50%.
At the end of the readout, the arriving time tA and the charge Q of both wire
ends for each hit is determined. The values are stored in a data bank to be used for
the reconstruction of the tracks.
140 APPENDIX C. Q AND T MEASUREMENT
Appendix D
Track reconstruction
A charged particle passing through the central tracking detector will describe a
helix trajectory due to the effect of the magnetic field acting over it1. For tracks
reconstruction, a projection in the rφ (or xy) plane is done to get some parame-
ters, which are then combined with the z dimension to have the three-dimensional
reconstructed trajectory of the particle.
In the rφ plane, the track projection is described as function of the curvature κ =
1/R, defined as positive (negative) if the direction of φ is clockwise (anticlockwise);
the closest distance to the origin of the rφ plane, closest distance of approach or dca,
with positive sign if the vector going from the origin to the dca point together with
the trajectory direction form a right-handed system; and the angle between the x
axis and the transverse momentum vector in the dca point, the so called azimuthal
angle φ0. The transverse momentum vector in the dca point is seen in the sz plane
as a straight line starting at a z0 position and forming an angle θ with respect to the
z axis, see Figure D.1.
The helix parameters dca and z0 are defined with respect to nominal position,
the origin (0, 0, 0), but a more appropriate definition would be at the real vertex of
the event (the primary), however this is different for each event.
The κ, dca and φ parameters are obtained by fitting the data hits to a circle using
1The Lorentz force ~F = q( ~E + ~vx ~B).
141
142 APPENDIX D. TRACK RECONSTRUCTION
φ 0
z0|d |ca
R = −|κ|1
x zorigin
track
θ
track
vertexprimary
y s
|d|
Figure D.1: Picture of the track reconstruction with the parameter definition tocharacterize them.
the non-iterative algorithm of Karimaki [82], the equation is in polar coordinates:
1
2κ (r2 + dca2) + (1 + κ dca) r sen(φ − ϕ) − dca = 0,
while θ and z0 are determined by a linear least-squares fit:
zi = z0 + Srφi (dz/dS),
where Srφi is the track length for the point zi in the rφ projection, when Srφ =0 at
dca, and the slope dz/dS is converted to θ by θ = arc tan(1/(dz/dS)).
The reconstruction of tracks is done by a software with a fast version at fourth
trigger level L4, which is efficient for tracks originating from the primary vertex with
momentum greater than 100 MeV/c, and by a standard track finding version more
complete and efficient for all kind of tracks but 10 times slower than the first one.
The fast reconstruction, used for background rejection and fast classification of
events, consists of the determination of the bunch crossing time T0 of the events and
the calculation of the drift time of each hit, the search for tracks elements defined
by three hits (triplets) and, from the triplets, assignation of individual trajectories
to get the track parameters.
The T0 of the event can be gotten from a drift time histogram, as mentioned in
appendix C. The drift time of each hit tA,i, stored in a data bank, can be transduced
143
in position information by si = vdrift(tA,i − T0) where si represents the distance
between the trajectory and the signal wire i, this is the drift distance of the electrons
from the primary ionization, and vdrift being the drift velocity considered as constant.
It is also important to consider the beginning time of each wire t0,i, the drift direction
known by the electric field and the Lorentz angle αLor. The values obtained provide
the new calibration constants which are stored in the H1 database.
The search of track elements start by taking three wires with a distance of two
wires (n − 2, n, n + 2) and trying all pairs of hits. Defining i, k as the hit index,
the drift distances dn are calculated by (dn−2i + dn+2
k )/2 and |dn−2i − dn+2
k |/2, if there
are small differences when it is compared to the measured value dnj (small |dn
j − dn|)then, the index of the hits at the triplet wires are stored as a possible track element
together with their κ and φ values calculated assuming dca ≡ 0. After trying all
different three wire combinations, there is a cluster of hit triplets with their own κ
and φ values; from their coordinates a iterative process is made to fit a circle but
now allowing dca 6= 0 to get a specific track candidate. Those with large |dca| and
κ are rejected.
The standard phase of track reconstruction also searches for track elements by
triplets but now on adjacent wires, so at the end chains of hits are extracted, which
are eventually split into two shorter chains if they are long. The accepted chains
are stored as track elements with parameters from the fit. When the track element
is short, it is merged with the previous ones within the same cells, then with the
neighbouring, within one ring and lastly from both CJC1 and CJC2.
The algorithm of merging start comparing pairs of track elements with similar
helix parameters. If the distance between them suggests that they could belong to
the same track, a χ2 fit is performed (in the rφ plane). In case that one element of
a pair has been used in the construction of a new element, the fit to the modified
element(s) is repeated and rejected eventually. In this way, wrong combinations of
short track elements are avoided with high probability.
Finally the drift length is calculated for all possible wires and for all track elements
144 APPENDIX D. TRACK RECONSTRUCTION
ordered by their length and compared to the measurement to reject incompatible
hits and the fits are repeated but now using the acceptable hits, so the track finding
efficiency is improved.
The energy loss dE/dx for a given track is determined from the mean of single-hit
values 1/√
ki = 1/√
(dE/dx)i, excluding hits which are close to another track.
Appendix E
Breit frame of reference
The DIS kinematic is mainly described by Q2, x, y and W 2 in the laboratory
frame (subsection 1.1.1), but there is another frame also commonly used to study the
dynamics of the hadronic final state in DIS, the Breit Frame [83] (BF). This frame
is special because makes things easier for comparison to results of e+e− colliders,
allowing the test of the universality concept of fragmentation in different processes.
The ep BF is reached when the laboratory frame is Lorentz boosted to the
hadronic center of mass frame, followed by a longitudinal boost along a common
z direction such that the incident virtual photon is space-like (has zero energy, zero
transverse momentum and a z component of momentum −Q). The z direction is
chosen to be, as in laboratory frame, positive in the direction of the incoming proton.
The Figure E.1 presents a illustration of the boost. The advantage of the BF is
the maximal separation of the incoming and outgoing partons in the QPM, the two
regions assigned according to the sign of the momentum in the z axis of the BF, pz.
The current hemisphere if pz < 0 and the target hemisphere if pz > 0.
The current region is dominated by the fragments of the struck quark alone
which makes it analogous to the single hemisphere of e+e− → qq annihilation.
The proton remnants go entirely into the target hemisphere. The incoming quark
have four-momentum (Q/2,0,0,Q/2), after the scattering the four-momentum is
(Q/2,0,0,−Q/2), so the maximum momentum a particle can have in current region
145
146 APPENDIX E. BREIT FRAME OF REFERENCE
q=(0,0,0,−Q) e
− Q / 2
q
P
+ Q / 2
q
_e’
z
Figure E.1: Breit frame scheme with the separation in current and target hemi-spheres.
is Q/2 while the target region with much higher momentum can reach a maximum
of Q(1 − x)/2x. The two regions are then asymmetric, particularly at low x, where
the target region occupies most of the available phase space. The central detector in
H1 provides excellent acceptance for the current region studies.
In e+e− annihilation, the two quarks are produced with equal and opposite mo-
menta (±√
see/2) and the scaled hadron momentum is xp = 2phadron/E∗, with E∗
being its center of mass energy. The fragmentation of the quarks in e+e− interactions
can be compared to that in the current region where the scaled momentum spectra
of the particles is then expressed in terms of xp = 2phadrons/Q (considering only
hadrons in the current hemisphere), the Q dependence is similar to that in e+e− at
energy√
see = Q and, as can be easily seen, E∗ is equivalent to Q.
The BF also enables the study of low pT tracks1 since low momenta tracks in the
laboratory frame can occasionally be boosted to higher momenta in the BF. In these
frames the pT arising from the electroweak recoil of the hadronic system against the
scattered lepton is removed, facilitating the observation of QCD effects.
The consideration of higher order processes can, however, affect the QPM in BF,
for instance the BGF and initial state QCDc contribute to the ep cross section but
1In the laboratory frame of reference, low pT tracks have poor acceptance and are removed below150 MeV/c to improve the simulation efficiency.
147
they are not present (and have no analogue) in e+e− annihilation. These processes,
together with final state QCDc (which does occur in hadronic e+e− collisions) can
de-populate the BF current region, even leading to a current hemisphere which is
empty, for further explanation go to reference [84]. Empty current hemisphere events
are included in this analysis for normalisation purposes.
148 APPENDIX E. BREIT FRAME OF REFERENCE
Appendix F
Fits to mass distributions
149
150A
PP
EN
DIX
F.
FIT
ST
OM
ASS
DIS
TR
IBU
TIO
NS
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
/ ndf 2χ 101 / 109
Prob 0.6963
N 20931± 4.949e+05
m 0.0002± 0.4967
σ 0.000238± 0.008507
ν 0.325± 2.031
0
p 38.2± 52.7
1p 0.1024± 0.3388
2p 4.97± 35.57
3
p 13.93± -67.77
4p 11.34± 37.38
HERA II/NDF ~ 0.9261632χ
0.000190±mass = 0.496702
0.000238± = 0.008507σ 305±) in range = 4200
s
0 N(K
S/B = 5.940089
Range = [0.345000,0.700000]
Bin 1
/ ndf 2χ 101 / 109
Prob 0.6963
N 20931± 4.949e+05
m 0.0002± 0.4967
σ 0.000238± 0.008507
ν 0.325± 2.031
0
p 38.2± 52.7
1p 0.1024± 0.3388
2p 4.97± 35.57
3
p 13.93± -67.77
4p 11.34± 37.38
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
/ ndf 2χ 101 / 109
Prob 0.6963
N 20931± 4.949e+05
m 0.0002± 0.4967
σ 0.000238± 0.008507
ν 0.325± 2.031
0
p 38.2± 52.7
1p 0.1024± 0.3388
2p 4.97± 35.57
3
p 13.93± -67.77
4p 11.34± 37.38
HERA II/NDF ~ 0.9261632χ
0.000190±mass = 0.496702
0.000238± = 0.008507σ 305±) in range = 4200
s
0 N(K
S/B = 5.940089
Range = [0.345000,0.700000]
Bin 1
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
600
700
800
900 / ndf 2χ 95.47 / 109
Prob 0.8189
N 26275± 7.46e+05
m 0.0002± 0.4967
σ 0.000192± 0.008419
ν 0.296± 2.097
0
p 55.1± 111.1
1p 0.0700± 0.4319
2p 4.21± 37.05
3
p 11.51± -70.88
4p 9.25± 38.18
HERA II/NDF ~ 0.8759142χ
0.000162±mass = 0.496729
0.000192± = 0.008419σ 374±) in range = 6269
s
0 N(K
S/B = 4.719892
Range = [0.345000,0.700000]
Bin 2
/ ndf 2χ 95.47 / 109
Prob 0.8189
N 26275± 7.46e+05
m 0.0002± 0.4967
σ 0.000192± 0.008419
ν 0.296± 2.097
0
p 55.1± 111.1
1p 0.0700± 0.4319
2p 4.21± 37.05
3
p 11.51± -70.88
4p 9.25± 38.18
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
600
700
800
900 / ndf 2χ 95.47 / 109
Prob 0.8189
N 26275± 7.46e+05
m 0.0002± 0.4967
σ 0.000192± 0.008419
ν 0.296± 2.097
0
p 55.1± 111.1
1p 0.0700± 0.4319
2p 4.21± 37.05
3
p 11.51± -70.88
4p 9.25± 38.18
HERA II/NDF ~ 0.8759142χ
0.000162±mass = 0.496729
0.000192± = 0.008419σ 374±) in range = 6269
s
0 N(K
S/B = 4.719892
Range = [0.345000,0.700000]
Bin 2
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
200
400
600
800
1000
1200
/ ndf 2χ 107.4 / 110
Prob 0.5516
N 41781± 1.158e+06
m 0.000± 0.497
σ 0.000189± 0.008931
ν 0.158± 1.326
0
p 13.0± 154.2
1p 0.0542± 0.3765
2p 2.33± 37.78
3
p 8.49± -76.55
4p 7.53± 45.23
HERA II/NDF ~ 0.9766352χ
0.000139±mass = 0.496967
0.000189± = 0.008931σ 637±) in range = 10197
s
0 N(K
S/B = 5.682566
Range = [0.344000,0.700000]
Bin 3
/ ndf 2χ 107.4 / 110
Prob 0.5516
N 41781± 1.158e+06
m 0.000± 0.497
σ 0.000189± 0.008931
ν 0.158± 1.326
0
p 13.0± 154.2
1p 0.0542± 0.3765
2p 2.33± 37.78
3
p 8.49± -76.55
4p 7.53± 45.23
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
200
400
600
800
1000
1200
/ ndf 2χ 107.4 / 110
Prob 0.5516
N 41781± 1.158e+06
m 0.000± 0.497
σ 0.000189± 0.008931
ν 0.158± 1.326
0
p 13.0± 154.2
1p 0.0542± 0.3765
2p 2.33± 37.78
3
p 8.49± -76.55
4p 7.53± 45.23
HERA II/NDF ~ 0.9766352χ
0.000139±mass = 0.496967
0.000189± = 0.008931σ 637±) in range = 10197
s
0 N(K
S/B = 5.682566
Range = [0.344000,0.700000]
Bin 3
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
200
400
600
800
1000
1200
/ ndf 2χ 114.3 / 110
Prob 0.3713
N 44591± 1.198e+06
m 0.0001± 0.4971
σ 0.000182± 0.008788
ν 0.150± 1.245
0
p 47.5± 139.9
1p 0.0466± 0.3531
2p 2.61± 36.99
3
p 7.69± -71.99
4p 6.56± 40.94
HERA II/NDF ~ 1.0387252χ
0.000134±mass = 0.497129
0.000182± = 0.008788σ 663±) in range = 10352
s
0 N(K
S/B = 4.953475
Range = [0.344000,0.700000]
Bin 4
/ ndf 2χ 114.3 / 110
Prob 0.3713
N 44591± 1.198e+06
m 0.0001± 0.4971
σ 0.000182± 0.008788
ν 0.150± 1.245
0
p 47.5± 139.9
1p 0.0466± 0.3531
2p 2.61± 36.99
3
p 7.69± -71.99
4p 6.56± 40.94
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
200
400
600
800
1000
1200
/ ndf 2χ 114.3 / 110
Prob 0.3713
N 44591± 1.198e+06
m 0.0001± 0.4971
σ 0.000182± 0.008788
ν 0.150± 1.245
0
p 47.5± 139.9
1p 0.0466± 0.3531
2p 2.61± 36.99
3
p 7.69± -71.99
4p 6.56± 40.94
HERA II/NDF ~ 1.0387252χ
0.000134±mass = 0.497129
0.000182± = 0.008788σ 663±) in range = 10352
s
0 N(K
S/B = 4.953475
Range = [0.344000,0.700000]
Bin 4
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
600
/ ndf 2χ 124.3 / 110
Prob 0.166
N 34214± 5.34e+05
m 0.0002± 0.4973 σ 0.0003± 0.0102 ν 0.250± 1.186
0p 59.1± 136.4
1
p 0.0604± 0.3943
2p 4.19± 35.82
3
p 12.38± -72.94
4p 10.44± 43.46
HERA II/NDF ~ 1.1300412χ
0.000233±mass = 0.497280
0.000339± = 0.010203σ 588±) in range = 5322
s
0 N(K
S/B = 4.574761
Range = [0.344000,0.700000]
Bin 5
/ ndf 2χ 124.3 / 110
Prob 0.166
N 34214± 5.34e+05
m 0.0002± 0.4973 σ 0.0003± 0.0102 ν 0.250± 1.186
0p 59.1± 136.4
1
p 0.0604± 0.3943
2p 4.19± 35.82
3
p 12.38± -72.94
4p 10.44± 43.46
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
600
/ ndf 2χ 124.3 / 110
Prob 0.166
N 34214± 5.34e+05
m 0.0002± 0.4973 σ 0.0003± 0.0102 ν 0.250± 1.186
0p 59.1± 136.4
1
p 0.0604± 0.3943
2p 4.19± 35.82
3
p 12.38± -72.94
4p 10.44± 43.46
HERA II/NDF ~ 1.1300412χ
0.000233±mass = 0.497280
0.000339± = 0.010203σ 588±) in range = 5322
s
0 N(K
S/B = 4.574761
Range = [0.344000,0.700000]
Bin 5
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
50
100
150
200
250
300
/ ndf 2χ 107.5 / 110
Prob 0.5507
N 28528± 3.363e+05
m 0.0003± 0.4971 σ 0.00083± 0.00992 ν 0.0528± 0.3982
0p 1.035± 3.371
1
p 0.0858± 0.6073
2p 3.72± 61.91
3
p 11.5± -129.5
4p 9.67± 81.93
HERA II/NDF ~ 0.9769382χ
0.000322±mass = 0.497150
0.000834± = 0.009920σ 568±) in range = 2630
s
0 N(K
S/B = 2.981262
Range = [0.344000,0.700000]
Bin 6
Figu
reF.1:
Fits
toth
ein
variant
mass
distrib
ution
fromdata
inbin
sof
Q2.
151
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
600
700
800 / ndf 2χ 91.82 / 110
Prob 0.8952
N 23504± 6.497e+05
m 0.0002± 0.4966
σ 0.000201± 0.008311
ν 0.320± 2.238
0
p 13.37± 19.86
1p 0.0651± 0.4251
2p 4.97± 46.53
3
p 12.54± -91.24
4p 9.84± 52.65
HERA II/NDF ~ 0.8347542χ
0.000167±mass = 0.496568
0.000201± = 0.008311σ 334±) in range = 5392
s
0 N(K
S/B = 5.230564
Range = [0.344000,0.700000]
Bin 1
/ ndf 2χ 91.82 / 110
Prob 0.8952
N 23504± 6.497e+05
m 0.0002± 0.4966
σ 0.000201± 0.008311
ν 0.320± 2.238
0
p 13.37± 19.86
1p 0.0651± 0.4251
2p 4.97± 46.53
3
p 12.54± -91.24
4p 9.84± 52.65
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
600
700
800 / ndf 2χ 91.82 / 110
Prob 0.8952
N 23504± 6.497e+05
m 0.0002± 0.4966
σ 0.000201± 0.008311
ν 0.320± 2.238
0
p 13.37± 19.86
1p 0.0651± 0.4251
2p 4.97± 46.53
3
p 12.54± -91.24
4p 9.84± 52.65
HERA II/NDF ~ 0.8347542χ
0.000167±mass = 0.496568
0.000201± = 0.008311σ 334±) in range = 5392
s
0 N(K
S/B = 5.230564
Range = [0.344000,0.700000]
Bin 1
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7E
ntrie
s / 3
.000
000
MeV
0
200
400
600
800
1000
1200
1400
1600
1800
/ ndf 2χ 129.2 / 109
Prob 0.09069
N 47804± 1.745e+06
m 0.0001± 0.4969
σ 0.000138± 0.008621
ν 0.151± 1.558
0
p 61.1± 120.3
1p 0.0495± 0.3456
2p 3.62± 38.39
3
p 9.07± -72.18
4p 7.06± 39.36
HERA II/NDF ~ 1.1853712χ
0.000109±mass = 0.496927
0.000138± = 0.008621σ 688±) in range = 14936
s
0 N(K
S/B = 5.298865
Range = [0.345000,0.700000]
Bin 2
/ ndf 2χ 129.2 / 109
Prob 0.09069
N 47804± 1.745e+06
m 0.0001± 0.4969
σ 0.000138± 0.008621
ν 0.151± 1.558
0
p 61.1± 120.3
1p 0.0495± 0.3456
2p 3.62± 38.39
3
p 9.07± -72.18
4p 7.06± 39.36
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7E
ntrie
s / 3
.000
000
MeV
0
200
400
600
800
1000
1200
1400
1600
1800
/ ndf 2χ 129.2 / 109
Prob 0.09069
N 47804± 1.745e+06
m 0.0001± 0.4969
σ 0.000138± 0.008621
ν 0.151± 1.558
0
p 61.1± 120.3
1p 0.0495± 0.3456
2p 3.62± 38.39
3
p 9.07± -72.18
4p 7.06± 39.36
HERA II/NDF ~ 1.1853712χ
0.000109±mass = 0.496927
0.000138± = 0.008621σ 688±) in range = 14936
s
0 N(K
S/B = 5.298865
Range = [0.345000,0.700000]
Bin 2
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
200
400
600
800
1000
1200
1400
/ ndf 2χ 109.5 / 109
Prob 0.4679
N 55420± 1.435e+06
m 0.0001± 0.4972
σ 0.000183± 0.009121
ν 0.130± 1.057
0
p 44.3± 125
1p 0.0559± 0.3304
2p 2.73± 39.67
3
p 8.29± -80.77
4p 7.05± 48.93
HERA II/NDF ~ 1.0047942χ
0.000133±mass = 0.497189
0.000183± = 0.009121σ 865±) in range = 12712
s
0 N(K
S/B = 5.520706
Range = [0.345000,0.700000]
Bin 3
/ ndf 2χ 109.5 / 109
Prob 0.4679
N 55420± 1.435e+06
m 0.0001± 0.4972
σ 0.000183± 0.009121
ν 0.130± 1.057
0
p 44.3± 125
1p 0.0559± 0.3304
2p 2.73± 39.67
3
p 8.29± -80.77
4p 7.05± 48.93
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
200
400
600
800
1000
1200
1400
/ ndf 2χ 109.5 / 109
Prob 0.4679
N 55420± 1.435e+06
m 0.0001± 0.4972
σ 0.000183± 0.009121
ν 0.130± 1.057
0
p 44.3± 125
1p 0.0559± 0.3304
2p 2.73± 39.67
3
p 8.29± -80.77
4p 7.05± 48.93
HERA II/NDF ~ 1.0047942χ
0.000133±mass = 0.497189
0.000183± = 0.009121σ 865±) in range = 12712
s
0 N(K
S/B = 5.520706
Range = [0.345000,0.700000]
Bin 3
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
600
700 / ndf 2χ 133 / 110
Prob 0.06667
N 30762± 5.372e+05
m 0.0002± 0.4972 σ 0.00032± 0.01017 ν 0.36± 1.62
0p 1.38± 12.45
1
p 0.0465± 0.4462
2p 1.90± 52.34
3
p 6.9± -100.9
4p 6.12± 58.28
HERA II/NDF ~ 1.2095122χ
0.000239±mass = 0.497165
0.000323± = 0.010167σ 517±) in range = 5417
s
0 N(K
S/B = 2.551003
Range = [0.344000,0.700000]
Bin 4
Figu
reF.2:
Fits
toth
ein
variant
mass
distrib
ution
fromdata
inbin
sof
x.
152A
PP
EN
DIX
F.
FIT
ST
OM
ASS
DIS
TR
IBU
TIO
NS
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
600
700
800
900 / ndf 2χ 89.31 / 110
Prob 0.9262
N 31050± 7.97e+05
m 0.0002± 0.4964
σ 0.000197± 0.008263
ν 0.24± 1.81
0
p 1.48± 15.86
1p 0.0787± 0.4408
2p 3.52± 48.44
3
p 12.48± -95.52
4p 10.97± 54.92
HERA II/NDF ~ 0.8118872χ
0.000156±mass = 0.496388
0.000197± = 0.008263σ 428±) in range = 6561
s
0 N(K
S/B = 6.846985
Range = [0.344000,0.700000]
Bin 1
/ ndf 2χ 89.31 / 110
Prob 0.9262
N 31050± 7.97e+05
m 0.0002± 0.4964
σ 0.000197± 0.008263
ν 0.24± 1.81
0
p 1.48± 15.86
1p 0.0787± 0.4408
2p 3.52± 48.44
3
p 12.48± -95.52
4p 10.97± 54.92
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
600
700
800
900 / ndf 2χ 89.31 / 110
Prob 0.9262
N 31050± 7.97e+05
m 0.0002± 0.4964
σ 0.000197± 0.008263
ν 0.24± 1.81
0
p 1.48± 15.86
1p 0.0787± 0.4408
2p 3.52± 48.44
3
p 12.48± -95.52
4p 10.97± 54.92
HERA II/NDF ~ 0.8118872χ
0.000156±mass = 0.496388
0.000197± = 0.008263σ 428±) in range = 6561
s
0 N(K
S/B = 6.846985
Range = [0.344000,0.700000]
Bin 1
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
200
400
600
800
1000
/ ndf 2χ 113.9 / 108
Prob 0.3297
N 51351± 1.041e+06
m 0.0002± 0.4967
σ 0.000216± 0.008904
ν 0.136± 0.932
0
p 3.34± 35.81
1p 0.1191± 0.4439
2p 4.58± 43.78
3
p 14.9± -88.6
4p 12.4± 53.4
HERA II/NDF ~ 1.0547882χ
0.000151±mass = 0.496659
0.000216± = 0.008904σ 783±) in range = 8901
s
0 N(K
S/B = 8.569452
Range = [0.350000,0.700000]
Bin 2
/ ndf 2χ 113.9 / 108
Prob 0.3297
N 51351± 1.041e+06
m 0.0002± 0.4967
σ 0.000216± 0.008904
ν 0.136± 0.932
0
p 3.34± 35.81
1p 0.1191± 0.4439
2p 4.58± 43.78
3
p 14.9± -88.6
4p 12.4± 53.4
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
200
400
600
800
1000
/ ndf 2χ 113.9 / 108
Prob 0.3297
N 51351± 1.041e+06
m 0.0002± 0.4967
σ 0.000216± 0.008904
ν 0.136± 0.932
0
p 3.34± 35.81
1p 0.1191± 0.4439
2p 4.58± 43.78
3
p 14.9± -88.6
4p 12.4± 53.4
HERA II/NDF ~ 1.0547882χ
0.000151±mass = 0.496659
0.000216± = 0.008904σ 783±) in range = 8901
s
0 N(K
S/B = 8.569452
Range = [0.350000,0.700000]
Bin 2
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
200
400
600
800
1000 / ndf 2χ 94.47 / 104
Prob 0.7376
N 49579± 1.005e+06
m 0.000± 0.497
σ 0.000232± 0.009305
ν 0.1482± 0.9693
0
p 7.274± 8.607
1p 0.15923± -0.07678
2p 5.58± 36.27
3
p 15.37± -57.95
4p 12.10± 27.62
HERA II/NDF ~ 0.9083202χ
0.000160±mass = 0.496962
0.000232± = 0.009305σ 798±) in range = 8982
s
0 N(K
S/B = 6.899873
Range = [0.360000,0.700000]
Bin 3
/ ndf 2χ 94.47 / 104
Prob 0.7376
N 49579± 1.005e+06
m 0.000± 0.497
σ 0.000232± 0.009305
ν 0.1482± 0.9693
0
p 7.274± 8.607
1p 0.15923± -0.07678
2p 5.58± 36.27
3
p 15.37± -57.95
4p 12.10± 27.62
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
200
400
600
800
1000 / ndf 2χ 94.47 / 104
Prob 0.7376
N 49579± 1.005e+06
m 0.000± 0.497
σ 0.000232± 0.009305
ν 0.1482± 0.9693
0
p 7.274± 8.607
1p 0.15923± -0.07678
2p 5.58± 36.27
3
p 15.37± -57.95
4p 12.10± 27.62
HERA II/NDF ~ 0.9083202χ
0.000160±mass = 0.496962
0.000232± = 0.009305σ 798±) in range = 8982
s
0 N(K
S/B = 6.899873
Range = [0.360000,0.700000]
Bin 3
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
200
400
600
800
1000
/ ndf 2χ 154.6 / 110
Prob 0.003296
N 40108± 1.001e+06
m 0.0002± 0.4972
σ 0.000183± 0.008361
ν 0.163± 1.545
0
p 2.06± 27.48
1p 0.0431± 0.3044
2p 2.07± 43.76
3
p 7.61± -81.06
4p 6.8± 44.5
HERA II/NDF ~ 1.4050022χ
0.000151±mass = 0.497151
0.000183± = 0.008361σ 542±) in range = 8309
s
0 N(K
S/B = 3.963126
Range = [0.344000,0.700000]
Bin 4
/ ndf 2χ 154.6 / 110
Prob 0.003296
N 40108± 1.001e+06
m 0.0002± 0.4972
σ 0.000183± 0.008361
ν 0.163± 1.545
0
p 2.06± 27.48
1p 0.0431± 0.3044
2p 2.07± 43.76
3
p 7.61± -81.06
4p 6.8± 44.5
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
200
400
600
800
1000
/ ndf 2χ 154.6 / 110
Prob 0.003296
N 40108± 1.001e+06
m 0.0002± 0.4972
σ 0.000183± 0.008361
ν 0.163± 1.545
0
p 2.06± 27.48
1p 0.0431± 0.3044
2p 2.07± 43.76
3
p 7.61± -81.06
4p 6.8± 44.5
HERA II/NDF ~ 1.4050022χ
0.000151±mass = 0.497151
0.000183± = 0.008361σ 542±) in range = 8309
s
0 N(K
S/B = 3.963126
Range = [0.344000,0.700000]
Bin 4
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
600
700
800 / ndf 2χ 137.4 / 109
Prob 0.03417
N 24721± 6.078e+05
m 0.0002± 0.4979 σ 0.00026± 0.01005 ν 0.545± 2.678
0p 17.30± 50.23
1
p 0.0509± 0.3817
2p 2.97± 44.93
3
p 8.04± -87.61
4p 6.37± 51.12
HERA II/NDF ~ 1.2606342χ
0.000206±mass = 0.497889
0.000262± = 0.010050σ 416±) in range = 6103
s
0 N(K
S/B = 2.348214
Range = [0.345000,0.700000]
Bin 5
Figu
reF.3:
Fits
toth
ein
variant
mass
distrib
ution
fromdata
inbin
sof
η.
153
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
200
400
600
800
1000
/ ndf 2χ 129.5 / 101
Prob 0.02963
N 29105± 8.351e+05
m 0.0001± 0.4967
σ 0.000179± 0.007051
ν 0.545± 3.118
0
p 15.93± 34.42
1p 0.0891± 0.1473
2p 3.98± 48.86
3
p 10.33± -98.01
4p 7.76± 58.32
HERA II/NDF ~ 1.2817842χ
0.000144±mass = 0.496704
0.000179± = 0.007051σ 360±) in range = 5887
s
0 N(K
S/B = 1.642742
Range = [0.370000,0.700000]
Bin 1
/ ndf 2χ 129.5 / 101
Prob 0.02963
N 29105± 8.351e+05
m 0.0001± 0.4967
σ 0.000179± 0.007051
ν 0.545± 3.118
0
p 15.93± 34.42
1p 0.0891± 0.1473
2p 3.98± 48.86
3
p 10.33± -98.01
4p 7.76± 58.32
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
200
400
600
800
1000
/ ndf 2χ 129.5 / 101
Prob 0.02963
N 29105± 8.351e+05
m 0.0001± 0.4967
σ 0.000179± 0.007051
ν 0.545± 3.118
0
p 15.93± 34.42
1p 0.0891± 0.1473
2p 3.98± 48.86
3
p 10.33± -98.01
4p 7.76± 58.32
HERA II/NDF ~ 1.2817842χ
0.000144±mass = 0.496704
0.000179± = 0.007051σ 360±) in range = 5887
s
0 N(K
S/B = 1.642742
Range = [0.370000,0.700000]
Bin 1
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7E
ntrie
s / 3
.000
000
MeV
0
100
200
300
400
500
600
700
800
900 / ndf 2χ 108.7 / 110
Prob 0.5159
N 24612± 7.134e+05
m 0.000± 0.497
σ 0.000189± 0.007539
ν 0.468± 3.041
0
p 1.9± 26
1p 0.0767± 0.4527
2p 3.00± 45.98
3
p 9.81± -90.33
4p 8.15± 53.07
HERA II/NDF ~ 0.9886012χ
0.000148±mass = 0.497012
0.000189± = 0.007539σ 325±) in range = 5377
s
0 N(K
S/B = 4.232534
Range = [0.344000,0.700000]
Bin 2
/ ndf 2χ 108.7 / 110
Prob 0.5159
N 24612± 7.134e+05
m 0.000± 0.497
σ 0.000189± 0.007539
ν 0.468± 3.041
0
p 1.9± 26
1p 0.0767± 0.4527
2p 3.00± 45.98
3
p 9.81± -90.33
4p 8.15± 53.07
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7E
ntrie
s / 3
.000
000
MeV
0
100
200
300
400
500
600
700
800
900 / ndf 2χ 108.7 / 110
Prob 0.5159
N 24612± 7.134e+05
m 0.000± 0.497
σ 0.000189± 0.007539
ν 0.468± 3.041
0
p 1.9± 26
1p 0.0767± 0.4527
2p 3.00± 45.98
3
p 9.81± -90.33
4p 8.15± 53.07
HERA II/NDF ~ 0.9886012χ
0.000148±mass = 0.497012
0.000189± = 0.007539σ 325±) in range = 5377
s
0 N(K
S/B = 4.232534
Range = [0.344000,0.700000]
Bin 2
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
600
700
800
900 / ndf 2χ 124 / 110
Prob 0.1713
N 26281± 8.216e+05
m 0.0002± 0.4968
σ 0.000190± 0.008883
ν 0.213± 1.898
0
p 124.5± 253.3
1p 0.0669± 0.3005
2p 3.3± 23.7
3
p 9.77± -42.16
4p 8.44± 21.96
HERA II/NDF ~ 1.1269472χ
0.000159±mass = 0.496778
0.000190± = 0.008883σ 402±) in range = 7273
s
0 N(K
S/B = 8.535026
Range = [0.344000,0.700000]
Bin 3
/ ndf 2χ 124 / 110
Prob 0.1713
N 26281± 8.216e+05
m 0.0002± 0.4968
σ 0.000190± 0.008883
ν 0.213± 1.898
0
p 124.5± 253.3
1p 0.0669± 0.3005
2p 3.3± 23.7
3
p 9.77± -42.16
4p 8.44± 21.96
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
600
700
800
900 / ndf 2χ 124 / 110
Prob 0.1713
N 26281± 8.216e+05
m 0.0002± 0.4968
σ 0.000190± 0.008883
ν 0.213± 1.898
0
p 124.5± 253.3
1p 0.0669± 0.3005
2p 3.3± 23.7
3
p 9.77± -42.16
4p 8.44± 21.96
HERA II/NDF ~ 1.1269472χ
0.000159±mass = 0.496778
0.000190± = 0.008883σ 402±) in range = 7273
s
0 N(K
S/B = 8.535026
Range = [0.344000,0.700000]
Bin 3
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
600
700
800
900
/ ndf 2χ 98.67 / 110
Prob 0.7722
N 31697± 8.439e+05
m 0.000± 0.497
σ 0.000219± 0.009493
ν 0.131± 1.195
0
p 4.2± 25.8
1p 0.1796± 0.6982
2p 5.86± 44.75
3
p 18.13± -91.14
4p 14.37± 56.66
HERA II/NDF ~ 0.8970352χ
0.000166±mass = 0.497041
0.000219± = 0.009493σ 528±) in range = 7846
s
0 N(K
S/B = 13.326587
Range = [0.344000,0.700000]
Bin 4
/ ndf 2χ 98.67 / 110
Prob 0.7722
N 31697± 8.439e+05
m 0.000± 0.497
σ 0.000219± 0.009493
ν 0.131± 1.195
0
p 4.2± 25.8
1p 0.1796± 0.6982
2p 5.86± 44.75
3
p 18.13± -91.14
4p 14.37± 56.66
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
600
700
800
900
/ ndf 2χ 98.67 / 110
Prob 0.7722
N 31697± 8.439e+05
m 0.000± 0.497
σ 0.000219± 0.009493
ν 0.131± 1.195
0
p 4.2± 25.8
1p 0.1796± 0.6982
2p 5.86± 44.75
3
p 18.13± -91.14
4p 14.37± 56.66
HERA II/NDF ~ 0.8970352χ
0.000166±mass = 0.497041
0.000219± = 0.009493σ 528±) in range = 7846
s
0 N(K
S/B = 13.326587
Range = [0.344000,0.700000]
Bin 4
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
600
700 / ndf 2χ 105.7 / 109
Prob 0.5715
N 28855± 6.692e+05
m 0.0002± 0.4972 σ 0.00031± 0.01199 ν 0.132± 1.039
0p 14.41± 40.82
1
p 0.587± 1.475
2p 15.4± 53.8
3
p 43.9± -112.3
4p 32.28± 68.83
HERA II/NDF ~ 0.9697802χ
0.000213±mass = 0.497214
0.000306± = 0.011988σ 623±) in range = 7703
s
0 N(K
S/B = 15.976900
Range = [0.344000,0.700000]
Bin 5
/ ndf 2χ 105.7 / 109
Prob 0.5715
N 28855± 6.692e+05
m 0.0002± 0.4972 σ 0.00031± 0.01199 ν 0.132± 1.039
0p 14.41± 40.82
1
p 0.587± 1.475
2p 15.4± 53.8
3
p 43.9± -112.3
4p 32.28± 68.83
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
600
700 / ndf 2χ 105.7 / 109
Prob 0.5715
N 28855± 6.692e+05
m 0.0002± 0.4972 σ 0.00031± 0.01199 ν 0.132± 1.039
0p 14.41± 40.82
1
p 0.587± 1.475
2p 15.4± 53.8
3
p 43.9± -112.3
4p 32.28± 68.83
HERA II/NDF ~ 0.9697802χ
0.000213±mass = 0.497214
0.000306± = 0.011988σ 623±) in range = 7703
s
0 N(K
S/B = 15.976900
Range = [0.344000,0.700000]
Bin 5
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV0
50
100
150
200
250
300
350
400
450 / ndf 2χ 151.3 / 110
Prob 0.005525
N 17744± 3.608e+05
m 0.0003± 0.4979 σ 0.00059± 0.01393 ν 0.16± 1.11
0p 3.569± 5.041
1
p 0.737± 2.141
2p 22.08± 77.05
3
p 58.1± -146
4p 41.27± 76.16
HERA II/NDF ~ 1.3755662χ
0.000341±mass = 0.497895
0.000592± = 0.013934σ 508±) in range = 4829
s
0 N(K
S/B = 4.612215
Range = [0.344000,0.700000]
Bin 6
Figu
reF.4:
Fits
toth
ein
variant
mass
distrib
ution
fromdata
inbin
sof
pT.
154A
PP
EN
DIX
F.
FIT
ST
OM
ASS
DIS
TR
IBU
TIO
NS
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
600
/ ndf 2χ 108.5 / 104
Prob 0.363
N 27511± 5.164e+05
m 0.0002± 0.4967
σ 0.000263± 0.007847
ν 0.397± 1.897
0
p 15.10± 29.89
1p 0.099± 0.224
2p 4.59± 47.35
3
p 12.41± -96.82
4p 9.62± 58.86
HERA II/NDF ~ 1.0427972χ
0.000205±mass = 0.496738
0.000263± = 0.007847σ 365±) in range = 4039
s
0 N(K
S/B = 2.176749
Range = [0.360000,0.700000]
Bin 1
/ ndf 2χ 108.5 / 104
Prob 0.363
N 27511± 5.164e+05
m 0.0002± 0.4967
σ 0.000263± 0.007847
ν 0.397± 1.897
0
p 15.10± 29.89
1p 0.099± 0.224
2p 4.59± 47.35
3
p 12.41± -96.82
4p 9.62± 58.86
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
600
/ ndf 2χ 108.5 / 104
Prob 0.363
N 27511± 5.164e+05
m 0.0002± 0.4967
σ 0.000263± 0.007847
ν 0.397± 1.897
0
p 15.10± 29.89
1p 0.099± 0.224
2p 4.59± 47.35
3
p 12.41± -96.82
4p 9.62± 58.86
HERA II/NDF ~ 1.0427972χ
0.000205±mass = 0.496738
0.000263± = 0.007847σ 365±) in range = 4039
s
0 N(K
S/B = 2.176749
Range = [0.360000,0.700000]
Bin 1
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
600
700
800
/ ndf 2χ 112.6 / 110
Prob 0.4124
N 33991± 8.028e+05
m 0.0002± 0.4965
σ 0.000212± 0.008478
ν 0.140± 1.124
0
p 6.64± 55.83
1p 0.1144± 0.6223
2p 4.19± 43.49
3
p 13.85± -91.24
4p 11.59± 56.86
HERA II/NDF ~ 1.0239902χ
0.000165±mass = 0.496538
0.000212± = 0.008478σ 502±) in range = 6656
s
0 N(K
S/B = 8.490764
Range = [0.344000,0.700000]
Bin 2
/ ndf 2χ 112.6 / 110
Prob 0.4124
N 33991± 8.028e+05
m 0.0002± 0.4965
σ 0.000212± 0.008478
ν 0.140± 1.124
0
p 6.64± 55.83
1p 0.1144± 0.6223
2p 4.19± 43.49
3
p 13.85± -91.24
4p 11.59± 56.86
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
600
700
800
/ ndf 2χ 112.6 / 110
Prob 0.4124
N 33991± 8.028e+05
m 0.0002± 0.4965
σ 0.000212± 0.008478
ν 0.140± 1.124
0
p 6.64± 55.83
1p 0.1144± 0.6223
2p 4.19± 43.49
3
p 13.85± -91.24
4p 11.59± 56.86
HERA II/NDF ~ 1.0239902χ
0.000165±mass = 0.496538
0.000212± = 0.008478σ 502±) in range = 6656
s
0 N(K
S/B = 8.490764
Range = [0.344000,0.700000]
Bin 2
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
/ ndf 2χ 96.31 / 110
Prob 0.8209
N 27154± 5.368e+05
m 0.0002± 0.4963
σ 0.00032± 0.01006 ν 0.154± 1.048
0p 5.32± 16.19
1
p 0.552± 1.344
2p 16.08± 56.71
3
p 46.5± -113.6
4p 34.77± 64.58
HERA II/NDF ~ 0.8755322χ
0.000219±mass = 0.496299
0.000317± = 0.010063σ 494±) in range = 5227
s
0 N(K
S/B = 12.040656
Range = [0.344000,0.700000]
Bin 3
/ ndf 2χ 96.31 / 110
Prob 0.8209
N 27154± 5.368e+05
m 0.0002± 0.4963
σ 0.00032± 0.01006 ν 0.154± 1.048
0p 5.32± 16.19
1
p 0.552± 1.344
2p 16.08± 56.71
3
p 46.5± -113.6
4p 34.77± 64.58
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
/ ndf 2χ 96.31 / 110
Prob 0.8209
N 27154± 5.368e+05
m 0.0002± 0.4963
σ 0.00032± 0.01006 ν 0.154± 1.048
0p 5.32± 16.19
1
p 0.552± 1.344
2p 16.08± 56.71
3
p 46.5± -113.6
4p 34.77± 64.58
HERA II/NDF ~ 0.8755322χ
0.000219±mass = 0.496299
0.000317± = 0.010063σ 494±) in range = 5227
s
0 N(K
S/B = 12.040656
Range = [0.344000,0.700000]
Bin 3
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
50
100
150
200
250
300
350
400
450 / ndf 2χ 113.8 / 107
Prob 0.3074
N 12216± 4.162e+05
m 0.0003± 0.4974 σ 0.00042± 0.01108 ν 0.1± 1
0p 24.54± 54.11
1
p 1.194± 2.707
2p 32.61± 77.69
3
p 89.7± -168.7
4p 64.40± 99.91
HERA II/NDF ~ 1.0639322χ
0.000260±mass = 0.497417
0.000424± = 0.011081σ 356±) in range = 4425
s
0 N(K
S/B = 12.365727
Range = [0.344000,0.700000]
Bin 4
/ ndf 2χ 113.8 / 107
Prob 0.3074
N 12216± 4.162e+05
m 0.0003± 0.4974 σ 0.00042± 0.01108 ν 0.1± 1
0p 24.54± 54.11
1
p 1.194± 2.707
2p 32.61± 77.69
3
p 89.7± -168.7
4p 64.40± 99.91
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
50
100
150
200
250
300
350
400
450 / ndf 2χ 113.8 / 107
Prob 0.3074
N 12216± 4.162e+05
m 0.0003± 0.4974 σ 0.00042± 0.01108 ν 0.1± 1
0p 24.54± 54.11
1
p 1.194± 2.707
2p 32.61± 77.69
3
p 89.7± -168.7
4p 64.40± 99.91
HERA II/NDF ~ 1.0639322χ
0.000260±mass = 0.497417
0.000424± = 0.011081σ 356±) in range = 4425
s
0 N(K
S/B = 12.365727
Range = [0.344000,0.700000]
Bin 4
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
20
40
60
80
100
120
140
160
180 / ndf 2χ 104.5 / 103
Prob 0.4401
N 7215± 1.562e+05
m 0.0005± 0.4971 σ 0.00063± 0.01407 ν 0.1± 1
0p 52.19± 99.84
1
p 17.23± 30.13
2p 329.8± 621.2
3
p 792.4± -1486
4p 510.3± 953
HERA II/NDF ~ 1.0145912χ
0.000545±mass = 0.497076
0.000632± = 0.014068σ 206±) in range = 2085
s
0 N(K
S/B = 18.712476
Range = [0.344000,0.700000]
Bin 5
Figu
reF.5:
Fits
toth
ein
variant
mass
distrib
ution
fromdata
inbin
sof
xC
BF
pfor
the
curren
them
isphere
inth
eB
reitFram
e.
155
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
50
100
150
200
250
300
/ ndf 2χ 141.3 / 104
Prob 0.008742
N 24286± 2.632e+05
m 0.0003± 0.4972
σ 0.000376± 0.007123
ν 0.448± 1.394
0
p 14.92± 15.62
1p 0.1313± 0.1598
2p 6.83± 48.41
3
p 17.2± -101.5
4p 13.06± 63.47
HERA II/NDF ~ 1.3590432χ
0.000284±mass = 0.497151
0.000376± = 0.007123σ 291±) in range = 1857
s
0 N(K
S/B = 1.790885
Range = [0.360000,0.700000]
Bin 1
/ ndf 2χ 141.3 / 104
Prob 0.008742
N 24286± 2.632e+05
m 0.0003± 0.4972
σ 0.000376± 0.007123
ν 0.448± 1.394
0
p 14.92± 15.62
1p 0.1313± 0.1598
2p 6.83± 48.41
3
p 17.2± -101.5
4p 13.06± 63.47
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
50
100
150
200
250
300
/ ndf 2χ 141.3 / 104
Prob 0.008742
N 24286± 2.632e+05
m 0.0003± 0.4972
σ 0.000376± 0.007123
ν 0.448± 1.394
0
p 14.92± 15.62
1p 0.1313± 0.1598
2p 6.83± 48.41
3
p 17.2± -101.5
4p 13.06± 63.47
HERA II/NDF ~ 1.3590432χ
0.000284±mass = 0.497151
0.000376± = 0.007123σ 291±) in range = 1857
s
0 N(K
S/B = 1.790885
Range = [0.360000,0.700000]
Bin 1
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7E
ntrie
s / 3
.000
000
MeV
0
100
200
300
400
500
/ ndf 2χ 128 / 109
Prob 0.103
N 15569± 4.173e+05
m 0.0002± 0.4969
σ 0.000220± 0.007777
ν 0.384± 3.485
0
p 0.0112± 0.0528
1p 0.0539± 0.2959
2p 2.54± 80.37
3
p 7.7± -156.7
4p 6.31± 94.35
HERA II/NDF ~ 1.1745172χ
0.000211±mass = 0.496889
0.000220± = 0.007777σ 216±) in range = 3245
s
0 N(K
S/B = 2.934986
Range = [0.345000,0.700000]
Bin 2
/ ndf 2χ 128 / 109
Prob 0.103
N 15569± 4.173e+05
m 0.0002± 0.4969
σ 0.000220± 0.007777
ν 0.384± 3.485
0
p 0.0112± 0.0528
1p 0.0539± 0.2959
2p 2.54± 80.37
3
p 7.7± -156.7
4p 6.31± 94.35
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7E
ntrie
s / 3
.000
000
MeV
0
100
200
300
400
500
/ ndf 2χ 128 / 109
Prob 0.103
N 15569± 4.173e+05
m 0.0002± 0.4969
σ 0.000220± 0.007777
ν 0.384± 3.485
0
p 0.0112± 0.0528
1p 0.0539± 0.2959
2p 2.54± 80.37
3
p 7.7± -156.7
4p 6.31± 94.35
HERA II/NDF ~ 1.1745172χ
0.000211±mass = 0.496889
0.000220± = 0.007777σ 216±) in range = 3245
s
0 N(K
S/B = 2.934986
Range = [0.345000,0.700000]
Bin 2
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500 / ndf 2χ 108.3 / 110
Prob 0.5285
N 18728± 3.965e+05
m 0.0002± 0.4973
σ 0.000259± 0.007799
ν 0.519± 2.556
0
p 15.67± 32.82
1p 0.0713± 0.4789
2p 4.36± 42.34
3
p 12.38± -81.82
4p 10.13± 45.64
HERA II/NDF ~ 0.9843792χ
0.000215±mass = 0.497348
0.000259± = 0.007799σ 254±) in range = 3090
s
0 N(K
S/B = 3.766627
Range = [0.344000,0.700000]
Bin 3
/ ndf 2χ 108.3 / 110
Prob 0.5285
N 18728± 3.965e+05
m 0.0002± 0.4973
σ 0.000259± 0.007799
ν 0.519± 2.556
0
p 15.67± 32.82
1p 0.0713± 0.4789
2p 4.36± 42.34
3
p 12.38± -81.82
4p 10.13± 45.64
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500 / ndf 2χ 108.3 / 110
Prob 0.5285
N 18728± 3.965e+05
m 0.0002± 0.4973
σ 0.000259± 0.007799
ν 0.519± 2.556
0
p 15.67± 32.82
1p 0.0713± 0.4789
2p 4.36± 42.34
3
p 12.38± -81.82
4p 10.13± 45.64
HERA II/NDF ~ 0.9843792χ
0.000215±mass = 0.497348
0.000259± = 0.007799σ 254±) in range = 3090
s
0 N(K
S/B = 3.766627
Range = [0.344000,0.700000]
Bin 3
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500 / ndf 2χ 108.8 / 110
Prob 0.5132
N 20271± 4.236e+05
m 0.0002± 0.4973
σ 0.000275± 0.008732
ν 0.384± 2.094
0
p 3.67± 20.12
1p 0.1123± 0.3721
2p 4.0± 31.5
3
p 13.79± -45.64
4p 11.75± 16.96
HERA II/NDF ~ 0.9894942χ
0.000215±mass = 0.497255
0.000275± = 0.008732σ 302±) in range = 3691
s
0 N(K
S/B = 5.725384
Range = [0.344000,0.700000]
Bin 4
/ ndf 2χ 108.8 / 110
Prob 0.5132
N 20271± 4.236e+05
m 0.0002± 0.4973
σ 0.000275± 0.008732
ν 0.384± 2.094
0
p 3.67± 20.12
1p 0.1123± 0.3721
2p 4.0± 31.5
3
p 13.79± -45.64
4p 11.75± 16.96
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500 / ndf 2χ 108.8 / 110
Prob 0.5132
N 20271± 4.236e+05
m 0.0002± 0.4973
σ 0.000275± 0.008732
ν 0.384± 2.094
0
p 3.67± 20.12
1p 0.1123± 0.3721
2p 4.0± 31.5
3
p 13.79± -45.64
4p 11.75± 16.96
HERA II/NDF ~ 0.9894942χ
0.000215±mass = 0.497255
0.000275± = 0.008732σ 302±) in range = 3691
s
0 N(K
S/B = 5.725384
Range = [0.344000,0.700000]
Bin 4
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
50
100
150
200
250
300
350
400
450
/ ndf 2χ 99.35 / 110
Prob 0.7571
N 22148± 4.103e+05
m 0.0002± 0.4978 σ 0.00030± 0.01047 ν 0.278± 1.465
0p 5.92± 20.94
1
p 0.1811± 0.5193
2p 5.88± 32.04
3
p 19.27± -47.59
4p 15.75± 18.41
HERA II/NDF ~ 0.9032082χ
0.000246±mass = 0.497767
0.000301± = 0.010472σ 382±) in range = 4244
s
0 N(K
S/B = 8.282987
Range = [0.344000,0.700000]
Bin 5
/ ndf 2χ 99.35 / 110
Prob 0.7571
N 22148± 4.103e+05
m 0.0002± 0.4978 σ 0.00030± 0.01047 ν 0.278± 1.465
0p 5.92± 20.94
1
p 0.1811± 0.5193
2p 5.88± 32.04
3
p 19.27± -47.59
4p 15.75± 18.41
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
50
100
150
200
250
300
350
400
450
/ ndf 2χ 99.35 / 110
Prob 0.7571
N 22148± 4.103e+05
m 0.0002± 0.4978 σ 0.00030± 0.01047 ν 0.278± 1.465
0p 5.92± 20.94
1
p 0.1811± 0.5193
2p 5.88± 32.04
3
p 19.27± -47.59
4p 15.75± 18.41
HERA II/NDF ~ 0.9032082χ
0.000246±mass = 0.497767
0.000301± = 0.010472σ 382±) in range = 4244
s
0 N(K
S/B = 8.282987
Range = [0.344000,0.700000]
Bin 5
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV0
5
10
15
20
25
30
35
/ ndf 2χ 62.84 / 91
Prob 0.9893
N 1810± 1.875e+04
m 0.0011± 0.4974 σ 0.00106± 0.01427 ν 1829.4± 132.1
0p 0.8282± 0.2704
1
p 0.4492± 0.1196
2p 19.00± 41.37
3
p 47.8± -67.1
4p 36.3± 33.5
/ ndf 2χ 141.3 / 104
Prob 0.008742
N 24286± 2.632e+05
m 0.0003± 0.4972
σ 0.000376± 0.007123
ν 0.448± 1.394
0
p 14.92± 15.62
1p 0.1313± 0.1598
2p 6.83± 48.41
3
p 17.2± -101.5
4p 13.06± 63.47
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
50
100
150
200
250
300
/ ndf 2χ 141.3 / 104
Prob 0.008742
N 24286± 2.632e+05
m 0.0003± 0.4972
σ 0.000376± 0.007123
ν 0.448± 1.394
0
p 14.92± 15.62
1p 0.1313± 0.1598
2p 6.83± 48.41
3
p 17.2± -101.5
4p 13.06± 63.47
HERA II/NDF ~ 1.3590432χ
0.000284±mass = 0.497151
0.000376± = 0.007123σ 291±) in range = 1857
s
0 N(K
S/B = 1.790885
Range = [0.360000,0.700000]
Bin 1
/ ndf 2χ 128 / 109
Prob 0.103
N 15569± 4.173e+05
m 0.0002± 0.4969
σ 0.000220± 0.007777
ν 0.384± 3.485
0
p 0.0112± 0.0528
1p 0.0539± 0.2959
2p 2.54± 80.37
3
p 7.7± -156.7
4p 6.31± 94.35
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7E
ntrie
s / 3
.000
000
MeV
0
100
200
300
400
500
/ ndf 2χ 128 / 109
Prob 0.103
N 15569± 4.173e+05
m 0.0002± 0.4969
σ 0.000220± 0.007777
ν 0.384± 3.485
0
p 0.0112± 0.0528
1p 0.0539± 0.2959
2p 2.54± 80.37
3
p 7.7± -156.7
4p 6.31± 94.35
HERA II/NDF ~ 1.1745172χ
0.000211±mass = 0.496889
0.000220± = 0.007777σ 216±) in range = 3245
s
0 N(K
S/B = 2.934986
Range = [0.345000,0.700000]
Bin 2
/ ndf 2χ 108.3 / 110
Prob 0.5285
N 18728± 3.965e+05
m 0.0002± 0.4973
σ 0.000259± 0.007799
ν 0.519± 2.556
0
p 15.67± 32.82
1p 0.0713± 0.4789
2p 4.36± 42.34
3
p 12.38± -81.82
4p 10.13± 45.64
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500 / ndf 2χ 108.3 / 110
Prob 0.5285
N 18728± 3.965e+05
m 0.0002± 0.4973
σ 0.000259± 0.007799
ν 0.519± 2.556
0
p 15.67± 32.82
1p 0.0713± 0.4789
2p 4.36± 42.34
3
p 12.38± -81.82
4p 10.13± 45.64
HERA II/NDF ~ 0.9843792χ
0.000215±mass = 0.497348
0.000259± = 0.007799σ 254±) in range = 3090
s
0 N(K
S/B = 3.766627
Range = [0.344000,0.700000]
Bin 3
/ ndf 2χ 108.8 / 110
Prob 0.5132
N 20271± 4.236e+05
m 0.0002± 0.4973
σ 0.000275± 0.008732
ν 0.384± 2.094
0
p 3.67± 20.12
1p 0.1123± 0.3721
2p 4.0± 31.5
3
p 13.79± -45.64
4p 11.75± 16.96
-) [GeV]π+,πM (0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500 / ndf 2χ 108.8 / 110
Prob 0.5132
N 20271± 4.236e+05
m 0.0002± 0.4973
σ 0.000275± 0.008732
ν 0.384± 2.094
0
p 3.67± 20.12
1p 0.1123± 0.3721
2p 4.0± 31.5
3
p 13.79± -45.64
4p 11.75± 16.96
HERA II/NDF ~ 0.9894942χ
0.000215±mass = 0.497255
0.000275± = 0.008732σ 302±) in range = 3691
s
0 N(K
S/B = 5.725384
Range = [0.344000,0.700000]
Bin 4
/ ndf 2χ 99.35 / 110
Prob 0.7571
N 22148± 4.103e+05
m 0.0002± 0.4978
σ 0.00030± 0.01047
ν 0.278± 1.465
0p 5.92± 20.94
1
p 0.1811± 0.5193
2p 5.88± 32.04
3
p 19.27± -47.59
4p 15.75± 18.41
-) [GeV]π+,πM (0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
50
100
150
200
250
300
350
400
450
/ ndf 2χ 99.35 / 110
Prob 0.7571
N 22148± 4.103e+05
m 0.0002± 0.4978
σ 0.00030± 0.01047
ν 0.278± 1.465
0p 5.92± 20.94
1
p 0.1811± 0.5193
2p 5.88± 32.04
3
p 19.27± -47.59
4p 15.75± 18.41
HERA II/NDF ~ 0.9032082χ
0.000246±mass = 0.497767
0.000301± = 0.010472σ 382±) in range = 4244
s
0 N(K
S/B = 8.282987
Range = [0.344000,0.700000]
Bin 5
/ ndf 2χ 62.84 / 91
Prob 0.9893
N 1810± 1.875e+04
m 0.0011± 0.4974
σ 0.00106± 0.01427
ν 1829.4± 132.1
0p 0.8282± 0.2704
1
p 0.4492± 0.1196
2p 19.00± 41.37
3
p 47.8± -67.1
4p 36.3± 33.5
-) [GeV]π+,πM (0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV0
5
10
15
20
25
30
35
/ ndf 2χ 62.84 / 91
Prob 0.9893
N 1810± 1.875e+04
m 0.0011± 0.4974
σ 0.00106± 0.01427
ν 1829.4± 132.1
0p 0.8282± 0.2704
1
p 0.4492± 0.1196
2p 19.00± 41.37
3
p 47.8± -67.1
4p 36.3± 33.5
/ ndf 2χ 141.3 / 104
Prob 0.008742
N 24286± 2.632e+05
m 0.0003± 0.4972
σ 0.000376± 0.007123
ν 0.448± 1.394
0p 14.92± 15.62
1
p 0.1313± 0.1598
2p 6.83± 48.41
3
p 17.2± -101.5
4p 13.06± 63.47
-) [GeV]π+,πM (0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
50
100
150
200
250
300
/ ndf 2χ 141.3 / 104
Prob 0.008742
N 24286± 2.632e+05
m 0.0003± 0.4972
σ 0.000376± 0.007123
ν 0.448± 1.394
0p 14.92± 15.62
1
p 0.1313± 0.1598
2p 6.83± 48.41
3
p 17.2± -101.5
4p 13.06± 63.47
HERA II/NDF ~ 1.3590432χ
0.000284±mass = 0.497151
0.000376± = 0.007123σ 291±) in range = 1857
s
0 N(K
S/B = 1.790885Range = [0.360000,0.700000]
Bin 1
/ ndf 2χ 128 / 109
Prob 0.103
N 15569± 4.173e+05
m 0.0002± 0.4969
σ 0.000220± 0.007777
ν 0.384± 3.485
0p 0.0112± 0.0528
1
p 0.0539± 0.2959
2p 2.54± 80.37
3
p 7.7± -156.7
4p 6.31± 94.35
-) [GeV]π+,πM (0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV0
100
200
300
400
500
/ ndf 2χ 128 / 109
Prob 0.103
N 15569± 4.173e+05
m 0.0002± 0.4969
σ 0.000220± 0.007777
ν 0.384± 3.485
0p 0.0112± 0.0528
1
p 0.0539± 0.2959
2p 2.54± 80.37
3
p 7.7± -156.7
4p 6.31± 94.35
HERA II/NDF ~ 1.1745172χ
0.000211±mass = 0.496889
0.000220± = 0.007777σ 216±) in range = 3245
s
0 N(K
S/B = 2.934986Range = [0.345000,0.700000]
Bin 2
/ ndf 2χ 108.3 / 110
Prob 0.5285
N 18728± 3.965e+05
m 0.0002± 0.4973
σ 0.000259± 0.007799
ν 0.519± 2.556
0p 15.67± 32.82
1
p 0.0713± 0.4789
2p 4.36± 42.34
3
p 12.38± -81.82
4p 10.13± 45.64
-) [GeV]π+,πM (0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500 / ndf 2χ 108.3 / 110
Prob 0.5285
N 18728± 3.965e+05
m 0.0002± 0.4973
σ 0.000259± 0.007799
ν 0.519± 2.556
0p 15.67± 32.82
1
p 0.0713± 0.4789
2p 4.36± 42.34
3
p 12.38± -81.82
4p 10.13± 45.64
HERA II/NDF ~ 0.9843792χ
0.000215±mass = 0.497348
0.000259± = 0.007799σ 254±) in range = 3090
s
0 N(K
S/B = 3.766627Range = [0.344000,0.700000]
Bin 3
/ ndf 2χ 108.8 / 110
Prob 0.5132
N 20271± 4.236e+05
m 0.0002± 0.4973
σ 0.000275± 0.008732
ν 0.384± 2.094
0p 3.67± 20.12
1
p 0.1123± 0.3721
2p 4.0± 31.5
3
p 13.79± -45.64
4p 11.75± 16.96
-) [GeV]π+,πM (0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500 / ndf 2χ 108.8 / 110
Prob 0.5132
N 20271± 4.236e+05
m 0.0002± 0.4973
σ 0.000275± 0.008732
ν 0.384± 2.094
0p 3.67± 20.12
1
p 0.1123± 0.3721
2p 4.0± 31.5
3
p 13.79± -45.64
4p 11.75± 16.96
HERA II/NDF ~ 0.9894942χ
0.000215±mass = 0.497255
0.000275± = 0.008732σ 302±) in range = 3691
s
0 N(K
S/B = 5.725384Range = [0.344000,0.700000]
Bin 4
/ ndf 2χ 99.35 / 110
Prob 0.7571
N 22148± 4.103e+05
m 0.0002± 0.4978 σ 0.00030± 0.01047
ν 0.278± 1.465
0p 5.92± 20.94
1
p 0.1811± 0.5193
2p 5.88± 32.04
3
p 19.27± -47.59
4p 15.75± 18.41
-) [GeV]π+,πM (0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
50
100
150
200
250
300
350
400
450
/ ndf 2χ 99.35 / 110
Prob 0.7571
N 22148± 4.103e+05
m 0.0002± 0.4978 σ 0.00030± 0.01047
ν 0.278± 1.465
0p 5.92± 20.94
1
p 0.1811± 0.5193
2p 5.88± 32.04
3
p 19.27± -47.59
4p 15.75± 18.41
HERA II/NDF ~ 0.9032082χ
0.000246±mass = 0.497767
0.000301± = 0.010472σ 382±) in range = 4244
s
0 N(K
S/B = 8.282987Range = [0.344000,0.700000]
Bin 5
/ ndf 2χ 62.84 / 91
Prob 0.9893
N 1810± 1.875e+04
m 0.0011± 0.4974 σ 0.00106± 0.01427
ν 1829.4± 132.1
0p 0.8282± 0.2704
1
p 0.4492± 0.1196
2p 19.00± 41.37
3
p 47.8± -67.1
4p 36.3± 33.5
-) [GeV]π+,πM (0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV0
5
10
15
20
25
30
35
/ ndf 2χ 62.84 / 91
Prob 0.9893
N 1810± 1.875e+04
m 0.0011± 0.4974 σ 0.00106± 0.01427
ν 1829.4± 132.1
0p 0.8282± 0.2704
1
p 0.4492± 0.1196
2p
Figu
reF.6:
Fits
toth
ein
variant
mass
distrib
ution
fromdata
inbin
sof
xT
BF
pfor
the
targethem
isphere
inth
eB
reitFram
e.
156A
PP
EN
DIX
F.
FIT
ST
OM
ASS
DIS
TR
IBU
TIO
NS
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
600 / ndf 2χ 130 / 109
Prob 0.08353
N 29890± 5.274e+05
m 0.0002± 0.4967
σ 0.000261± 0.008243
ν 0.325± 1.537
0
p 1.57± 28.22
1p 0.0591± 0.2837
2p 2.94± 48.89
3
p 10.4± -101.4
4p 9.1± 61.4
HERA II/NDF ~ 1.1922312χ
0.000207±mass = 0.496734
0.000261± = 0.008243σ 406±) in range = 4316
s
0 N(K
S/B = 2.850369
Range = [0.345000,0.700000]
Bin 1
/ ndf 2χ 130 / 109
Prob 0.08353
N 29890± 5.274e+05
m 0.0002± 0.4967
σ 0.000261± 0.008243
ν 0.325± 1.537
0
p 1.57± 28.22
1p 0.0591± 0.2837
2p 2.94± 48.89
3
p 10.4± -101.4
4p 9.1± 61.4
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
600 / ndf 2χ 130 / 109
Prob 0.08353
N 29890± 5.274e+05
m 0.0002± 0.4967
σ 0.000261± 0.008243
ν 0.325± 1.537
0
p 1.57± 28.22
1p 0.0591± 0.2837
2p 2.94± 48.89
3
p 10.4± -101.4
4p 9.1± 61.4
HERA II/NDF ~ 1.1922312χ
0.000207±mass = 0.496734
0.000261± = 0.008243σ 406±) in range = 4316
s
0 N(K
S/B = 2.850369
Range = [0.345000,0.700000]
Bin 1
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
600
700 / ndf 2χ 111.9 / 110
Prob 0.4319
N 32556± 6.148e+05
m 0.0002± 0.4965
σ 0.000254± 0.008728
ν 0.217± 1.273
0
p 2.1± 25.1
1p 0.0986± 0.4588
2p 4.10± 46.84
3
p 13.76± -97.46
4p 11.70± 60.54
HERA II/NDF ~ 1.0171832χ
0.000190±mass = 0.496463
0.000254± = 0.008728σ 477±) in range = 5284
s
0 N(K
S/B = 6.249479
Range = [0.344000,0.700000]
Bin 2
/ ndf 2χ 111.9 / 110
Prob 0.4319
N 32556± 6.148e+05
m 0.0002± 0.4965
σ 0.000254± 0.008728
ν 0.217± 1.273
0
p 2.1± 25.1
1p 0.0986± 0.4588
2p 4.10± 46.84
3
p 13.76± -97.46
4p 11.70± 60.54
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
600
700 / ndf 2χ 111.9 / 110
Prob 0.4319
N 32556± 6.148e+05
m 0.0002± 0.4965
σ 0.000254± 0.008728
ν 0.217± 1.273
0
p 2.1± 25.1
1p 0.0986± 0.4588
2p 4.10± 46.84
3
p 13.76± -97.46
4p 11.70± 60.54
HERA II/NDF ~ 1.0171832χ
0.000190±mass = 0.496463
0.000254± = 0.008728σ 477±) in range = 5284
s
0 N(K
S/B = 6.249479
Range = [0.344000,0.700000]
Bin 2
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
600
700 / ndf 2χ 112.9 / 109
Prob 0.3808
N 17733± 6.874e+05
m 0.0002± 0.4967
σ 0.000265± 0.008968
ν 0.1± 1
0
p 3.81± 20.11
1p 0.2375± 0.6983
2p 7.66± 40.83
3
p 23.2± -72
4p 18.04± 36.61
HERA II/NDF ~ 1.0354152χ
0.000183±mass = 0.496700
0.000265± = 0.008968σ 358±) in range = 5962
s
0 N(K
S/B = 9.374162
Range = [0.344000,0.700000]
Bin 3
/ ndf 2χ 112.9 / 109
Prob 0.3808
N 17733± 6.874e+05
m 0.0002± 0.4967
σ 0.000265± 0.008968
ν 0.1± 1
0
p 3.81± 20.11
1p 0.2375± 0.6983
2p 7.66± 40.83
3
p 23.2± -72
4p 18.04± 36.61
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
600
700 / ndf 2χ 112.9 / 109
Prob 0.3808
N 17733± 6.874e+05
m 0.0002± 0.4967
σ 0.000265± 0.008968
ν 0.1± 1
0
p 3.81± 20.11
1p 0.2375± 0.6983
2p 7.66± 40.83
3
p 23.2± -72
4p 18.04± 36.61
HERA II/NDF ~ 1.0354152χ
0.000183±mass = 0.496700
0.000265± = 0.008968σ 358±) in range = 5962
s
0 N(K
S/B = 9.374162
Range = [0.344000,0.700000]
Bin 3
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
50
100
150
200
250
300
350
400
450 / ndf 2χ 134.2 / 109
Prob 0.05073
N 22251± 4.147e+05
m 0.0003± 0.4966 σ 0.00037± 0.01118 ν 0.207± 1.221
0p 11.26± 25.36
1
p 0.460± 1.069
2p 13.05± 39.01
3
p 38.86± -63.75
4p 29.4± 27.6
HERA II/NDF ~ 1.2316512χ
0.000266±mass = 0.496632
0.000367± = 0.011184σ 442±) in range = 4529
s
0 N(K
S/B = 11.033285
Range = [0.344000,0.700000]
Bin 4
/ ndf 2χ 134.2 / 109
Prob 0.05073
N 22251± 4.147e+05
m 0.0003± 0.4966 σ 0.00037± 0.01118 ν 0.207± 1.221
0p 11.26± 25.36
1
p 0.460± 1.069
2p 13.05± 39.01
3
p 38.86± -63.75
4p 29.4± 27.6
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
50
100
150
200
250
300
350
400
450 / ndf 2χ 134.2 / 109
Prob 0.05073
N 22251± 4.147e+05
m 0.0003± 0.4966 σ 0.00037± 0.01118 ν 0.207± 1.221
0p 11.26± 25.36
1
p 0.460± 1.069
2p 13.05± 39.01
3
p 38.86± -63.75
4p 29.4± 27.6
HERA II/NDF ~ 1.2316512χ
0.000266±mass = 0.496632
0.000367± = 0.011184σ 442±) in range = 4529
s
0 N(K
S/B = 11.033285
Range = [0.344000,0.700000]
Bin 4
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
20
40
60
80
100
120
140
160
180
200 / ndf 2χ 114.3 / 106
Prob 0.2733
N 7518± 1.762e+05
m 0.0004± 0.4981 σ 0.00083± 0.01215 ν 0.1± 1
0p 8.14± 13.98
1
p 2.457± 3.435
2p 66.85± 89.31
3
p 180.7± -182.7
4p 128.2± 100.9
HERA II/NDF ~ 1.0785292χ
0.000424±mass = 0.498139
0.000830± = 0.012146σ 248±) in range = 2045
s
0 N(K
S/B = 7.613454
Range = [0.344000,0.700000]
Bin 5
Figu
reF.7:
Fits
toth
ein
variant
mass
distrib
ution
fromdata
inbin
sof
pC
BF
Tfor
the
curren
them
isphere
inth
eB
reitFram
e.
157
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
20
40
60
80
100
120
140
160
/ ndf 2χ 147 / 109
Prob 0.008888
N 21552± 1.417e+05
m 0.0004± 0.4967
σ 0.000533± 0.006248
ν 1.270± 1.047
0
p 3.12± 42.03
1p 0.0753± 0.3124
2p 3.4± 46.9
3
p 11.8± -106.1
4p 10.19± 70.31
HERA II/NDF ~ 1.3490402χ
0.000381±mass = 0.496703
0.000533± = 0.006248σ 238±) in range = 868
s
0 N(K
S/B = 1.153838
Range = [0.345000,0.700000]
Bin 1
/ ndf 2χ 147 / 109
Prob 0.008888
N 21552± 1.417e+05
m 0.0004± 0.4967
σ 0.000533± 0.006248
ν 1.270± 1.047
0
p 3.12± 42.03
1p 0.0753± 0.3124
2p 3.4± 46.9
3
p 11.8± -106.1
4p 10.19± 70.31
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
20
40
60
80
100
120
140
160
/ ndf 2χ 147 / 109
Prob 0.008888
N 21552± 1.417e+05
m 0.0004± 0.4967
σ 0.000533± 0.006248
ν 1.270± 1.047
0
p 3.12± 42.03
1p 0.0753± 0.3124
2p 3.4± 46.9
3
p 11.8± -106.1
4p 10.19± 70.31
HERA II/NDF ~ 1.3490402χ
0.000381±mass = 0.496703
0.000533± = 0.006248σ 238±) in range = 868
s
0 N(K
S/B = 1.153838
Range = [0.345000,0.700000]
Bin 1
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7E
ntrie
s / 3
.000
000
MeV
0
50
100
150
200
250
300
350
400 / ndf 2χ 108.3 / 104
Prob 0.3672
N 17654± 3.152e+05
m 0.0002± 0.4971
σ 0.000279± 0.007217
ν 0.790± 2.951
0
p 2.75± 25.26
1p 0.12134± 0.04328
2p 4.25± 39.26
3
p 13.50± -75.18
4p 10.94± 42.48
HERA II/NDF ~ 1.0412012χ
0.000233±mass = 0.497071
0.000279± = 0.007217σ 220±) in range = 2273
s
0 N(K
S/B = 2.092653
Range = [0.360000,0.700000]
Bin 2
/ ndf 2χ 108.3 / 104
Prob 0.3672
N 17654± 3.152e+05
m 0.0002± 0.4971
σ 0.000279± 0.007217
ν 0.790± 2.951
0
p 2.75± 25.26
1p 0.12134± 0.04328
2p 4.25± 39.26
3
p 13.50± -75.18
4p 10.94± 42.48
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7E
ntrie
s / 3
.000
000
MeV
0
50
100
150
200
250
300
350
400 / ndf 2χ 108.3 / 104
Prob 0.3672
N 17654± 3.152e+05
m 0.0002± 0.4971
σ 0.000279± 0.007217
ν 0.790± 2.951
0
p 2.75± 25.26
1p 0.12134± 0.04328
2p 4.25± 39.26
3
p 13.50± -75.18
4p 10.94± 42.48
HERA II/NDF ~ 1.0412012χ
0.000233±mass = 0.497071
0.000279± = 0.007217σ 220±) in range = 2273
s
0 N(K
S/B = 2.092653
Range = [0.360000,0.700000]
Bin 2
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
600
/ ndf 2χ 100.7 / 104
Prob 0.5743
N 18564± 5.178e+05
m 0.000± 0.497
σ 0.000207± 0.008223
ν 0.701± 3.732
0
p 1.98± 16.02
1p 0.1442± 0.1445
2p 4.74± 37.14
3
p 14.65± -61.88
4p 11.57± 30.02
HERA II/NDF ~ 0.9679532χ
0.000186±mass = 0.497023
0.000207± = 0.008223σ 264±) in range = 4257
s
0 N(K
S/B = 3.708699
Range = [0.360000,0.700000]
Bin 3
/ ndf 2χ 100.7 / 104
Prob 0.5743
N 18564± 5.178e+05
m 0.000± 0.497
σ 0.000207± 0.008223
ν 0.701± 3.732
0
p 1.98± 16.02
1p 0.1442± 0.1445
2p 4.74± 37.14
3
p 14.65± -61.88
4p 11.57± 30.02
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
600
/ ndf 2χ 100.7 / 104
Prob 0.5743
N 18564± 5.178e+05
m 0.000± 0.497
σ 0.000207± 0.008223
ν 0.701± 3.732
0
p 1.98± 16.02
1p 0.1442± 0.1445
2p 4.74± 37.14
3
p 14.65± -61.88
4p 11.57± 30.02
HERA II/NDF ~ 0.9679532χ
0.000186±mass = 0.497023
0.000207± = 0.008223σ 264±) in range = 4257
s
0 N(K
S/B = 3.708699
Range = [0.360000,0.700000]
Bin 3
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
600
700 / ndf 2χ 109.5 / 110
Prob 0.4961
N 23308± 5.937e+05
m 0.0002± 0.4974 σ 0.00023± 0.00864 ν 0.287± 2.081
0p 101.4± 172.6
1
p 0.0970± 0.4927
2p 5.4± 25.9
3
p 14.81± -42.41
4p 11.77± 18.23
HERA II/NDF ~ 0.9952592χ
0.000179±mass = 0.497419
0.000228± = 0.008640σ 346±) in range = 5118
s
0 N(K
S/B = 7.226262
Range = [0.344000,0.700000]
Bin 4
/ ndf 2χ 109.5 / 110
Prob 0.4961
N 23308± 5.937e+05
m 0.0002± 0.4974 σ 0.00023± 0.00864 ν 0.287± 2.081
0p 101.4± 172.6
1
p 0.0970± 0.4927
2p 5.4± 25.9
3
p 14.81± -42.41
4p 11.77± 18.23
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
600
700 / ndf 2χ 109.5 / 110
Prob 0.4961
N 23308± 5.937e+05
m 0.0002± 0.4974 σ 0.00023± 0.00864 ν 0.287± 2.081
0p 101.4± 172.6
1
p 0.0970± 0.4927
2p 5.4± 25.9
3
p 14.81± -42.41
4p 11.77± 18.23
HERA II/NDF ~ 0.9952592χ
0.000179±mass = 0.497419
0.000228± = 0.008640σ 346±) in range = 5118
s
0 N(K
S/B = 7.226262
Range = [0.344000,0.700000]
Bin 4
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
50
100
150
200
250
300
350
400
450 / ndf 2χ 106.1 / 109
Prob 0.5615
N 23896± 3.648e+05
m 0.0003± 0.4979 σ 0.00042± 0.01222 ν 0.241± 1.163
0p 2.439± 4.536
1
p 0.3399± 0.4476
2p 9.69± 28.14
3
p 31.08± -29.66
4p 24.565± 4.239
HERA II/NDF ~ 0.9731572χ
0.000296±mass = 0.497945
0.000421± = 0.012221σ 500±) in range = 4324
s
0 N(K
S/B = 15.284040
Range = [0.344000,0.700000]
Bin 5
Figu
reF.8:
Fit
toth
ein
variant
mass
distrib
ution
fromdata
inbin
sof
pT
BF
Tfor
the
targethem
isphere
inth
eB
reitFram
e.
158A
PP
EN
DIX
F.
FIT
ST
OM
ASS
DIS
TR
IBU
TIO
NS
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
600
700 / ndf 2χ 142.7 / 110
Prob 0.01973
N 6655± 6.523e+05
m 0.0000± 0.4982
σ 0.000047± 0.006554
ν 0.064± 1.907
0
p 2.25± 95.76
1p 0.0240± 0.3779
2p 1.09± 33.66
3
p 3.7± -67.7
4p 3.20± 38.51
Django MC/NDF ~ 1.2969002χ
0.000039±mass = 0.498236
0.000047± = 0.006554σ 75±) in range = 4267
s
0 N(K
S/B = 8.008803
Range = [0.344000,0.700000]
Bin 1
/ ndf 2χ 142.7 / 110
Prob 0.01973
N 6655± 6.523e+05
m 0.0000± 0.4982
σ 0.000047± 0.006554
ν 0.064± 1.907
0
p 2.25± 95.76
1p 0.0240± 0.3779
2p 1.09± 33.66
3
p 3.7± -67.7
4p 3.20± 38.51
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
600
700 / ndf 2χ 142.7 / 110
Prob 0.01973
N 6655± 6.523e+05
m 0.0000± 0.4982
σ 0.000047± 0.006554
ν 0.064± 1.907
0
p 2.25± 95.76
1p 0.0240± 0.3779
2p 1.09± 33.66
3
p 3.7± -67.7
4p 3.20± 38.51
Django MC/NDF ~ 1.2969002χ
0.000039±mass = 0.498236
0.000047± = 0.006554σ 75±) in range = 4267
s
0 N(K
S/B = 8.008803
Range = [0.344000,0.700000]
Bin 1
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
200
400
600
800
1000
1200 / ndf 2χ 182.6 / 110
Prob 1.67e-05
N 8798± 1.042e+06
m 0.0000± 0.4982
σ 0.000040± 0.006661
ν 0.054± 1.911
0
p 16.1± 139
1p 0.0170± 0.3685
2p 1.11± 32.58
3
p 3.18± -62.36
4p 2.60± 33.43
Django MC/NDF ~ 1.6602262χ
0.000032±mass = 0.498155
0.000040± = 0.006661σ 101±) in range = 6929
s
0 N(K
S/B = 7.475634
Range = [0.344000,0.700000]
Bin 2
/ ndf 2χ 182.6 / 110
Prob 1.67e-05
N 8798± 1.042e+06
m 0.0000± 0.4982
σ 0.000040± 0.006661
ν 0.054± 1.911
0
p 16.1± 139
1p 0.0170± 0.3685
2p 1.11± 32.58
3
p 3.18± -62.36
4p 2.60± 33.43
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
200
400
600
800
1000
1200 / ndf 2χ 182.6 / 110
Prob 1.67e-05
N 8798± 1.042e+06
m 0.0000± 0.4982
σ 0.000040± 0.006661
ν 0.054± 1.911
0
p 16.1± 139
1p 0.0170± 0.3685
2p 1.11± 32.58
3
p 3.18± -62.36
4p 2.60± 33.43
Django MC/NDF ~ 1.6602262χ
0.000032±mass = 0.498155
0.000040± = 0.006661σ 101±) in range = 6929
s
0 N(K
S/B = 7.475634
Range = [0.344000,0.700000]
Bin 2
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
200
400
600
800
1000
1200
1400
1600
/ ndf 2χ 182.7 / 110
Prob 1.659e-05
N 10359± 1.58e+06
m 0.0000± 0.4982
σ 0.000030± 0.006758
ν 0.037± 1.731
0
p 6.88± 52.15
1p 0.0135± 0.3751
2p 0.95± 42.79
3
p 2.52± -85.17
4p 2.02± 49.74
Django MC/NDF ~ 1.6605132χ
0.000025±mass = 0.498210
0.000030± = 0.006758σ 120±) in range = 10646
s
0 N(K
S/B = 7.292815
Range = [0.344000,0.700000]
Bin 3
/ ndf 2χ 182.7 / 110
Prob 1.659e-05
N 10359± 1.58e+06
m 0.0000± 0.4982
σ 0.000030± 0.006758
ν 0.037± 1.731
0
p 6.88± 52.15
1p 0.0135± 0.3751
2p 0.95± 42.79
3
p 2.52± -85.17
4p 2.02± 49.74
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
200
400
600
800
1000
1200
1400
1600
/ ndf 2χ 182.7 / 110
Prob 1.659e-05
N 10359± 1.58e+06
m 0.0000± 0.4982
σ 0.000030± 0.006758
ν 0.037± 1.731
0
p 6.88± 52.15
1p 0.0135± 0.3751
2p 0.95± 42.79
3
p 2.52± -85.17
4p 2.02± 49.74
Django MC/NDF ~ 1.6605132χ
0.000025±mass = 0.498210
0.000030± = 0.006758σ 120±) in range = 10646
s
0 N(K
S/B = 7.292815
Range = [0.344000,0.700000]
Bin 3
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
200
400
600
800
1000
1200
1400
1600
/ ndf 2χ 167.2 / 109
Prob 0.0002852
N 9620± 1.532e+06
m 0.0000± 0.4982
σ 0.000029± 0.007003
ν 0.034± 1.612
0
p 36.8± 217
1p 0.0151± 0.3307
2p 1.11± 32.06
3
p 2.67± -60.56
4p 2.04± 32.43
Django MC/NDF ~ 1.5341412χ
0.000023±mass = 0.498189
0.000029± = 0.007003σ 114±) in range = 10680
s
0 N(K
S/B = 6.391179
Range = [0.345000,0.700000]
Bin 4
/ ndf 2χ 167.2 / 109
Prob 0.0002852
N 9620± 1.532e+06
m 0.0000± 0.4982
σ 0.000029± 0.007003
ν 0.034± 1.612
0
p 36.8± 217
1p 0.0151± 0.3307
2p 1.11± 32.06
3
p 2.67± -60.56
4p 2.04± 32.43
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
200
400
600
800
1000
1200
1400
1600
/ ndf 2χ 167.2 / 109
Prob 0.0002852
N 9620± 1.532e+06
m 0.0000± 0.4982
σ 0.000029± 0.007003
ν 0.034± 1.612
0
p 36.8± 217
1p 0.0151± 0.3307
2p 1.11± 32.06
3
p 2.67± -60.56
4p 2.04± 32.43
Django MC/NDF ~ 1.5341412χ
0.000023±mass = 0.498189
0.000029± = 0.007003σ 114±) in range = 10680
s
0 N(K
S/B = 6.391179
Range = [0.345000,0.700000]
Bin 4
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
600
700
800 / ndf 2χ 181.6 / 110
Prob 2.086e-05
N 6466± 7.128e+05
m 0.0000± 0.4982
σ 0.000042± 0.007379
ν 0.042± 1.546
0
p 0.357± 3.303
1p 0.015± 0.345
2p 1.01± 53.49
3
p 2.8± -100.3
4p 2.30± 56.44
Django MC/NDF ~ 1.6506282χ
0.000033±mass = 0.498178
0.000042± = 0.007379σ 80±) in range = 5229
s
0 N(K
S/B = 4.822199
Range = [0.344000,0.700000]
Bin 5
/ ndf 2χ 181.6 / 110
Prob 2.086e-05
N 6466± 7.128e+05
m 0.0000± 0.4982
σ 0.000042± 0.007379
ν 0.042± 1.546
0
p 0.357± 3.303
1p 0.015± 0.345
2p 1.01± 53.49
3
p 2.8± -100.3
4p 2.30± 56.44
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
600
700
800 / ndf 2χ 181.6 / 110
Prob 2.086e-05
N 6466± 7.128e+05
m 0.0000± 0.4982
σ 0.000042± 0.007379
ν 0.042± 1.546
0
p 0.357± 3.303
1p 0.015± 0.345
2p 1.01± 53.49
3
p 2.8± -100.3
4p 2.30± 56.44
Django MC/NDF ~ 1.6506282χ
0.000033±mass = 0.498178
0.000042± = 0.007379σ 80±) in range = 5229
s
0 N(K
S/B = 4.822199
Range = [0.344000,0.700000]
Bin 5
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
50
100
150
200
250
300
/ ndf 2χ 140.3 / 110
Prob 0.02727
N 4358± 2.898e+05
m 0.0001± 0.4983
σ 0.000073± 0.008215
ν 0.067± 1.313
0
p 34.3± 155.5
1p 0.0152± 0.3398
2p 1.48± 30.58
3
p 3.43± -61.36
4p 2.59± 35.66
Django MC/NDF ~ 1.2751192χ
0.000057±mass = 0.498282
0.000073± = 0.008215σ 61±) in range = 2350
s
0 N(K
S/B = 3.313297
Range = [0.344000,0.700000]
Bin 6
Figu
reF.9:
Fits
toth
ein
variant
mass
distrib
ution
fromD
jango
Mon
teC
arloin
bin
sof
Q2.
159
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
600
700
800
900
/ ndf 2χ 182.5 / 110
Prob 1.71e-05
N 6828± 8.571e+05
m 0.0000± 0.4983
σ 0.000037± 0.006616
ν 0.055± 2.027
0
p 37.5± 121.9
1p 0.0178± 0.3711
2p 1.92± 33.42
3
p 4.23± -66.19
4p 3.09± 36.86
Django MC/NDF ~ 1.6592092χ
0.000031±mass = 0.498311
0.000037± = 0.006616σ 78±) in range = 5662
s
0 N(K
S/B = 7.802170
Range = [0.344000,0.700000]
Bin 1
/ ndf 2χ 182.5 / 110
Prob 1.71e-05
N 6828± 8.571e+05
m 0.0000± 0.4983
σ 0.000037± 0.006616
ν 0.055± 2.027
0
p 37.5± 121.9
1p 0.0178± 0.3711
2p 1.92± 33.42
3
p 4.23± -66.19
4p 3.09± 36.86
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
600
700
800
900
/ ndf 2χ 182.5 / 110
Prob 1.71e-05
N 6828± 8.571e+05
m 0.0000± 0.4983
σ 0.000037± 0.006616
ν 0.055± 2.027
0
p 37.5± 121.9
1p 0.0178± 0.3711
2p 1.92± 33.42
3
p 4.23± -66.19
4p 3.09± 36.86
Django MC/NDF ~ 1.6592092χ
0.000031±mass = 0.498311
0.000037± = 0.006616σ 78±) in range = 5662
s
0 N(K
S/B = 7.802170
Range = [0.344000,0.700000]
Bin 1
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7E
ntrie
s / 3
.000
000
MeV
0
500
1000
1500
2000
2500
/ ndf 2χ 216.7 / 109
Prob 4.026e-09
N 12558± 2.393e+06
m 0.0000± 0.4982
σ 0.000024± 0.006658
ν 0.031± 1.775
0
p 7.54± 45.55
1p 0.0144± 0.3265
2p 1.11± 43.32
3
p 2.62± -83.16
4p 1.96± 47.06
Django MC/NDF ~ 1.9876682χ
0.000020±mass = 0.498170
0.000024± = 0.006658σ 143±) in range = 15888
s
0 N(K
S/B = 7.431128
Range = [0.345000,0.700000]
Bin 2
/ ndf 2χ 216.7 / 109
Prob 4.026e-09
N 12558± 2.393e+06
m 0.0000± 0.4982
σ 0.000024± 0.006658
ν 0.031± 1.775
0
p 7.54± 45.55
1p 0.0144± 0.3265
2p 1.11± 43.32
3
p 2.62± -83.16
4p 1.96± 47.06
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7E
ntrie
s / 3
.000
000
MeV
0
500
1000
1500
2000
2500
/ ndf 2χ 216.7 / 109
Prob 4.026e-09
N 12558± 2.393e+06
m 0.0000± 0.4982
σ 0.000024± 0.006658
ν 0.031± 1.775
0
p 7.54± 45.55
1p 0.0144± 0.3265
2p 1.11± 43.32
3
p 2.62± -83.16
4p 1.96± 47.06
Django MC/NDF ~ 1.9876682χ
0.000020±mass = 0.498170
0.000024± = 0.006658σ 143±) in range = 15888
s
0 N(K
S/B = 7.431128
Range = [0.345000,0.700000]
Bin 2
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
200
400
600
800
1000
1200
1400
1600
1800
2000 / ndf 2χ 184.3 / 109
Prob 8.905e-06
N 11613± 1.816e+06
m 0.0000± 0.4982
σ 0.00003± 0.00705 ν 0.03± 1.54
0p 355.3± 1539
1
p 0.0154± 0.3763
2p 1.32± 23.42
3
p 2.92± -45.92
4p 2.14± 24.05
Django MC/NDF ~ 1.6906402χ
0.000023±mass = 0.498176
0.000029± = 0.007050σ 139±) in range = 12733
s
0 N(K
S/B = 6.422628
Range = [0.345000,0.700000]
Bin 3
/ ndf 2χ 184.3 / 109
Prob 8.905e-06
N 11613± 1.816e+06
m 0.0000± 0.4982
σ 0.00003± 0.00705 ν 0.03± 1.54
0p 355.3± 1539
1
p 0.0154± 0.3763
2p 1.32± 23.42
3
p 2.92± -45.92
4p 2.14± 24.05
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
200
400
600
800
1000
1200
1400
1600
1800
2000 / ndf 2χ 184.3 / 109
Prob 8.905e-06
N 11613± 1.816e+06
m 0.0000± 0.4982
σ 0.00003± 0.00705 ν 0.03± 1.54
0p 355.3± 1539
1
p 0.0154± 0.3763
2p 1.32± 23.42
3
p 2.92± -45.92
4p 2.14± 24.05
Django MC/NDF ~ 1.6906402χ
0.000023±mass = 0.498176
0.000029± = 0.007050σ 139±) in range = 12733
s
0 N(K
S/B = 6.422628
Range = [0.345000,0.700000]
Bin 3
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
600
700
800
/ ndf 2χ 193.7 / 110
Prob 1.479e-06
N 7019± 7.642e+05
m 0.0000± 0.4982
σ 0.000043± 0.007904
ν 0.046± 1.447
0
p 20.8± 149.3
1p 0.011± 0.347
2p 0.96± 34.83
3
p 2.33± -67.94
4p 1.80± 38.53
Django MC/NDF ~ 1.7606662χ
0.000032±mass = 0.498190
0.000043± = 0.007904σ 93±) in range = 5989
s
0 N(K
S/B = 3.895350
Range = [0.344000,0.700000]
Bin 4
Figu
reF.10:
Fits
toth
ein
variant
mass
distrib
ution
fromD
jango
Mon
teC
arloin
bin
sof
x.
160A
PP
EN
DIX
F.
FIT
ST
OM
ASS
DIS
TR
IBU
TIO
NS
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
200
400
600
800
1000
/ ndf 2χ 218 / 110
Prob 4.051e-09
N 6621± 1.008e+06
m 0.0000± 0.4983
σ 0.000032± 0.006652
ν 0.051± 2.269
0
p 28.25± 50.18
1p 0.0196± 0.3306
2p 3.1± 36.2
3
p 6.13± -68.29
4p 4.05± 36.58
Django MC/NDF ~ 1.9819762χ
0.000027±mass = 0.498289
0.000032± = 0.006652σ 77±) in range = 6697
s
0 N(K
S/B = 9.132876
Range = [0.344000,0.700000]
Bin 1
/ ndf 2χ 218 / 110
Prob 4.051e-09
N 6621± 1.008e+06
m 0.0000± 0.4983
σ 0.000032± 0.006652
ν 0.051± 2.269
0
p 28.25± 50.18
1p 0.0196± 0.3306
2p 3.1± 36.2
3
p 6.13± -68.29
4p 4.05± 36.58
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
200
400
600
800
1000
/ ndf 2χ 218 / 110
Prob 4.051e-09
N 6621± 1.008e+06
m 0.0000± 0.4983
σ 0.000032± 0.006652
ν 0.051± 2.269
0
p 28.25± 50.18
1p 0.0196± 0.3306
2p 3.1± 36.2
3
p 6.13± -68.29
4p 4.05± 36.58
Django MC/NDF ~ 1.9819762χ
0.000027±mass = 0.498289
0.000032± = 0.006652σ 77±) in range = 6697
s
0 N(K
S/B = 9.132876
Range = [0.344000,0.700000]
Bin 1
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
200
400
600
800
1000
1200
1400 / ndf 2χ 213.3 / 110
Prob 1.358e-08
N 10406± 1.323e+06
m 0.0000± 0.4981
σ 0.00003± 0.00645 ν 0.031± 1.326
0p 21.97± 75.07
1
p 0.0185± 0.4221
2p 1.77± 37.55
3
p 3.93± -72.41
4p 2.89± 39.95
Django MC/NDF ~ 1.9386562χ
0.000026±mass = 0.498072
0.000033± = 0.006450σ 116±) in range = 8455
s
0 N(K
S/B = 8.349084
Range = [0.344000,0.700000]
Bin 2
/ ndf 2χ 213.3 / 110
Prob 1.358e-08
N 10406± 1.323e+06
m 0.0000± 0.4981
σ 0.00003± 0.00645 ν 0.031± 1.326
0p 21.97± 75.07
1
p 0.0185± 0.4221
2p 1.77± 37.55
3
p 3.93± -72.41
4p 2.89± 39.95
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
200
400
600
800
1000
1200
1400 / ndf 2χ 213.3 / 110
Prob 1.358e-08
N 10406± 1.323e+06
m 0.0000± 0.4981
σ 0.00003± 0.00645 ν 0.031± 1.326
0p 21.97± 75.07
1
p 0.0185± 0.4221
2p 1.77± 37.55
3
p 3.93± -72.41
4p 2.89± 39.95
Django MC/NDF ~ 1.9386562χ
0.000026±mass = 0.498072
0.000033± = 0.006450σ 116±) in range = 8455
s
0 N(K
S/B = 8.349084
Range = [0.344000,0.700000]
Bin 2
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
200
400
600
800
1000
1200
1400 / ndf 2χ 221 / 110
Prob 1.888e-09
N 11064± 1.342e+06
m 0.0000± 0.4982
σ 0.000034± 0.006822
ν 0.030± 1.224
0
p 1.19± 64.87
1p 0.0163± 0.4188
2p 0.72± 40.03
3
p 2.52± -78.26
4p 2.20± 44.27
Django MC/NDF ~ 2.0088542χ
0.000027±mass = 0.498234
0.000034± = 0.006822σ 128±) in range = 9041
s
0 N(K
S/B = 7.401748
Range = [0.344000,0.700000]
Bin 3
/ ndf 2χ 221 / 110
Prob 1.888e-09
N 11064± 1.342e+06
m 0.0000± 0.4982
σ 0.000034± 0.006822
ν 0.030± 1.224
0
p 1.19± 64.87
1p 0.0163± 0.4188
2p 0.72± 40.03
3
p 2.52± -78.26
4p 2.20± 44.27
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
200
400
600
800
1000
1200
1400 / ndf 2χ 221 / 110
Prob 1.888e-09
N 11064± 1.342e+06
m 0.0000± 0.4982
σ 0.000034± 0.006822
ν 0.030± 1.224
0
p 1.19± 64.87
1p 0.0163± 0.4188
2p 0.72± 40.03
3
p 2.52± -78.26
4p 2.20± 44.27
Django MC/NDF ~ 2.0088542χ
0.000027±mass = 0.498234
0.000034± = 0.006822σ 128±) in range = 9041
s
0 N(K
S/B = 7.401748
Range = [0.344000,0.700000]
Bin 3
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
200
400
600
800
1000
1200
1400
/ ndf 2χ 143.1 / 110
Prob 0.01854
N 8943± 1.328e+06
m 0.0000± 0.4982
σ 0.000031± 0.006756
ν 0.04± 1.85
0
p 26.1± 164.5
1p 0.0118± 0.3379
2p 0.98± 34.96
3
p 2.29± -68.97
4p 1.76± 39.38
Django MC/NDF ~ 1.3009962χ
0.000026±mass = 0.498201
0.000031± = 0.006756σ 103±) in range = 8954
s
0 N(K
S/B = 5.788455
Range = [0.344000,0.700000]
Bin 4
/ ndf 2χ 143.1 / 110
Prob 0.01854
N 8943± 1.328e+06
m 0.0000± 0.4982
σ 0.000031± 0.006756
ν 0.04± 1.85
0
p 26.1± 164.5
1p 0.0118± 0.3379
2p 0.98± 34.96
3
p 2.29± -68.97
4p 1.76± 39.38
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
200
400
600
800
1000
1200
1400
/ ndf 2χ 143.1 / 110
Prob 0.01854
N 8943± 1.328e+06
m 0.0000± 0.4982
σ 0.000031± 0.006756
ν 0.04± 1.85
0
p 26.1± 164.5
1p 0.0118± 0.3379
2p 0.98± 34.96
3
p 2.29± -68.97
4p 1.76± 39.38
Django MC/NDF ~ 1.3009962χ
0.000026±mass = 0.498201
0.000031± = 0.006756σ 103±) in range = 8954
s
0 N(K
S/B = 5.788455
Range = [0.344000,0.700000]
Bin 4
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
200
400
600
800
1000 / ndf 2χ 184.9 / 109
Prob 7.767e-06
N 7054± 8.634e+05
m 0.0000± 0.4982
σ 0.000045± 0.008263
ν 0.082± 2.389
0
p 12.09± 86.54
1p 0.0140± 0.3018
2p 1.02± 38.29
3
p 2.52± -73.36
4p 1.92± 41.21
Django MC/NDF ~ 1.6964192χ
0.000037±mass = 0.498205
0.000045± = 0.008263σ 98±) in range = 7126
s
0 N(K
S/B = 3.720535
Range = [0.345000,0.700000]
Bin 5
Figu
reF.11:
Fits
toth
ein
variant
mass
distrib
ution
fromD
jango
Mon
teC
arloin
bin
sof
η.
161
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
200
400
600
800
1000
1200
1400 / ndf 2χ 146.4 / 104
Prob 0.003892
N 8095± 1.145e+06
m 0.0000± 0.4984
σ 0.00003± 0.00579 ν 0.106± 3.189
0p 5.97± 30.46
1
p 0.0183± 0.2022
2p 1.21± 49.34
3
p 2.75± -98.74
4p 1.99± 57.72
Django MC/NDF ~ 1.4079882χ
0.000025±mass = 0.498387
0.000030± = 0.005790σ 81±) in range = 6629
s
0 N(K
S/B = 2.367369
Range = [0.360000,0.700000]
Bin 1
/ ndf 2χ 146.4 / 104
Prob 0.003892
N 8095± 1.145e+06
m 0.0000± 0.4984
σ 0.00003± 0.00579 ν 0.106± 3.189
0p 5.97± 30.46
1
p 0.0183± 0.2022
2p 1.21± 49.34
3
p 2.75± -98.74
4p 1.99± 57.72
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
200
400
600
800
1000
1200
1400 / ndf 2χ 146.4 / 104
Prob 0.003892
N 8095± 1.145e+06
m 0.0000± 0.4984
σ 0.00003± 0.00579 ν 0.106± 3.189
0p 5.97± 30.46
1
p 0.0183± 0.2022
2p 1.21± 49.34
3
p 2.75± -98.74
4p 1.99± 57.72
Django MC/NDF ~ 1.4079882χ
0.000025±mass = 0.498387
0.000030± = 0.005790σ 81±) in range = 6629
s
0 N(K
S/B = 2.367369
Range = [0.360000,0.700000]
Bin 1
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7E
ntrie
s / 3
.000
000
MeV
0
200
400
600
800
1000
/ ndf 2χ 145.9 / 110
Prob 0.0124
N 6929± 9.881e+05
m 0.0000± 0.4982
σ 0.000033± 0.006287
ν 0.075± 2.749
0
p 7.44± 49.68
1p 0.0159± 0.3829
2p 1.10± 39.22
3
p 2.82± -75.85
4p 2.20± 43.06
Django MC/NDF ~ 1.3267812χ
0.000028±mass = 0.498248
0.000033± = 0.006287σ 76±) in range = 6210
s
0 N(K
S/B = 6.199042
Range = [0.344000,0.700000]
Bin 2
/ ndf 2χ 145.9 / 110
Prob 0.0124
N 6929± 9.881e+05
m 0.0000± 0.4982
σ 0.000033± 0.006287
ν 0.075± 2.749
0
p 7.44± 49.68
1p 0.0159± 0.3829
2p 1.10± 39.22
3
p 2.82± -75.85
4p 2.20± 43.06
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7E
ntrie
s / 3
.000
000
MeV
0
200
400
600
800
1000
/ ndf 2χ 145.9 / 110
Prob 0.0124
N 6929± 9.881e+05
m 0.0000± 0.4982
σ 0.000033± 0.006287
ν 0.075± 2.749
0
p 7.44± 49.68
1p 0.0159± 0.3829
2p 1.10± 39.22
3
p 2.82± -75.85
4p 2.20± 43.06
Django MC/NDF ~ 1.3267812χ
0.000028±mass = 0.498248
0.000033± = 0.006287σ 76±) in range = 6210
s
0 N(K
S/B = 6.199042
Range = [0.344000,0.700000]
Bin 2
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
200
400
600
800
1000
1200
/ ndf 2χ 189.9 / 110
Prob 3.422e-06
N 7539± 1.163e+06
m 0.0000± 0.4981
σ 0.000032± 0.006786
ν 0.048± 2.157
0
p 16.59± 63.93
1p 0.0211± 0.4232
2p 1.66± 34.41
3
p 3.76± -63.74
4p 2.75± 34.65
Django MC/NDF ~ 1.7267092χ
0.000026±mass = 0.498129
0.000032± = 0.006786σ 89±) in range = 7881
s
0 N(K
S/B = 10.025541
Range = [0.344000,0.700000]
Bin 3
/ ndf 2χ 189.9 / 110
Prob 3.422e-06
N 7539± 1.163e+06
m 0.0000± 0.4981
σ 0.000032± 0.006786
ν 0.048± 2.157
0
p 16.59± 63.93
1p 0.0211± 0.4232
2p 1.66± 34.41
3
p 3.76± -63.74
4p 2.75± 34.65
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
200
400
600
800
1000
1200
/ ndf 2χ 189.9 / 110
Prob 3.422e-06
N 7539± 1.163e+06
m 0.0000± 0.4981
σ 0.000032± 0.006786
ν 0.048± 2.157
0
p 16.59± 63.93
1p 0.0211± 0.4232
2p 1.66± 34.41
3
p 3.76± -63.74
4p 2.75± 34.65
Django MC/NDF ~ 1.7267092χ
0.000026±mass = 0.498129
0.000032± = 0.006786σ 89±) in range = 7881
s
0 N(K
S/B = 10.025541
Range = [0.344000,0.700000]
Bin 3
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
200
400
600
800
1000
/ ndf 2χ 147.7 / 110
Prob 0.009555
N 7819± 1.077e+06
m 0.0000± 0.4981
σ 0.000037± 0.007435
ν 0.035± 1.608
0
p 2.19± 43.59
1p 0.0333± 0.4912
2p 1.10± 33.03
3
p 3.63± -58.85
4p 2.99± 31.37
Django MC/NDF ~ 1.3429212χ
0.000030±mass = 0.498054
0.000037± = 0.007435σ 100±) in range = 7968
s
0 N(K
S/B = 14.698323
Range = [0.344000,0.700000]
Bin 4
/ ndf 2χ 147.7 / 110
Prob 0.009555
N 7819± 1.077e+06
m 0.0000± 0.4981
σ 0.000037± 0.007435
ν 0.035± 1.608
0
p 2.19± 43.59
1p 0.0333± 0.4912
2p 1.10± 33.03
3
p 3.63± -58.85
4p 2.99± 31.37
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
200
400
600
800
1000
/ ndf 2χ 147.7 / 110
Prob 0.009555
N 7819± 1.077e+06
m 0.0000± 0.4981
σ 0.000037± 0.007435
ν 0.035± 1.608
0
p 2.19± 43.59
1p 0.0333± 0.4912
2p 1.10± 33.03
3
p 3.63± -58.85
4p 2.99± 31.37
Django MC/NDF ~ 1.3429212χ
0.000030±mass = 0.498054
0.000037± = 0.007435σ 100±) in range = 7968
s
0 N(K
S/B = 14.698323
Range = [0.344000,0.700000]
Bin 4
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
600
700
800
900 / ndf 2χ 182.5 / 110
Prob 1.711e-05
N 8022± 8.769e+05
m 0.0000± 0.4981
σ 0.000049± 0.008539
ν 0.027± 1.083
0
p 0.504± 8.398
1p 0.0830± 0.8357
2p 2.61± 46.45
3
p 7.71± -87.78
4p 5.85± 50.48
Django MC/NDF ~ 1.6591862χ
0.000037±mass = 0.498110
0.000049± = 0.008539σ 121±) in range = 7303
s
0 N(K
S/B = 19.699603
Range = [0.344000,0.700000]
Bin 5
/ ndf 2χ 182.5 / 110
Prob 1.711e-05
N 8022± 8.769e+05
m 0.0000± 0.4981
σ 0.000049± 0.008539
ν 0.027± 1.083
0
p 0.504± 8.398
1p 0.0830± 0.8357
2p 2.61± 46.45
3
p 7.71± -87.78
4p 5.85± 50.48
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
600
700
800
900 / ndf 2χ 182.5 / 110
Prob 1.711e-05
N 8022± 8.769e+05
m 0.0000± 0.4981
σ 0.000049± 0.008539
ν 0.027± 1.083
0
p 0.504± 8.398
1p 0.0830± 0.8357
2p 2.61± 46.45
3
p 7.71± -87.78
4p 5.85± 50.48
Django MC/NDF ~ 1.6591862χ
0.000037±mass = 0.498110
0.000049± = 0.008539σ 121±) in range = 7303
s
0 N(K
S/B = 19.699603
Range = [0.344000,0.700000]
Bin 5
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV0
100
200
300
400
500 / ndf 2χ 334.5 / 109
Prob 9.477e-25
N 3330± 4.824e+05
m 0.0001± 0.4984 σ 0.00009± 0.01038 ν 0.0± 1
0p 8.53± 31.07
1
p 0.098± 1.287
2p 3.36± 49.24
3
p 9.0± -91.6
4p 6.62± 47.28
Django MC/NDF ~ 3.0692522χ
0.000058±mass = 0.498385
0.000091± = 0.010382σ 75±) in range = 4818
s
0 N(K
S/B = 7.711979
Range = [0.345000,0.700000]
Bin 6
Figu
reF.12:
Fits
toth
ein
variant
mass
distrib
ution
fromD
jango
Mon
teC
arloin
bin
sof
pT.
162A
PP
EN
DIX
F.
FIT
ST
OM
ASS
DIS
TR
IBU
TIO
NS
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
600
700
800
/ ndf 2χ 141.9 / 109
Prob 0.01869
N 6378± 6.947e+05
m 0.0000± 0.4982
σ 0.000040± 0.006214
ν 0.086± 2.351
0
p 10.11± 81.94
1p 0.0125± 0.3045
2p 0.90± 42.37
3
p 2.31± -87.32
4p 1.81± 51.91
Django MC/NDF ~ 1.3019432χ
0.000033±mass = 0.498178
0.000040± = 0.006214σ 68±) in range = 4314
s
0 N(K
S/B = 2.684429
Range = [0.345000,0.700000]
Bin 1
/ ndf 2χ 141.9 / 109
Prob 0.01869
N 6378± 6.947e+05
m 0.0000± 0.4982
σ 0.000040± 0.006214
ν 0.086± 2.351
0
p 10.11± 81.94
1p 0.0125± 0.3045
2p 0.90± 42.37
3
p 2.31± -87.32
4p 1.81± 51.91
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
600
700
800
/ ndf 2χ 141.9 / 109
Prob 0.01869
N 6378± 6.947e+05
m 0.0000± 0.4982
σ 0.000040± 0.006214
ν 0.086± 2.351
0
p 10.11± 81.94
1p 0.0125± 0.3045
2p 0.90± 42.37
3
p 2.31± -87.32
4p 1.81± 51.91
Django MC/NDF ~ 1.3019432χ
0.000033±mass = 0.498178
0.000040± = 0.006214σ 68±) in range = 4314
s
0 N(K
S/B = 2.684429
Range = [0.345000,0.700000]
Bin 1
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
200
400
600
800
1000
/ ndf 2χ 152.8 / 110
Prob 0.004359
N 7599± 9.539e+05
m 0.0000± 0.4981
σ 0.0000± 0.0068 ν 0.041± 1.628
0p 0.44± 17.22
1
p 0.0237± 0.4041
2p 0.92± 41.63
3
p 3.07± -78.03
4p 2.59± 43.52
Django MC/NDF ~ 1.3892232χ
0.000031±mass = 0.498090
0.000037± = 0.006800σ 89±) in range = 6459
s
0 N(K
S/B = 9.213581
Range = [0.344000,0.700000]
Bin 2
/ ndf 2χ 152.8 / 110
Prob 0.004359
N 7599± 9.539e+05
m 0.0000± 0.4981
σ 0.0000± 0.0068 ν 0.041± 1.628
0p 0.44± 17.22
1
p 0.0237± 0.4041
2p 0.92± 41.63
3
p 3.07± -78.03
4p 2.59± 43.52
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
200
400
600
800
1000
/ ndf 2χ 152.8 / 110
Prob 0.004359
N 7599± 9.539e+05
m 0.0000± 0.4981
σ 0.0000± 0.0068 ν 0.041± 1.628
0p 0.44± 17.22
1
p 0.0237± 0.4041
2p 0.92± 41.63
3
p 3.07± -78.03
4p 2.59± 43.52
Django MC/NDF ~ 1.3892232χ
0.000031±mass = 0.498090
0.000037± = 0.006800σ 89±) in range = 6459
s
0 N(K
S/B = 9.213581
Range = [0.344000,0.700000]
Bin 2
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
600
700 / ndf 2χ 151 / 110
Prob 0.00583
N 7348± 7.096e+05
m 0.0000± 0.4982
σ 0.000048± 0.007414
ν 0.034± 1.186
0
p 5.68± 10.65
1p 0.0658± 0.6843
2p 4.04± 42.84
3
p 9.53± -81.06
4p 6.84± 45.83
Django MC/NDF ~ 1.3724342χ
0.000038±mass = 0.498157
0.000048± = 0.007414σ 94±) in range = 5178
s
0 N(K
S/B = 17.177114
Range = [0.344000,0.700000]
Bin 3
/ ndf 2χ 151 / 110
Prob 0.00583
N 7348± 7.096e+05
m 0.0000± 0.4982
σ 0.000048± 0.007414
ν 0.034± 1.186
0
p 5.68± 10.65
1p 0.0658± 0.6843
2p 4.04± 42.84
3
p 9.53± -81.06
4p 6.84± 45.83
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
600
700 / ndf 2χ 151 / 110
Prob 0.00583
N 7348± 7.096e+05
m 0.0000± 0.4982
σ 0.000048± 0.007414
ν 0.034± 1.186
0
p 5.68± 10.65
1p 0.0658± 0.6843
2p 4.04± 42.84
3
p 9.53± -81.06
4p 6.84± 45.83
Django MC/NDF ~ 1.3724342χ
0.000038±mass = 0.498157
0.000048± = 0.007414σ 94±) in range = 5178
s
0 N(K
S/B = 17.177114
Range = [0.344000,0.700000]
Bin 3
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
/ ndf 2χ 219.4 / 110
Prob 2.813e-09
N 6168± 5.117e+05
m 0.0000± 0.4981
σ 0.000064± 0.008063
ν 0.034± 1.056
0
p 8.43± 24.67
1p 0.148± 1.455
2p 4.36± 52.66
3
p 12.3± -105.1
4p 9.23± 58.83
Django MC/NDF ~ 1.9948602χ
0.000048±mass = 0.498101
0.000064± = 0.008063σ 89±) in range = 4022
s
0 N(K
S/B = 14.128829
Range = [0.344000,0.700000]
Bin 4
/ ndf 2χ 219.4 / 110
Prob 2.813e-09
N 6168± 5.117e+05
m 0.0000± 0.4981
σ 0.000064± 0.008063
ν 0.034± 1.056
0
p 8.43± 24.67
1p 0.148± 1.455
2p 4.36± 52.66
3
p 12.3± -105.1
4p 9.23± 58.83
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
/ ndf 2χ 219.4 / 110
Prob 2.813e-09
N 6168± 5.117e+05
m 0.0000± 0.4981
σ 0.000064± 0.008063
ν 0.034± 1.056
0
p 8.43± 24.67
1p 0.148± 1.455
2p 4.36± 52.66
3
p 12.3± -105.1
4p 9.23± 58.83
Django MC/NDF ~ 1.9948602χ
0.000048±mass = 0.498101
0.000064± = 0.008063σ 89±) in range = 4022
s
0 N(K
S/B = 14.128829
Range = [0.344000,0.700000]
Bin 4
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
20
40
60
80
100
120
140
160
180
200
/ ndf 2χ 160.8 / 110
Prob 0.001145
N 3995± 2.102e+05
m 0.0001± 0.4983
σ 0.000112± 0.008924
ν 0.052± 1.013
0
p 7.99± 14.58
1p 0.27± 1.57
2p 9.13± 46.34
3
p 23.54± -80.16
4p 16.79± 35.75
Django MC/NDF ~ 1.4619152χ
0.000080±mass = 0.498294
0.000112± = 0.008924σ 65±) in range = 1816
s
0 N(K
S/B = 11.103964
Range = [0.344000,0.700000]
Bin 5
Figu
reF.13:
Fits
toth
ein
variant
mass
distrib
ution
fromD
jango
Mon
teC
arloin
bin
sof
xC
BF
pfor
the
curren
them
isphere
inth
eB
reitFram
e.
163
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
50
100
150
200
250
300
350
/ ndf 2χ 95.03 / 101
Prob 0.6485
N 4268± 3.102e+05
m 0.0001± 0.4983
σ 0.000061± 0.006066
ν 0.204± 3.094
0
p 0.56± 16.65
1p 0.0451± 0.2212
2p 1.5± 45.5
3
p 4.43± -90.33
4p 3.48± 52.41
Django MC/NDF ~ 0.9409012χ
0.000050±mass = 0.498338
0.000061± = 0.006066σ 44±) in range = 1881
s
0 N(K
S/B = 2.071586
Range = [0.370000,0.700000]
Bin 1
/ ndf 2χ 95.03 / 101
Prob 0.6485
N 4268± 3.102e+05
m 0.0001± 0.4983
σ 0.000061± 0.006066
ν 0.204± 3.094
0
p 0.56± 16.65
1p 0.0451± 0.2212
2p 1.5± 45.5
3
p 4.43± -90.33
4p 3.48± 52.41
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
50
100
150
200
250
300
350
/ ndf 2χ 95.03 / 101
Prob 0.6485
N 4268± 3.102e+05
m 0.0001± 0.4983
σ 0.000061± 0.006066
ν 0.204± 3.094
0
p 0.56± 16.65
1p 0.0451± 0.2212
2p 1.5± 45.5
3
p 4.43± -90.33
4p 3.48± 52.41
Django MC/NDF ~ 0.9409012χ
0.000050±mass = 0.498338
0.000061± = 0.006066σ 44±) in range = 1881
s
0 N(K
S/B = 2.071586
Range = [0.370000,0.700000]
Bin 1
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7E
ntrie
s / 3
.000
000
MeV
0
100
200
300
400
500
600
700 / ndf 2χ 121.6 / 110
Prob 0.211
N 5900± 6.158e+05
m 0.0000± 0.4983
σ 0.000043± 0.006168
ν 0.090± 2.466
0
p 14.98± 84.58
1p 0.0165± 0.3513
2p 1.3± 38
3
p 3.3± -78.6
4p 2.57± 46.77
Django MC/NDF ~ 1.1057832χ
0.000036±mass = 0.498317
0.000043± = 0.006168σ 63±) in range = 3796
s
0 N(K
S/B = 4.780039
Range = [0.344000,0.700000]
Bin 2
/ ndf 2χ 121.6 / 110
Prob 0.211
N 5900± 6.158e+05
m 0.0000± 0.4983
σ 0.000043± 0.006168
ν 0.090± 2.466
0
p 14.98± 84.58
1p 0.0165± 0.3513
2p 1.3± 38
3
p 3.3± -78.6
4p 2.57± 46.77
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7E
ntrie
s / 3
.000
000
MeV
0
100
200
300
400
500
600
700 / ndf 2χ 121.6 / 110
Prob 0.211
N 5900± 6.158e+05
m 0.0000± 0.4983
σ 0.000043± 0.006168
ν 0.090± 2.466
0
p 14.98± 84.58
1p 0.0165± 0.3513
2p 1.3± 38
3
p 3.3± -78.6
4p 2.57± 46.77
Django MC/NDF ~ 1.1057832χ
0.000036±mass = 0.498317
0.000043± = 0.006168σ 63±) in range = 3796
s
0 N(K
S/B = 4.780039
Range = [0.344000,0.700000]
Bin 2
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
600
/ ndf 2χ 173.7 / 110
Prob 0.0001027
N 5755± 5.959e+05
m 0.0000± 0.4982
σ 0.000045± 0.006471
ν 0.074± 2.202
0
p 26.5± 139.4
1p 0.0195± 0.3712
2p 1.48± 30.72
3
p 3.83± -61.04
4p 3.01± 34.41
Django MC/NDF ~ 1.5795072χ
0.000037±mass = 0.498230
0.000045± = 0.006471σ 64±) in range = 3853
s
0 N(K
S/B = 6.768148
Range = [0.344000,0.700000]
Bin 3
/ ndf 2χ 173.7 / 110
Prob 0.0001027
N 5755± 5.959e+05
m 0.0000± 0.4982
σ 0.000045± 0.006471
ν 0.074± 2.202
0
p 26.5± 139.4
1p 0.0195± 0.3712
2p 1.48± 30.72
3
p 3.83± -61.04
4p 3.01± 34.41
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
600
/ ndf 2χ 173.7 / 110
Prob 0.0001027
N 5755± 5.959e+05
m 0.0000± 0.4982
σ 0.000045± 0.006471
ν 0.074± 2.202
0
p 26.5± 139.4
1p 0.0195± 0.3712
2p 1.48± 30.72
3
p 3.83± -61.04
4p 3.01± 34.41
Django MC/NDF ~ 1.5795072χ
0.000037±mass = 0.498230
0.000045± = 0.006471σ 64±) in range = 3853
s
0 N(K
S/B = 6.768148
Range = [0.344000,0.700000]
Bin 3
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
600
700 / ndf 2χ 127.8 / 110
Prob 0.1176
N 5792± 6.204e+05
m 0.0000± 0.4982 σ 0.00005± 0.00702 ν 0.062± 1.959
0p 12.65± 33.75
1
p 0.0245± 0.4046
2p 2.43± 36.54
3
p 5.43± -69.99
4p 3.95± 39.48
Django MC/NDF ~ 1.1621182χ
0.000038±mass = 0.498249
0.000046± = 0.007020σ 70±) in range = 4347
s
0 N(K
S/B = 9.041011
Range = [0.344000,0.700000]
Bin 4
/ ndf 2χ 127.8 / 110
Prob 0.1176
N 5792± 6.204e+05
m 0.0000± 0.4982 σ 0.00005± 0.00702 ν 0.062± 1.959
0p 12.65± 33.75
1
p 0.0245± 0.4046
2p 2.43± 36.54
3
p 5.43± -69.99
4p 3.95± 39.48
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
600
700 / ndf 2χ 127.8 / 110
Prob 0.1176
N 5792± 6.204e+05
m 0.0000± 0.4982 σ 0.00005± 0.00702 ν 0.062± 1.959
0p 12.65± 33.75
1
p 0.0245± 0.4046
2p 2.43± 36.54
3
p 5.43± -69.99
4p 3.95± 39.48
Django MC/NDF ~ 1.1621182χ
0.000038±mass = 0.498249
0.000046± = 0.007020σ 70±) in range = 4347
s
0 N(K
S/B = 9.041011
Range = [0.344000,0.700000]
Bin 4
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
600 / ndf 2χ 169.3 / 110
Prob 0.0002439
N 5636± 5.542e+05
m 0.0000± 0.4982
σ 0.000054± 0.008147
ν 0.054± 1.629
0
p 3.28± 10.69
1p 0.042± 0.459
2p 2.39± 36.96
3
p 6.08± -63.37
4p 4.6± 32.2
Django MC/NDF ~ 1.5389062χ
0.000044±mass = 0.498223
0.000054± = 0.008147σ 78±) in range = 4489
s
0 N(K
S/B = 12.400990
Range = [0.344000,0.700000]
Bin 5
/ ndf 2χ 169.3 / 110
Prob 0.0002439
N 5636± 5.542e+05
m 0.0000± 0.4982
σ 0.000054± 0.008147
ν 0.054± 1.629
0
p 3.28± 10.69
1p 0.042± 0.459
2p 2.39± 36.96
3
p 6.08± -63.37
4p 4.6± 32.2
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
600 / ndf 2χ 169.3 / 110
Prob 0.0002439
N 5636± 5.542e+05
m 0.0000± 0.4982
σ 0.000054± 0.008147
ν 0.054± 1.629
0
p 3.28± 10.69
1p 0.042± 0.459
2p 2.39± 36.96
3
p 6.08± -63.37
4p 4.6± 32.2
Django MC/NDF ~ 1.5389062χ
0.000044±mass = 0.498223
0.000054± = 0.008147σ 78±) in range = 4489
s
0 N(K
S/B = 12.400990
Range = [0.344000,0.700000]
Bin 5
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV0
5
10
15
20
25
30
35
40
/ ndf 2χ 141.1 / 104
Prob 0.009124
N 951± 3.962e+04
m 0.0002± 0.4987 σ 0.0003± 0.0112 ν 0.028± 1.013
0p 9.11± 10.47
1
p 0.770± 1.368
2p 19.06± 37.03
3
p 54.90± -74.11
4p 39.60± 42.97
Django MC/NDF ~ 1.3563562χ
0.000195±mass = 0.498712
0.000294± = 0.011195σ 22±) in range = 424
s
0 N(K
S/B = 22.400183
Range = [0.360000,0.700000]
Bin 6
Figu
reF.14:
Fits
toth
ein
variant
mass
distrib
ution
fromD
jango
Mon
teC
arloin
bin
sof
xT
BF
pfor
the
targethem
isphere
inth
eB
reitFram
e.
164A
PP
EN
DIX
F.
FIT
ST
OM
ASS
DIS
TR
IBU
TIO
NS
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
600
700
800 / ndf 2χ 142.9 / 110
Prob 0.0192
N 7153± 6.84e+05
m 0.0000± 0.4981
σ 0.000045± 0.006516
ν 0.080± 2.009
0
p 14.1± 127.7
1p 0.0110± 0.3426
2p 0.88± 40.22
3
p 2.4± -84.2
4p 1.99± 49.76
Django MC/NDF ~ 1.2987062χ
0.000037±mass = 0.498087
0.000045± = 0.006516σ 78±) in range = 4451
s
0 N(K
S/B = 3.324243
Range = [0.344000,0.700000]
Bin 1
/ ndf 2χ 142.9 / 110
Prob 0.0192
N 7153± 6.84e+05
m 0.0000± 0.4981
σ 0.000045± 0.006516
ν 0.080± 2.009
0
p 14.1± 127.7
1p 0.0110± 0.3426
2p 0.88± 40.22
3
p 2.4± -84.2
4p 1.99± 49.76
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
600
700
800 / ndf 2χ 142.9 / 110
Prob 0.0192
N 7153± 6.84e+05
m 0.0000± 0.4981
σ 0.000045± 0.006516
ν 0.080± 2.009
0
p 14.1± 127.7
1p 0.0110± 0.3426
2p 0.88± 40.22
3
p 2.4± -84.2
4p 1.99± 49.76
Django MC/NDF ~ 1.2987062χ
0.000037±mass = 0.498087
0.000045± = 0.006516σ 78±) in range = 4451
s
0 N(K
S/B = 3.324243
Range = [0.344000,0.700000]
Bin 1
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
600
700
800
/ ndf 2χ 142.6 / 110
Prob 0.01981
N 6835± 7.611e+05
m 0.0000± 0.4981
σ 0.000041± 0.006738
ν 0.049± 1.687
0
p 1043.6± 2198
1p 0.015± 0.474
2p 2.55± 17.81
3
p 4.87± -36.73
4p 3.15± 18.93
Django MC/NDF ~ 1.2966402χ
0.000034±mass = 0.498123
0.000041± = 0.006738σ 79±) in range = 5111
s
0 N(K
S/B = 6.887736
Range = [0.344000,0.700000]
Bin 2
/ ndf 2χ 142.6 / 110
Prob 0.01981
N 6835± 7.611e+05
m 0.0000± 0.4981
σ 0.000041± 0.006738
ν 0.049± 1.687
0
p 1043.6± 2198
1p 0.015± 0.474
2p 2.55± 17.81
3
p 4.87± -36.73
4p 3.15± 18.93
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
600
700
800
/ ndf 2χ 142.6 / 110
Prob 0.01981
N 6835± 7.611e+05
m 0.0000± 0.4981
σ 0.000041± 0.006738
ν 0.049± 1.687
0
p 1043.6± 2198
1p 0.015± 0.474
2p 2.55± 17.81
3
p 4.87± -36.73
4p 3.15± 18.93
Django MC/NDF ~ 1.2966402χ
0.000034±mass = 0.498123
0.000041± = 0.006738σ 79±) in range = 5111
s
0 N(K
S/B = 6.887736
Range = [0.344000,0.700000]
Bin 2
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
600
700
800
/ ndf 2χ 178.9 / 110
Prob 3.631e-05
N 7962± 8.135e+05
m 0.0000± 0.4981
σ 0.000043± 0.007041
ν 0.038± 1.326
0
p 1.16± 26.55
1p 0.0314± 0.4177
2p 1.10± 34.22
3
p 3.71± -60.04
4p 3.12± 31.12
Django MC/NDF ~ 1.6263682χ
0.000034±mass = 0.498139
0.000043± = 0.007041σ 95±) in range = 5670
s
0 N(K
S/B = 11.323935
Range = [0.344000,0.700000]
Bin 3
/ ndf 2χ 178.9 / 110
Prob 3.631e-05
N 7962± 8.135e+05
m 0.0000± 0.4981
σ 0.000043± 0.007041
ν 0.038± 1.326
0
p 1.16± 26.55
1p 0.0314± 0.4177
2p 1.10± 34.22
3
p 3.71± -60.04
4p 3.12± 31.12
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
600
700
800
/ ndf 2χ 178.9 / 110
Prob 3.631e-05
N 7962± 8.135e+05
m 0.0000± 0.4981
σ 0.000043± 0.007041
ν 0.038± 1.326
0
p 1.16± 26.55
1p 0.0314± 0.4177
2p 1.10± 34.22
3
p 3.71± -60.04
4p 3.12± 31.12
Django MC/NDF ~ 1.6263682χ
0.000034±mass = 0.498139
0.000043± = 0.007041σ 95±) in range = 5670
s
0 N(K
S/B = 11.323935
Range = [0.344000,0.700000]
Bin 3
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
600 / ndf 2χ 170.4 / 110
Prob 0.0001973
N 6752± 5.782e+05
m 0.0000± 0.4982
σ 0.000056± 0.007814
ν 0.04± 1.11
0
p 4.90± 10.52
1p 0.0788± 0.7578
2p 3.62± 40.68
3
p 9.02± -71.31
4p 6.60± 36.31
Django MC/NDF ~ 1.5490102χ
0.000043±mass = 0.498160
0.000056± = 0.007814σ 92±) in range = 4424
s
0 N(K
S/B = 14.298769
Range = [0.344000,0.700000]
Bin 4
/ ndf 2χ 170.4 / 110
Prob 0.0001973
N 6752± 5.782e+05
m 0.0000± 0.4982
σ 0.000056± 0.007814
ν 0.04± 1.11
0
p 4.90± 10.52
1p 0.0788± 0.7578
2p 3.62± 40.68
3
p 9.02± -71.31
4p 6.60± 36.31
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
600 / ndf 2χ 170.4 / 110
Prob 0.0001973
N 6752± 5.782e+05
m 0.0000± 0.4982
σ 0.000056± 0.007814
ν 0.04± 1.11
0
p 4.90± 10.52
1p 0.0788± 0.7578
2p 3.62± 40.68
3
p 9.02± -71.31
4p 6.60± 36.31
Django MC/NDF ~ 1.5490102χ
0.000043±mass = 0.498160
0.000056± = 0.007814σ 92±) in range = 4424
s
0 N(K
S/B = 14.298769
Range = [0.344000,0.700000]
Bin 4
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
50
100
150
200
250 / ndf 2χ 199 / 109
Prob 3.18e-07
N 2336± 2.461e+05
m 0.0001± 0.4983
σ 0.000097± 0.008789
ν 0.0± 1
0
p 1.60± 4.21
1p 0.200± 1.338
2p 6.50± 54.62
3
p 17.5± -103.1
4p 12.7± 55.7
Django MC/NDF ~ 1.8254872χ
0.000068±mass = 0.498289
0.000097± = 0.008789σ 43±) in range = 2093
s
0 N(K
S/B = 11.731857
Range = [0.345000,0.700000]
Bin 5
Figu
reF.15:
Fits
toth
ein
variant
mass
distrib
ution
fromD
jango
Mon
teC
arloin
bin
sof
pC
BF
Tfor
the
curren
them
isphere
inth
eB
reitFram
e.
165
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
20
40
60
80
100
120
140
160
180 / ndf 2χ 129.9 / 110
Prob 0.09478
N 3042± 1.44e+05
m 0.0001± 0.4984
σ 0.00009± 0.00558 ν 0.405± 3.474
0p 8.76± 56.09
1
p 0.0175± 0.3517
2p 0.96± 42.26
3
p 2.64± -90.51
4p 2.2± 55.5
Django MC/NDF ~ 1.1807932χ
0.000075±mass = 0.498413
0.000091± = 0.005580σ 30±) in range = 803
s
0 N(K
S/B = 1.200464
Range = [0.344000,0.700000]
Bin 1
/ ndf 2χ 129.9 / 110
Prob 0.09478
N 3042± 1.44e+05
m 0.0001± 0.4984
σ 0.00009± 0.00558 ν 0.405± 3.474
0p 8.76± 56.09
1
p 0.0175± 0.3517
2p 0.96± 42.26
3
p 2.64± -90.51
4p 2.2± 55.5
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
20
40
60
80
100
120
140
160
180 / ndf 2χ 129.9 / 110
Prob 0.09478
N 3042± 1.44e+05
m 0.0001± 0.4984
σ 0.00009± 0.00558 ν 0.405± 3.474
0p 8.76± 56.09
1
p 0.0175± 0.3517
2p 0.96± 42.26
3
p 2.64± -90.51
4p 2.2± 55.5
Django MC/NDF ~ 1.1807932χ
0.000075±mass = 0.498413
0.000091± = 0.005580σ 30±) in range = 803
s
0 N(K
S/B = 1.200464
Range = [0.344000,0.700000]
Bin 1
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7E
ntrie
s / 3
.000
000
MeV
0
100
200
300
400
500 / ndf 2χ 120 / 108
Prob 0.2018
N 4951± 4.339e+05
m 0.0000± 0.4983
σ 0.000051± 0.006048
ν 0.160± 3.118
0
p 16.23± 61.39
1p 0.0226± 0.2842
2p 1.69± 40.21
3
p 3.99± -83.14
4p 3.00± 49.17
Django MC/NDF ~ 1.1114162χ
0.000042±mass = 0.498320
0.000051± = 0.006048σ 52±) in range = 2623
s
0 N(K
S/B = 3.073640
Range = [0.350000,0.700000]
Bin 2
/ ndf 2χ 120 / 108
Prob 0.2018
N 4951± 4.339e+05
m 0.0000± 0.4983
σ 0.000051± 0.006048
ν 0.160± 3.118
0
p 16.23± 61.39
1p 0.0226± 0.2842
2p 1.69± 40.21
3
p 3.99± -83.14
4p 3.00± 49.17
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7E
ntrie
s / 3
.000
000
MeV
0
100
200
300
400
500 / ndf 2χ 120 / 108
Prob 0.2018
N 4951± 4.339e+05
m 0.0000± 0.4983
σ 0.000051± 0.006048
ν 0.160± 3.118
0
p 16.23± 61.39
1p 0.0226± 0.2842
2p 1.69± 40.21
3
p 3.99± -83.14
4p 3.00± 49.17
Django MC/NDF ~ 1.1114162χ
0.000042±mass = 0.498320
0.000051± = 0.006048σ 52±) in range = 2623
s
0 N(K
S/B = 3.073640
Range = [0.350000,0.700000]
Bin 2
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
600
700
800
900 / ndf 2χ 134.2 / 110
Prob 0.05804
N 6490± 7.997e+05
m 0.0000± 0.4983
σ 0.000039± 0.006396
ν 0.077± 2.549
0
p 18.7± 108.4
1p 0.0178± 0.3818
2p 1.28± 34.24
3
p 3.28± -67.45
4p 2.6± 38.1
Django MC/NDF ~ 1.2203012χ
0.000032±mass = 0.498325
0.000039± = 0.006396σ 72±) in range = 5112
s
0 N(K
S/B = 6.367626
Range = [0.344000,0.700000]
Bin 3
/ ndf 2χ 134.2 / 110
Prob 0.05804
N 6490± 7.997e+05
m 0.0000± 0.4983
σ 0.000039± 0.006396
ν 0.077± 2.549
0
p 18.7± 108.4
1p 0.0178± 0.3818
2p 1.28± 34.24
3
p 3.28± -67.45
4p 2.6± 38.1
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
600
700
800
900 / ndf 2χ 134.2 / 110
Prob 0.05804
N 6490± 7.997e+05
m 0.0000± 0.4983
σ 0.000039± 0.006396
ν 0.077± 2.549
0
p 18.7± 108.4
1p 0.0178± 0.3818
2p 1.28± 34.24
3
p 3.28± -67.45
4p 2.6± 38.1
Django MC/NDF ~ 1.2203012χ
0.000032±mass = 0.498325
0.000039± = 0.006396σ 72±) in range = 5112
s
0 N(K
S/B = 6.367626
Range = [0.344000,0.700000]
Bin 3
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
600
700
800
900 / ndf 2χ 148 / 110
Prob 0.009118
N 6311± 8.197e+05
m 0.0000± 0.4982
σ 0.000040± 0.007154
ν 0.052± 2.046
0
p 6.40± 30.98
1p 0.0260± 0.4238
2p 1.62± 34.88
3
p 4.2± -63.6
4p 3.26± 34.55
Django MC/NDF ~ 1.3457702χ
0.000033±mass = 0.498172
0.000040± = 0.007154σ 79±) in range = 5854
s
0 N(K
S/B = 11.865443
Range = [0.344000,0.700000]
Bin 4
/ ndf 2χ 148 / 110
Prob 0.009118
N 6311± 8.197e+05
m 0.0000± 0.4982
σ 0.000040± 0.007154
ν 0.052± 2.046
0
p 6.40± 30.98
1p 0.0260± 0.4238
2p 1.62± 34.88
3
p 4.2± -63.6
4p 3.26± 34.55
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
600
700
800
900 / ndf 2χ 148 / 110
Prob 0.009118
N 6311± 8.197e+05
m 0.0000± 0.4982
σ 0.000040± 0.007154
ν 0.052± 2.046
0
p 6.40± 30.98
1p 0.0260± 0.4238
2p 1.62± 34.88
3
p 4.2± -63.6
4p 3.26± 34.55
Django MC/NDF ~ 1.3457702χ
0.000033±mass = 0.498172
0.000040± = 0.007154σ 79±) in range = 5854
s
0 N(K
S/B = 11.865443
Range = [0.344000,0.700000]
Bin 4
-) [GeV]π+,πM (
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Ent
ries
/ 3.0
0000
0 M
eV
0
100
200
300
400
500
/ ndf 2χ 191.7 / 110
Prob 2.307e-06
N 5759± 5.401e+05
m 0.0000± 0.4983
σ 0.000059± 0.008621
ν 0.037± 1.202
0
p 6.41± 13.97
1p 0.0906± 0.7555
2p 3.86± 38.42
3
p 9.9± -68.7
4p 7.31± 36.54
Django MC/NDF ~ 1.7427662χ
0.000046±mass = 0.498260
0.000059± = 0.008621σ 87±) in range = 4572
s
0 N(K
S/B = 17.322227
Range = [0.344000,0.700000]
Bin 5
Figu
reF.16:
Fits
toth
ein
variant
mass
distrib
ution
fromD
jango
Mon
teC
arloin
bin
sof
pT
BF
Tfor
the
targethem
isphere
inth
eB
reitFram
e.
166 APPENDIX F. FITS TO MASS DISTRIBUTIONS
Appendix G
Resumen del trabajo de tesis
Produccion de K0
S a Q2 altas endispersion ep inelastica profunda en H1
En esta tesis se presentan los resultados correspondientes a la primera medicion
de la produccion de mesones K0S a altas Q2 usando los datos colectados con el de-
tector H1 en el laboratorio DESY en Hamburgo, Alemania. Los datos analizados
corresponden al perıodo conocido como HERA II, que comprende los anos 2004-2007
con una luminosidad acumulada de 340 pb−1.
El laboratorio DESY cuenta con un colisionador de partıculas llamado HERA que
acelera protones hasta una energıa de 920 GeV y electrones (o positrones) a energıas
de hasta 27.5 GeV haciendolas colisionar en cuatro puntos estrategicos alrededor de
su circunsferencia, uno de ellos donde se localiza el detector H1 (Figura 3.1).
Este analisis se lleva a cabo despues de seleccionar la muestra de eventos de
dispersion inelastica profunda (DIS por sus siglas en ingles) como se muestra en la
Figura 1.1. Los eventos DIS de corriente neutra se caracterizan por la interaccion
dura de un electron con un proton a traves del intercambio de un boson neutro (γ
o Z0), como resultado se tiene un electron dispersado y un conjunto de partıculas
167
168 APPENDIX G. RESUMEN DEL TRABAJO DE TESIS
hadronicas resultantes del rompimiento del proton, a este conjunto se le denomina
sistema de estados finales hadronicos.
En el detector H1, los eventos DIS a Q2 altas se identifican por la medicion del
electron dispersado usando el calorımetro de Argon lıquido (LAr) mientras que los
estados finales hadronicos son reconstruidos con los detectores centrales de trajectoria
para determinar su carga y momento, y por el calorımetro LAr para la determinacion
de su angulo polar y su energıa. Los eventos DIS se describen usando dos de las
siguientes variables invariantes de Lorentz, el cuadrimomento transferido al cuadrado
del foton Q2, la inelasticidad y y la variable de Bjorken x.
El meson K0S puede ser producido por cuatro mecanismos diferentes, ver Figura 2.3:
a) El proceso de produccion dura del modelo de quarks partonicos (QPM) que
consiste en la interaccion directa de un quark extrano procedente del mar de
quarks en el proton con el foton virtual emitido por el electron.
b) Por fusion de boson gluon (BGF), en el cual un gluon del quark se divide en
un par quark-antiquark extrano y uno de ellos interactua con el electron.
c) Por decaimiento de quarks pesados, producidos primeramente por el proceso
BGF, a quarks extranos.
d) Por el proceso de hadronizacion que se da a partir de la fragmentacion del
campo de color en pares quark-antiquark.
A Q2 altas los cuatro procesos mencionados arriba contribuyen significativamente
a la produccion de K0S .
Los estudios de extraneza son importantes no solo por la medicion de la pro-
duccion, sino tambien porque permiten probar modelos teoricos basados en proce-
sos de hadronizacion y fragmentacion. La comparacion directa de las simulaciones
Monte Carlo con las mediciones del experimento ayudan a mejorar el entendimiento
actual de aspectos de CromoDinamica Cuantica (QCD) ası como a optimizar los
parametros de los programas de simulacion. En particular, para los programas que
169
describen el proceso de hadronizacion por medio del modelo de cuerdas Lund, estas
comparaciones de prediccion-medicion proporcionan una prueba de la universalidad
del factor de supresion de extraneza λs.
En este caso de usan dos programas de simulacion de eventos DIS, Rapgap y
Django, referidos como MEPS y CDM respectivamente en la Figura 1.3. MEPS se
basa en elementos de matriz mas la cascada de partones descritas por medio de las
ecuaciones de evolucion DGLAP que tienen un orden muy fuerte en el momento
transverso kT de los gluones emitidos. CDM tambien usa elementos de matrices pero
la emision de gluones es independiente del momento transverso (no hay orden en kT )
tal cual lo hace el modelo de color dipolar. Ambos modelos tienen una interfase al
modelo Lund para describir la hadronizacion.
El modelo Lund cuenta con tres parametros importantes para describir la pro-
duccion de quarks, el factor de supresion de extraneza λs y los factores de supresion
di-quark, λqq y λsq, que describen la probabilidad relativa de produccion de un par
quark-antiquark extrano con respecto a los pares quark-antiquark ligeros apartir del
campo de color, la probabilidad relativa de creacion de un di-par de quarks con re-
specto a un par de ellos, y la probabilidad de crear di-pares de quarks respecto a
pares. Estos parametros son fijados a los valores proporcionados por la colaboracion
ALEPH: λs = 0.286, λqq = 0.108 y λsq = 0.690. Tanto CDM y MEPS son simulados
con la funcion de densidad de partones (PDF) CTEQ6L.
El meson K0S se identifica por medio de su canal de decaimiento mas frecuente:
K0s → π+π−. Las partıculas hijas, π±, se reconstruyen a partir de trajectorias de
buena calidad medidas en los detectores de trajectoria de H1 que coinciden en un
vertice secundario comun, el cual esta desplazado cierta distancia del vertice primario
de interaccion ep. El espacio de fase elegido para esta tesis se define por 145 < Q2 <
20000 GeV2, 0.2 < y < 0.6, -1.5 < η(K0S) < 1.5 y pT (K0
S) > 0.3 GeV, es decir para
regiones centrales del detector.
La distribucion de masa invariante de los candidatos a K0S seleccionados se aprecia
en la Figura 4.4 de donde se extraen 38154 K0S despues de hacer un ajuste con una
170 APPENDIX G. RESUMEN DEL TRABAJO DE TESIS
distribucion t-student para describir la senal y la funcion p0(x− 0.344)p1 ∗ exp(p2x+
p3x2 + p4x
3) para el ruido.
La seccion transversal inclusiva medida en la region cinematica accesible es de
σvis = 531 ± 17 (stat)+37−39 (sys) pb donde varias fuentes de error sistematico son
consideradas. La produccion diferencial de K0S en funcion de las variables Q2, x, η
y pT del marco de referencia del laboratorio se presentan en la Figura 6.2 donde la
medicion corresponde a los puntos negros y la comparacion con los modelos CDM
y MEPS con λs = 0.22 y λs = 0.286 respectivamente, se aprecia en la parte baja
de cada grafica. Tambien es posible ver que las mediciones decrecen rapidamente
cuando Q2 y pT toman valores cada vez mas altos, mientras que el comportamiento
en funcion de x y η es mas bien de subida y bajada. Los datos son mejor descritos
en forma y normalizacion por los modelos que tienen el valor de λs = 0.286. Tanto
CDM como MEPS tienen comportamientos similares.
Las secciones trasversales tambien son medidas diferencialmente en el marco de
referencia Breit (Figure 6.3), tanto en la region de corriente (CBF) como en la region
del blanco (TBF), en funcion de la fraccion de momento xp y de momento trasverso
pT . La produccion de K0S decrece a medida que los valores de estas variables son
mayores. Los modelos CDM y MEPS con λs = 0.286 dan buena descripcion de los
resultados en la region de corriente donde el mecanismo de produccion preferido es
el proceso de interaccion dura, mientras que en el hemisferio del blanco los diferentes
modelos permiten observar cierta sensibilidad al parametro λs que es lo esperado
debido a que el proceso de hadronizacion es el que domina en esta region.
Las razon de seccion transversal de los mesones K0S con respecto a la de partıculas
cargadas seleccionadas en el mismo espacio de fase, tambien se mide en el marco del
laboratorio y se presentan en la Figura 6.4, una de las ventajas es la reduccion
de las fuentes de incertidumbre sistematica y por tanto la disminucion del error
sistematico total. La razon de produccion es casi plana en funcion de Q2, hay una
pequena caıda en funcion de x y η, y sube a medida que pT incrementa. Este ultimo
comportamiento se debe a que los mesones llevan mas momento comparado con
171
las partıculas cargadas mas ligeras que en su mayorıa son piones. La forma y la
normalizacion de las mediciones son descritas por los modelos con λs = 0.286.
Las graficas de densidad, que se definen como la razon de la produccion de K0S
con respecto a los eventos DIS seleccionados en la misma region cinematica, se mi-
den diferencialmente en funcion de Q2 y x (Figura 6.5). La razon promedio des-
cansa aproximadamente en 0.4 independientemente de las variables, indicando que
la fraccion de produccion es igual en cualquier region. Los modelos con λs = 0.286
describen los resultados bastante bien en Q2 pero predicen una pequena caıda en x
que no corresponde a la medicion.
La grafica 6.6 muestra los resultados de K0S en funcion de xCBF
p en la region de
corriente para tres regiones distintas de Q2 normalizadas a la seccion trasversal total
de eventos DIS en cada region de Q2. Es posible ver el factor de escalamiento de las
funciones de fragmentacion.
Otros estudios realizados son la comparacion de las secciones trasversales difer-
enciales a modelos CDM con los diferentes PDFs: CTEQ6L, H12000LO y GRVLO,
ver Figura 6.7. Los modelos dan descripciones similares en la forma pero solamente
CTEQ6L y H12000LO describen las mediciones en normalizacion, GRVLO subestima
los resultados debido a la ausencia de contribucion de los quarks pesados encanto c
y belleza b. Resultados similares se obtienen en el marco de referencia Breit.
La contribucion de los sabores de quarks es estudiada usando el programa Rapgap
con λs = 0.286 como es posible ver en la Figuras 6.8 y 6.9. Los quarks ligeros u y d del
proceso de fragmentacion dominan en funcion de todas las variables, ası el mecanismo
de produccion principal de mesones K0S es la hadronizacion. La contribucion de los
quarks pesados c y b son la segunda mas alta en la mayorıa de los bins, estos provienen
del proceso de decaimiento principalmente. La contribucion del quark s permanece
como la mas baja pero llega a ser relevante a valores altos de Q2, x y pT (no olvidar
la escala logarıtmica), mientras que en funcion de η es casi constante. Los procesos
de produccion para s son principalmente la interaccion dura QPM y la fusion de
boson gluon. En funcion de variables del marco de referencia Breit, la contribucion
172 APPENDIX G. RESUMEN DEL TRABAJO DE TESIS
del quark s a la produccion de K0S llega a ser mas importantes a valores altos de xp y
pT , especialmente en el hemisferio de corriente donde incluso iguala a la contribucion
de quarks pesados.
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