comparison of hadron production in monte-carlo models and … · 2017. 1. 5. · faculty of physics...
TRANSCRIPT
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CER
N-T
HES
IS-2
013-
427
University of Warsaw
Faculty of Physics
Agnieszka Ilnicka
Student’s book no.: 262431
Comparison of hadron production
in Monte-Carlo models and
experimental data in p+p
interactions at the SPS energies
second cycle degree thesis
field of study Physics
speciality Particle and Nuclear Physics
within Inter-Faculty Individual Studies in Mathematics and Natural
Sciences (MISMaP)
The thesis written under the supervision of
Prof. dr hab. Wojciech Dominik
Institute of Experimental Physics
Section of Particles and Fundamental Interactions
September 2013
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Statement of the Supervisor on Submission of the Thesis
I hereby certify that the thesis submitted has been prepared under my supervision
and I declare that it satisfies the requirements of submission in the proceedings for
the award of a degree.
Date Signature of the Supervisor
Statement of the Author(s) on Submission of the Thesis
Aware of legal liability I certify that the thesis submitted has been prepared by
myself and does not include information gathered contrary to the law.
I also declare that the thesis submitted has not been the subject of proceedings
resulting in the award of a university degree.
Furthermore I certify that the submitted version of the thesis is identical with
its attached electronic version.
Date Signature of the Author(s) of the thesis
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Summary
The aim of this thesis is the comparison of the particle production in proton-proton
interactions simulated by Monte Carlo (MC) models used in NA61/SHINE collaboration:
EPOS and VENUS with the available experimental data. The analysis of total multiplic-
ities of strange particles (Λ, Λ̄, K0s , K+ and K−) and negatively charged pions showed
that the EPOS model describes better the experimental data. Also the analysis of trans-
verse mass was done, and the inverse slope parameter of transverse mass spectra T were
obtained and compared with existing experimental data. The comparison was the base to
tune to the particle spectra obtained with the MC models. The adjustments were then em-
ployed in analysis of spectra of negatively charged pions, obtained with the data collected
in NA61/SHINE experiment. The methods of application of correction were compared to
choose the best one.
Key words
NA61/SHINE, SPS, EPOS, VENUS, proton-proton interaction, p+p
Area of study (codes according to Erasmus Subject Area Codes List)
13.2 Physics
The title of the thesis in Polish
Porównanie produkcji hadronów w modelach Monte Carlo oraz danych eksperymentalnych
z oddzia lywań proton-proton przy energiach SPSu.
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Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.1. NA61/SHINE Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.1.1. Physical Goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.1.2. NA61 Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.1.3. Reconstruction of Events . . . . . . . . . . . . . . . . . . . . . . . . 13
1.2. Nuclear-Scattering Models for Monte Carlo Simulations . . . . . . . . . . . 15
1.2.1. Monte Carlo simulations in Particle Physics . . . . . . . . . . . . . . 15
1.2.2. Nuclear Scattering Models: EPOS and VENUS . . . . . . . . . . . . 17
2. Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3. Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.1. Multiplicities of Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.2. Transverse Mass and T Parameter . . . . . . . . . . . . . . . . . . . . . . . 30
3.3. Tuning of the Particle Spectra from Monte Carlo simulations . . . . . . . . 33
3.4. The h− Corrections: Methods of Application and Inclusion of Particle Ad-
justments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4. Conclusions and Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
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Chapter 1
Introduction
The aim of this thesis is the comparison of hadron production in the Monte Carlo (MC)
simulations and from the reference experimental data. It is then used to construct the
corrections to the data obtained in the experiment NA61/SHINE. In this section will be
presented the overview of the experiment and the use of the Monte Carlo simulations in
the particle physics.
1.1. NA61/SHINE Experiment
The NA61/SHINE (SPS Heavy Ion and Neutrino Experiment) is a fixed-target experiment
located in the North Area of the European Organization for Nuclear Research (CERN)
and is a collaboration of over 150 physicists associated with 27 institutions. The detector
is a large acceptance hadron spectrometer with the time-projection chambers (TPCs) as
the main detectors. The experiment is supplied with the beam from the Super Proton
Synchrotron (SPS) accelerator. The equipment was inherited from the NA49 experiment
and then modified and modernized. The equipment is capable of performing precise mea-
surements of hadron final states and thus may be used not only for its own physical
programme, but also to collect the reference data for other experiments: neutrino and
cosmic ray. In subsequent sections the physical program, detector setup and principles of
reconstruction will be described.
1.1.1. Physical Goals
Ion program: the search of the onset of deconfinement and critical point
The results presented by the NA49 collaboration suggested the existence of the Quark-
Gluon Plasma (QGP) in the early stage after Pb+Pb collision at the high SPS energy
range. This is indicated by rapid change of hadron production properties in this energy
range, as can be seen in plots presented in Figure 1.1. This suggests that the SPS-based
experiment may be of use in a study of the onset of the deconfinement as well as the
critical point of the strongly interacting matter [1, 2]. The onset of deconfinement referes
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Figure 1.1: NA49 results compiled with the world data [4]: (a) The pion multiplicitydivided by the number of wounded nucleon in the Fermi energy. In the Pb+Pb data isobservable the steepening from the linear dependence present in p+p case. (b) Ratio of thepositive kaon to pion multiplicities versus center-of-mass energy
√s. The sharp maximum
is observed in the Pb+Pb data, lacked in the p+p interaction. (c) The inverse slopeparameter T of transverse mass spectra of positive kaons versus center-of-mass energy. Incase of Pb+Pb interaction the plateau is observed, not present in p+p data.
to the creation of deconfined states of strongly interacting matter (such as quark-gluon
plasma) while critical point is the limit over which not phase transitions occure (see Figure
1.2. The interaction of hadrons at different energies and with different system sizes (the
number of nucleons) enable the exploration of the phase space diagram in the temperature
and the baryonic potential of strongly interacting matter, what is schematically shown in
Figure 1.2. Thus, the NA61/SHINE experiment has a rich ion program: it consists of
collisions within the SPS energy range (at 13, 20, 30, 40, 80 and 158 GeV/c) of protons
and ions: with A around 8 (Be+Be), 30 (Ar+Ca) and 110 (Xe+La). The interactions
occur on targets with a similar atomic mass as the beam.
The energy range available in SPS fits between the energies available in AGS and RHIC
accelerators of the Brookhaven National Laboratory, thus the data obtained by NA61 will
be complementary to the data obtained elsewhere. There is a prediction that the rise
in fluctuations in the multiplicities and the transverse momentum of produced particles
would be the signature of the critical point [4]. Currently the first measurements of ion-ion
interactions are analyzed, and next runs are planned for the future. For the full plan of
ion program see Figure 1.3
Large statistic of p+p and p+Pb interactions
The data coming from the nucleus-nucleus interactions are usually compared and inter-
preted with respect to the proton-proton and proton-nucleus data. Thus large statistic
of such interaction would be desirable, and by the time they were not systematically
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Figure 1.2: The phase diagram of the strongly interacting matter [3]. (a) The currentlyavailable world data. (b) The planned scan of the phase diagram by the NA61/SHINEexperiment. Scan is done with the different system size and energy.
Figure 1.3: The scheme of the planned ion program of NA61/SHINE experiment.
measured. The additional advantage of data recorded by NA61/SHINE is that all the
interactions, together with nucleus-nusleus measured by NA49 exeriment, are recorded by
the same detector. The NA61/SHINE experiment intends to collect massive data set on
the p+p and p+Pb interactions at 158 GeV/c. The analysis of records, which will be
collected, will be focused on the particles with high transverse momentum (pT ). This data
are also needed in the iinterpretation of the measurements of Pb+Pb interactions made
by NA49 experiment.
Reference data for neutrino and cosmic-ray experiments
The additional goal of the experiment is to collect the reference data for the neutrino and
cosmic ray experiments. Na61/SHINE experiment in the collaboration with T2K (Tokai-
to-Kamioka) experiment have measured the products of proton-carbon interactions on the
energy 31 GeV, whichc is the same reaction as this leading to production of neutrino beam.
The measurements enabled a better estimation of the neutrino flux by the analysis of the
hadron production, from which decays the nutrinos are produced. The measurements were
performed on a thin (2 cm) carbon target, and also on the exact replica (1 m) of the target
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used in the J-Parc laboratory, where neutrinos for T2K experiment are produced. The
measurements of pions and positive kaons yields were already partially analyzed and pub-
lished [5, 6, 7], and used in the T2K analysis leading to the determination of the neutrino
flux [8].
Moreover the data from the hadronic collisions are also useful as the reference for the
cosmic ray experiments [9]. The theoretical models, used in the analysis of the data, have
unphysical discontinuities in predictions. Additionally to the proton-proton and nuclear
collisions, there were also two dedicated runs, with pions (π−) from secondary beam
interacting on the carbon target with energies of 158 and 350 GeV. This setup mimics
well the interaction in air showers: pions colliding with nitrogen and oxygen atoms due to
the similar atomic mass (A) as carbon (equal to 14, 16, and 12 respectively).
1.1.2. NA61 Detector
The detector of NA61/SHINE experiment is the upgraded NA49 detector [10]. Its outline
is presented in Figure 1.4. As can be seen, the most upstream part of detector is a set of
beam detectors, which checks the quality and the composition of a beam, as well as plays
the role of triggers. This consists of:
CEDAR (Cherenkov Differential counter with Achromatic Ring Focus; C1) and
Cherenkov threshold counter (C2): used for the beam particle identification and
for the analysis;
a set of scintillator counters: there are 3 veto counters (V0, V1, V2) - with a hole
at the beam axis to neglect particles divergent form the beam, as well as 4 counters
at the beam axis: both for the beam triggering (before the target: S1, S2) and the
interaction triggering (after the target: S4, S5);
BPD (Beam Position Detector: BPD-1, BPD-2, BPD-3): consisting of three propor-
tional chambers, used for determining the position of the beam, then extrapolated
to the point of interaction with the target.
The target can be liquid (hydrogen target) or solid (carbon, beryllium target), and 10%
of the data is collected with target removed. The data collected without the target are
important in analysis to take into account the non-target interaction verticles in detector
material. Next there is a set of Time Projector Chamber (TPC) detectors: two vertex
TPCs (VTPC1, VTPC2) inside the magnetic field of two dipole magnets, with a small
gap TPC (GTPC) between them and two main TPCs (MTPC-L, MTPC-R). The setup
of TPCs as well as the principle of their work is described in the next section. Behind the
MTPCs there are three Time-of-Flight (TOF-L, TOF-R, TOF-F) scintillator detectors.
The most downstream part of the detector is the Projectile Spectator Detector (PSD) used
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Figure 1.4: The outline of the NA61/SHINE detector setup.
in ion programme: a calorimeter created with scintillator and lead layers. The calorimeter
is used to count the number of non-interacting nucleons in the beam particle.
Time Projection Chambers
The Time Projector Chamber (TPC) is the detector measuring the three-dimensional
tracks of many particles at the same time. The Time Projection Chamber may be viewed
as the combination of a multi-wire proportional chamber (MWPC) with a drift chamber.
The scheme in Figure 1.5 presents the principle of the operation of the detector. Due to
the electric field in the volume of detector, the electrons, created by ionization caused by
the passage of a charged particle, are transported to the readout pads. Then, when the
detector is active, they pass through the gating grid wires, which have electric field set as
in environment, and come to the MWPC-like part of the detector. The closed gating grid
avoids the undesired multiplication of electrons in time between measured events. Close to
the sense wires the electric field is much higher than the average in the whole volume. It
causes the acceleration of the electrons and their multiplication due to the collisions with
gas. In the same time the ions are created and they drift into the opposite direction than
the electrons. The electrons are then collected by the sense wires, and the excess of ions
causes a change in the electric field, which is registered on the readout pads. Thus, from
the information on the position of an activated readout pad the position of particle track
in two dimensions is obtained. Information about the third dimension is obtained from the
time of drift in the detector volume. Thus the calibration and precise determination of the
drift velocity are essential. Additionally, the amplitude of the signal is measured, which
then is used in analysis leading to identify the mass of the particle by the characteristic
energy loss (dEdx ). The set of information: the position and amplitude of signal is called a
cluster. It is important to note, that due to the gaseous, sparse interior of the detector
the production of particles in secondary vertices is kept at a low level, thus limiting the
contamination of the particles from the interaction vertex.
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In the NA61/SHINE experimental setup there are five TPCs of total volume about
Figure 1.5: The scheme of Time Projection Chamber detector and the detection procedure[9].
40 m2. Two front TPCs with dimensions 2m Ö2.5m Ö1m are located inside the magnet
coils; in their volume there is a magnetic field of maximally 1.5T and 1.1T (for VTPC-1
and VTPC-2 respectively) parallel to the electric field. This setup reduces the distortion of
the electron drift to the readout. The magnetic field bends the trajectories of the charged
particles depending on their momenta, thus introducing a tool for its determination. VT-
PCs have a gap along the beam line to reduce interference from the noninteracting beam
particles, e.g. ions causing massive ionization in the TPCs. There is GTPC between
VTPCs and it enables to track the particles with small production angle. Down the
beamline, after the VTPCs and GTPC, there are two MTPCs (R and L for right and left)
of dimension 3.9m Ö3.9m Ö1.8m. The tracks in the MTPCs are straight due to the lack
of magnetic field, but the detectors are optimized to precisely measure the energy loss.
Combined with the information on the momentum from the track curvature it enables the
identification of a particle.
The important feature of the TPCs is the choice of a gas mixture as it has effects
on every step of the detection process: the ionization, the electron drift and the gas
amplification. Thus the gas mixture should be chosen in such a way that it will:
maximize the ionization and the gas amplification to maximize the sensitivity of the
detector,
have a output signal proportional to the primary charge to enable dEdx analysis,
have a high drift velocity to enable the full readout of the cluster in the time between
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subsequent events,
keep a low diffusion rate of electrons to maximize the spatial resolution,
have a low photons production rate during electron drift to avoid secondary electron
avalanches.
To optimize the fulfillment of, sometimes contradictory, requirements above a set of tests
needed to be done [11]. This resulted in the following composition of a gas mixture:
VTPC and GTPC: 90% Ar and 10% CO2,
MTPC: 95% Ar and 5% CO2.
The addition of the so-called quenching gas, here CO2, reduces the diffusion rate of elec-
trons, but at the same time it also decreases the drift velocity, thus its content needs to
be balanced. The level of oxygen and water impurity in TPCs needs to be controlled and
minimized, as they cause the loss in the drifting charge.
1.1.3. Reconstruction of Events
The outcome of the detection procedure is raw data, which needs to be then postprocessed
to obtain the final format which then may be analyzed. The reconstruction is based
on the external parameters and the detector characteristics, determined by calibration
procedure. The main effort lies in the track reconstruction and particle identification.
The reconstruction of events is done by reconstructing the tracks of particles in TPCs.
This enables the determination of momentum of particles. The identification of particles
is done using just the information on energy loss in TPCs, or also with the additional
information from TOFs.
Track reconstruction
The track reconstruction is based on 4 steps:
finding the clusters: the position and amplitude of a signal,
reconstructing the track segments in each TPC separately,
reconstructing global tracks from all TPCs and fitting them to the interaction point,
determining the momentum from the fitted tracks curvature.
The particle traversing the detector ionizes the gas and leaves clusters along its track.
The procedure, taking into account the magnetic field in the TPC, combines the clusters
into the track, and then tracks from all TPCs are combined into global tracks. The tracks
may start in the main vertex, but there are also well-defined tracks from the neutral par-
ticles produced in the vertex, so called V0-tracks, which are then appearing in TPC after
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the neutral particle’s decay. The secondary particles produced in the detector material, or
coming from unknown sources decrease the efficiency of the reconstruction procedure. The
direction of the readout pads is optimized to the ”right-side track” (RST): the particles,
whose tracks are on the same side of the detector as the side on which it was produced,
and thus the ”wrong-side tracks” (WST) from the particles, whose tracks were bend on
the other side of the detector than the side on which it was produced are removed from the
analysis. Then to the reconstructed track the momentum, from the bending of the track,
is assigned. Figure 1.6 shows the reconstructed tracks from the p-C interaction (NA61)
and Pb-Pb interaction (NA49). It is clearly visible that multiplicity of particles increases
with the growth of the mass number of the interacting nuclei.
Figure 1.6: The tracks reconstructed in the NA61/SHINE and NA49 detectors: (a) thep+C interaction at 31 GeV/c; (b) the Pb+Pb interaction at 158 GeV/c [3].
Particle identification
The particle identification is based on the energy loss measurement in the TPC volume (dEdx ), in case of intermediate momentum of particles supported by information from Time-
of-Flight detectors (ToF).
The dEdx identification is based on the Bethe-Bloch formula:
−〈dEdx〉 = Kz2Z
A
1
β2·[ln
(2mec
2β2TmaxI2(1− β2)
)− β2 − δ(βγ)
2
](1.1)
where c is the speed of light, �0 the vacuum permittivity, β = v/c, me the electron charge
and rest mass respectively, n electron density, z is the charge of the particle travelling
through the material in units of electron charg, A and Z are atmic mass and number of
absorber, Tmax is a maximum kinetic energy that can be imparted to a free electron in a
single collision, K is a constant and δ(βγ) is the density-effect correction. The measure-
ments of the energy-loss are based on the measure of charge of clusters on the track of
the particle. The plot of energy loss (〈dEdx 〉) versus the particle momentum leads to the
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separation of different particles (see Figure 1.7), as the Bethe-Bloch formula depends on
the velocity (β). The Bethe-Bloch formula, however, is not monotonic, thus the plots are
crossing. As could be noticed, due to the crossing of a plots, the dEdx is reliable in the
relativistic region (over few GeV/c) and for the low momentum region.
Figure 1.7: The plots of energy loss with respect to the particle’s momentum for positive(a) and negative (b) particles. The data intersects in the middle momentum region [3].
In the region which is problematic for the dEdx identifications the combined energy
loss and Time-of-Flight procedure is used. The Time-of-Flight (ToF) detector, combined
with the track reconstruction allows determining the mass of the particle according to the
equation
m2 = p2(c2t2TOFl2
− 1), (1.2)
where p is particle momentum, tTOF is time of flight from the interaction point to the ToF
detector and l is length of the trajectory of particle. Figure 1.8(a) presents the plot of
reconstructed squared mass with respect to the momentum of the particle, which is well
separated in low and middle momentum range. Figure 1.8(b) also presents the identifi-
cation through the information obtained from energy loss and ToF. As can be seen the
signals of different particles are well separated, and combined dEdx -ToF method is most
desired in the middle momentum range.
1.2. Nuclear-Scattering Models for Monte Carlo Simulations
1.2.1. Monte Carlo simulations in Particle Physics
The Monte Carlo (MC) simulations play a key role in every stage of a particle physics
experiment:
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Figure 1.8: (a) The graph of the reconstructed squared mass with respect to the momentumobtained with ToF detector. (b) The 2D graph of particle identification obtained fromcombined information from ToF detector and energy loss for middle momentum region[3].
during the planning of the detector: enabling simulation of its performance
supporting the calibration
during data-analysis used to correct the measurements for the detector and known
physical effects
used for comparison between experimental data and the theory.
One can distinguish two main steps in the particle physics MC simulations: simulating
passage of particles through detector and generating particles in an interaction. The
first type of simulation needs the precise description of geometry of the detector, as the
behavior of the particle depends on the material in which it travels. In every step of
the simulation, based on the random-number generator, the interaction of particle with
detector is determined. All secondary particles produced during this step need also to be
followed in the simulations making the task very computationally demanding. The latter
branch of MC simulations is governed by the Standard Model for partonic (hard QCD)
or electroweak interactions or by hadronic models for so-called soft QCD processes. As
the processes on the hadronic level, such as nucleus-nucleus or nucleon-nucleon collisions,
cannot be described by the perturbative quantum chromodynamics (QCD), there is a
need to use hadronic models based on semi-empirical theories. They will be described in
more details in the next section. In an experiment such as NA61/SHINE the choice of
proper hadronic model is essential, as the obtained data are outside of regime described
by perturbative QCD. Additionally the processes investigated by the experiment, such as
the phase transition or existence of QGP, may not give evident signals and a quantitative
analysis needs to be done. Monte Carlo simulations may be useful in such a situation on
two ways: supporting the precise data-analysis and giving the reference for the different
scenarios of the state of matter after collision.
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1.2.2. Nuclear Scattering Models: EPOS and VENUS
The hadronic models VENUS [12, 13] and EPOS [14] are based on the Gribov-Regge theory
(GRT). This theory was a basis for various models, which proved to be in good agree-
ment with the experimental data. As this theory is appropriate for the interaction with
relatively low particles density, it needs an extension for the high-energy and heavy-nuclei
collisions. In such situation there is a need to include so-called rescattering: procedure in
which the produced hadrons scatter again, as the energy density in such collisions is high.
After the initial interaction the avalanche of secondary interactions may occur leading to
the thermal equilibrium.
The hadron-hadron interaction is described by the parton model having two contribu-
tions: the parton distribution of a hadron and the elementary parton-parton cross-section
obtained with perturbative QCD. Partons are the elementary constituents of the hadrons
carrying the fraction of total hadron’s momentum. For the high-parton density, which
is the case in the proton-nucleus and nucleus-nucleus collisions, the interaction is treated
by the pomeron-pomeron interactions, where pomerons are the so-called parton ladders
showed in Figure 1.9. This parton ladder contribution needs to be augmented by the de-
scription of the remnants of the hadron (diquarks or antiquarks), which may be viewed as
the ”spectators” of the interaction. The interaction is described by the multiple scattering
in which open parton ladders are present, representing the inelastic scattering, as well
as closed ones, for the elastic scattering, both showed in Figure 1.9. In the next step of
procedure of the scattering, the momentum fractions and the transverse momentum are
assigned for the ends of the ladders. With this information may be calculated the partial
cross-section as a function of the impact parameter b: the perpendicular distance between
the path of a projectile and a target. The partial cross-section is the basis for the Monte
Carlo algorithm.
Figure 1.9: (a) The Feynman diagram presenting the creation of parton ladder in interac-tion of two nuclei and a schematic graph; (b) open and closed parton ladders correspondingto the inelastic and elastic scattering respectively [14].
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To retrieve the information about the hadrons produced in the interaction there is a
need to construct the strings from the free parton lines of pomerons. The classical string
approach, with the string being the two-dimensional surface in four-dimensional spacetime
and with the transformations governed by the gauge group representation is a basis of the
description of the strong interactions of GRT. It can be viewed that the string’s endpoints
represent the quarks and the string interior represents the gluons. An important feature
of the procedure is the algorithm for the string fragmentation: that is the description of
the evolution of the system and the prescript for final hadron’s production. Figure 1.10
represents the string fragmentation and the continuation in the future of two new strings.
The string fragmentation is governed by random-number generators. The fragmentation
model used in the VENUS and EPOS is based on the AMOR (Artru-Mennessier Off-
shell Resonance) model, which determines the point in which fragmentation takes place
to maintain all the required properties such as locality and covariance. In the used model
the fragmentation does not occur on the mass shell, which means that the masses of frag-
mented strings do not refer to the masses of the hadrons but they need to be greater than
minimal mass of the hadron constituted from the given quark. The fragmentation then
continues until the final strings have masses below cutoff, and then they are identified with
the resonances. During every fragmentation also the transverse momentum is assigned.
Additionally, to obtain the heavy quark final states, during fragmentation there is a set of
probabilities to create a heavy quark-antiquark pair.
Figure 1.10: The scheme of string fragmentation leading to production of two new strings:graph presents the propagation of a string, which breaks (line segment AC) into two newstrings continuing the propagation to the future. The lines correspond to the endpointsof the string, which correspond to the quark or antiquark [13].
To conclude, both models, VENUS and EPOS, belong to the group of models based on
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the Gribov-Regge theory of partons and phenomenological model of the string fragmen-
tation. They are both well suited and designed to take into account high-density effects
such as the formation of the quark-gluon plasma, which is hypothetically possible final
state of the nucleus-nucleus high energy collisions. EPOS model have been developed
from VENUS model, which is sometimes referred as the old generation model [15]. Thus,
EPOS model, which is still developed and updated [16], may be viewed as the successor
of VENUS model.
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Chapter 2
Analysis
The analysis leading to tuning of particles spectra and the so-called h− correction in h−
analysis were based on the Monte-Carlo productions used by the NA61/SHINE experi-
ment. The h− analysis retrieves the spectra of negatively charged pions from the spectra
of all negative particles. The MC productions were generated with the hadron models
VENUS and EPOS. The particles were propagated through the detector with use of the
GEANT3.2.1 package. The postprocessing was the same as with the experimental data.
The records from the particles from the simulated p+p interaction together with their
following strong and electromagnetic decays will be referred as the ”generated”, and these
data after the reconstruction procedure will be referred as the ”reconstructed”. The anal-
ysis was done using series of programs, written with use of ROOT61 package in C++
programming language.
In the first step of the project the total multiplicities of strange particles: Λ , Λ̄, K0s ,
K− and K+ as well as the negatively charged pions were analyzed as a function of the
interaction energy. The information obtained with the Monte Carlo models were com-
pared with the available reference data from the literature [17, 18] and the preliminary
NA61/SHINE measurements [19, 20]. The results were then used in the next steps of the
work to tune to the spectra obtained from MC models.
Next step of comparison between measured and simulated records was based on a con-
struction of the transverse mass spectra, where transverse mass is defined by the equation:
mT =√m2 + p2T , (2.1)
where m is particle’s mass and pT is the transverse momentum, without any constrains
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on rapidity. Rapidity is the kinematic variable, which may be defined as:
y =1
2ln
(E + pzE − pz
)=
1
2ln
(E + pzmT
), (2.2)
where pz is longitudinal momentum and E is energy. Important note is that the rapidity
is different for particles with the same momentum but different mass. Then to the spectra
an exponential function was fitted:
1
mT
dn
dmT= AT · e−
mTT . (2.3)
The inverse slope parameters T were then plotted with respect to the energy of the proton
beam and compared with the experimental reference data [21, 22].
The second task of the project was the construction of corrections to the rapidity-
transverse momentum spectra of particles important in h− analysis obtained from MC
simulations. The corrections to the MC spectra constructed with use of reference experi-
mental data will be called the adjustments to avoid confusion with h− correction described
in last part of analysis. The h− analysis is based on the theoretical and experimental ob-
servations that the vast majority of negatively charged particles are π− with admixture
of electrons, negative kaons, antiprotons, etc. Actually electrons may be eliminated in
the early stage of analysis due to the good separation in energy loss analysis (see Figure
1.7). Thus when in the thesis the expression negatively charged particles is used it refferes
to negatively charged particles except electrons. The h− analysis enables, after series of
corrections, to obtain the pions spectra without the need for direct identification. The
particles which were the subject of the adjustments are the negatively charged particles:
K− and p̄ and secondary pions produced in decays of neutral particles: K0s and Λ. The
proposed adjustments were based on the comparison done in the first part of the project
and preliminary results of NA61/SHINE experiment. The adjustment was applied as the
multiplicative correction cN to the MC reconstructed spectra:
nMC,adjustedN (y, pT , E) = cN (y, pT , E) · nMC,reconstructedN (y, pT , E), (2.4)
where y is rapidity, pT transverse momentum and E the energy of p+p interaction. Thus
the adjustments may be viewed as the spectra in rapidity and transverse momentum which
are multiplying the reconstructed MC spectra bin by bin to tune them to the experimental
data. The adjustments and spectra of particles are presented as 2D spectra with bin’s size
0.2 in rapidity and increasingly from 50 to 250 MeV/c in transverse momentum, as can be
seen in Figures in Sections 3.3. The particle spectra were tuned in three ways, depending
on the available data, and are presented below:
for π−: Every bin of spectra was rescaled by the divided preliminary spectra mea-
22
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sured by NA61/SHINE experiment [19] and spectra generated from MC models and
additionally whole spectra were scaled by the total pion multiplicities:
cπ−(y, pT , E) =〈π−〉refdata〈π−〉NA61
· nNA61(y, pT , E)nMC,generated(y, pT , E)
, (2.5)
where 〈π−〉 are the total multiplicities and n(y, pT , E) are the spectra bins.
for secondary π− from Λ and Ks0 decays: the spectra were scaled by a constant factor
constructed from total multiplicities:
cΛ/K0s (E) =〈Λ/K0s 〉refdata(E)〈Λ/K0s 〉MC,gen(E)
, (2.6)
where 〈Λ/K0s 〉 are the total multiplicities.
for p̄ and K−: the adjustment was based on the divided preliminary NA61/SHINE
spectra [20] and spectra generated from MC models for interaction energy 158 GeV,
to which was fitted the bi-linear function:
fp̄/K−(y, pT ) = A · y +B · pT + C. (2.7)
The first step of analysis showed that the discrepancies between data from MC model
and experiment increase with the energy, thus for lower interaction energies the fitted
function was scaled down linearly:
Sp̄/K−(E) = 1 +E − 20
158− 20. (2.8)
In the result the correction is defined as:
cp̄/K−(y, pT , E) = 1 +E − 20
158− 20· (A · y +B · pT + C − 1) (2.9)
Last part of the project was a construction of the h− corrections, which is needed in
h− analysis to correct the spectra of negatively charged particles (marked h−) for parti-
cles different than primary pions (π−(V 0)). The particles contributing to the correction
are other negative particles (µ−, K− , p̄), secondary pions from decays of neutral parti-
cles called feed-down (π−(Λ), π−(K0s )) and other negative particles, mostly pions from
secondary interaction vertices (marked as others):
h− = π−(V 0) +K− + p̄+ π(K0s ) + π(Λ) + µ− + others. (2.10)
The feed-down are the secondary pions which were falsely fitted to the primary vertex, and
thus their reconstructed momentum is different than the real momentum. Additionally,
the momentum of secondary pions is weakly correlated with the momentum of particles
from which they were produced.
23
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The correction is done with use of spectra generated from MC models and then recon-
structed. The three ways of applying the corrections were proposed, which in the ideal
situation, when the MC models describe exactly the experimental data, should be the
same.
h− additive correction: the contribution from particles other than primary pions was
subtracted from the spectra
[π−]add = [h−]NA61 − ([h−]− [π−(V 0)])MC,rec (2.11)
h− multiplicative correction: the spectra were scaled by the fraction of primary pions
in all negative particles
[π−]mul = [h−]NA61 ·[π−(V 0)]MC,rec
[h−]MC,rec(2.12)
h− mixed correction: the contribution from the secondary pions and other interfering
particles was subtracted and then it was scaled by fraction of primary pions to sum
of primary negative particles
[π−]mix =([h−]NA61 − ([π−(Λ)] + [π−(Ks0)] + [others])MC,rec)·
·[π−(V 0)]MC,rec
([π−(V 0)] + [K−] + [p̄] + [µ−])MC,rec,
(2.13)
where [h−]NA61 stands for spectra of negatively charged partciles except electrons mea-
sured by NA61/SHINE experiment and [x]MC,rec for spectra of particle x (as listed above)
generated and reconstructed from Monte Carlo model. The corrections were also improved
by the adjustments to the particles constructed in previous step of project. The methods
of application of the h− correction were compared to find the most suitable one. The
corrections enabled also the assessment of the adjustments.
24
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Chapter 3
Results and Discussion
The results of the comparison of the Monte-Carlo models and experimental data are
presented on the series of plots. Also the adjustments to the particles responsible for the
h− correction and the corrections itself are presented in the form of the 2D histograms
for the better overview. The analysis was done for all the available interaction energies,
but in thesis are presented only the spectra for the extreme interaction energies: 20 and
158 GeV. In the next sections the results will be discussed and related to the existing
literature data and preliminary measurements of NA61/SHINE experiment.
3.1. Multiplicities of Particles
Figure 3.1 presents the total multiplicities of the particles from the proton-proton collisions
generated from the Monte Carlo models: VENUS and EPOS and reference experimental
data [17, 18]. The data was parameterized with the logarithmic or polynomial function.
The five beam energies from MC simulations (20, 31, 40, 80, 158 GeV) correspond to the
energies used in the NA61/SHINE experiment.
What needs to be noted is that pion multiplicity is plotted against Fermi’s energy:
F [GeV12 ] =
(√s− 2mp)
34
(√s)
14
(3.1)
where√s is center of mass interaction energy and mp is proton mass. The 〈π−〉 multiplic-
ity increases linearly with F in p+p interaction [23]. This linear fit to 〈π−〉 was used toconstruct the ratio of strange particle’s multiplicities to the pion’s multiplicity presented in
Figure 3.2. For better comparison the MC multiplicities divided by the experimental data
fits are plotted in Figure 3.3. Additionally, the graphs with strange particle multiplicities
divided by the multiplicities of negative pions are presented in Figure 3.2. These graphs
are presented to demonstrate the contribution of the particles in h− analysis. Finally, in
Table 3.1 are collected the particle’s multiplicities from the MC data and functions fitted
25
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Figure 3.1: The total multiplicities of particles with respect to the interaction energy. Theliterature data were parametrised by polynomial or logarythmic function.
to the reference data of Figure 3.1.
It is visible in Figure 3.1 that the total multiplicity of EPOS model agrees better
with the experimental reference data. It is consistent with the fact, that it is a later
model, which was revised with respect to VENUS. From Figures 3.1 and 3.2 it can be
also noticed that both models usually overestimate the multiplicities of the particles. The
negative pions multiplicities are well described by both models, as can be seen in Figures
3.1 and 3.3. The discrepancies are lower than 10%. In case of Λ baryon it is clearly visible
that the overestimation is growing with the decrease of the interaction energy and yields
over factor 2 for VENUS and 1.5 for EPOS for the lowest energy: 20 GeV. From the
26
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graph of the relative multiplicities it is visible, that Λ is produced on the level of 10% of
pion production. It is important, as the branching ratio of lambda’s decaying in negative
pion is on the level of 60%, and thus have significant contribution in feed-down correction,
especially at low energies, where the yields of other interfering particles are low, but also
the discrepancies between the experimental data and MC models are the largest.
Figure 3.2: The ratio of total multiplicities of strange particles to negative pions withplotted versus the interaction energy.
The antilambda baryons are much more rarely produced, on the level lower than 1%.
They are described better than lambdas by the MC simulations. The VENUS data are
slightly overestimated, but also the experimental values have large uncertainties. In the
case of positive kaons main discrepancies between experimental data and MC models are
visible in low-energy region, and they are decreasing for the higher energies. In both cases
of charged kaons EPOS model performs slightly better than VENUS. Especially in the
27
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Figure 3.3: The total multiplicities of particles generated from MC models divided by theparameterization of experimental data, plotted with respect to the interaction energy.
case of positive kaons, the EPOS model is in good agreement with experimental data with
discrepancies lower than 10%. Negative kaons are more important for h− analysis, as
they, as negatively charged particles, need to be included in the correction to obtain the
negative pions spectra. Although that in Figure 3.3 it seems that the discrepancies are
the biggest in the low energy region, but in Figure 3.1 it is visible, that the absolute error
is larger for the two highest energies. The additional problem is the lack of experimental
points in the region of 158 GeV for charged kaons: the neighboring experimental records
are from the energy around 70 GeV and 500 GeV. The neutral short-living kaons, similarly
as Λ baryons contribute to the h− analysis via the secondary π−, with branching ratio on
their production equal to around 70%. Both models overestimate the multiplicities of K0s ,
with better performance of EPOS.
28
-
Energy 〈π−〉 [ref] 〈π−〉 [NA61] 〈π−〉 [EPOS] 〈π−〉 [VENUS]158 2.393 2.424 2.404 2.31180 1.866 1.927 1.989 1.76040 1.398 1.497 1.569 1.34031 1.242 1.333 1.412 1.21920 0.988 1.066 1.146 1.010
Energy [GeV] 〈Λ〉 [ref] 〈Λ〉 [EPOS] 〈Λ〉 [VENUS]158 0.110 0.116 0.12580 0.109 0.108 0.14340 0.080 0.099 0.13931 0.072 0.094 0.13720 0.061 0.093 0.133
Energy [GeV] 〈K0s 〉 [ref] 〈K0s 〉 [EPOS] 〈K0s 〉 [VENUS]158 0.160 0.183 0.16680 0.116 0.138 0.15540 0.071 0.096 0.11631 0.059 0.080 0.10320 0.044 0.054 0.085
Energy [GeV] 〈K+〉 [ref] 〈K+〉 [EPOS] 〈K+〉 [VENUS]158 0.282 0.243 0.27780 0.219 0.195 0.22640 0.155 0.146 0.18331 0.131 0.128 0.17120 0.091 0.098 0.148
Energy [GeV] 〈K−〉 [ref] 〈K−〉 [EPOS] 〈K−〉 [VENUS]158 0.180 0.141 0.14880 0.125 0.099 0.10240 0.070 0.060 0.06431 0.049 0.046 0.05420 0.014 0.025 0.036
Energy [GeV] 〈Λ̄〉 [ref] 〈Λ̄〉 [EPOS] 〈Λ̄〉 [VENUS]158 0.019 0.011 0.01680 0.005 0.006 0.01140 0.002 0.002 0.00431 0.001 0.001 0.00220 0.001 0.001 0.002
Table 3.1: The total multiplicities of particles from MC models parameterized referencedata and for pions from preliminary NA61/SHINE experiment.
Table 3.1 collects the total multiplicities obtained during analysis. The reference data
comes from the parameterization of the reference data from literature. For negative pions
are also included the preliminary multiplicity obtained with NA61/SHINE experiment. It
agrees well with other experimental data on the level of few percent.
29
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3.2. Transverse Mass and T Parameter
Next part of the project was based on the transverse mass analysis of events generated
with MC models and comparison of the obtained inverse slope parameter (T ) with the
experimental data. The Figure 3.4 presents the spectra in transverse mass ( 1mT ·dndmT
).
The spectra were derived without any constraints on the rapidity or production angle.
Exponential function (2.2) was fitted to the points. The exponential function is in good
agreement, especially for the kaons and for hyperons for low mT region, what is consistent
with experimental records: the experimental data were available up to 0.6 GeV [22]. In
case of hyperons, the agreement holds in range 0-0.4 GeV, which is in accordance with
experimental data [21]. The exponential function fitted to the MC spectra describes well
the same region as the available experimental data, thus enables the comparison of T pa-
rameter of full spectra. On the other hand, the logarythmic scale shades that the absolute
errors of fit in the region of high 1mTdndmT
.
In Figure 3.5 the T parameter versus the interaction energy was plotted for both MC
models and in the last row also from experimental records. The solid, straight line on the
plots is the fit to the experimental data taken from the references [21, 22]. According to
the authors, the dependence of inverse slope parameter T on the collision energy should
be linear. It is important to note, that the fit was made for the wide range of interaction
energy, up to nearly 2 TeV. In the range of interest (30-160 GeV), however, there are few
data-points and they usually have large errors. Since the errors are bigger as the discrep-
ancies between the models, the analysis may not be conclusive.
The discrepancies are the most significant in case of Λ hyperons. The linear fit to
the experimental data lays between these two models, but VENUS datapoints are closer
to it. In case of the Λ̄ baryons the discrepancies between MC models also are significant,
but unfortuantelly the experimental records are lacking. In case of kaons all points of MC
models lay below the experimental linear fit. In case of data from MC models for the
neutral and positive kaons the points have similar values with VENUS points having more
flat dependence on the beam momentum than EPOS, and crossing around 60 GeV/c. For
the negative kaons the EPOS points increase faster with the interaction momentum, and
are always lying above VENUS points, and are thus closer to the experimental fit.
30
-
EPOS VENUS
Λ :
Λ̄ :
K0s :
K− :
K+ :
Figure 3.4: The spectra of transverse mass obtained with MC models with the fittedexponential functions.
31
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Figure 3.5: The inverse slope parameter T versus the interaction energy. Solid line rep-resents the parameterization from the experimental records. In last row are presentedexperimental records with fits from [21, 22]
32
-
3.3. Tuning of the Particle Spectra from Monte Carlo simu-
lations
In Figure 3.6 there are presented the negative pion spectra and spectra relative to the
all negatively charged particles. As can be noticed from plots the spectra produced from
both models are in good agreement, what is in agreement with Figure 3.1, showing good
agreement of models in case of total multiplicities. With the increase of interaction energy
the total multiplicity grows and the rapidity range is wider, especially in the low transverse
momentum region. Negative pions’ contribution to all negative particles is on the level of
90% for interaction energy 20GeV, and it increases for higher energy. The relative spec-
trum of EPOS model is slightly higher than this of VENUS model. The regions in which
contribution of particles other than pions is important is especially the low transverse
momentum region for low interaction energies and high transverse momentum region for
high interaction energies.
Figure 3.7 shows the adjustment of the pion spectrum as described in Analysis section
(see eq. (2.5)). The adjustment is the highest for the interaction energy 20GeV. In general,
the tendency is that the number of pions from MC simulations needs to be increased in
high pT region, and decreased in low pt and high y region. The adjustment is decreasing
with the interaction energy in case of EPOS models, but in case of VENUS model the
adjustment is smallest for the intermediate interaction energies.
In the h− analysis the important step is to take into account the fact that the recon-
structed primary particles can originate from the secondary pions produced in the decays
of the neutral particles: hyperons Λ or neutral kaons K0s . The adjustment of the spectra
reconstructed from MC models was a constantfactor according to the total multiplicities,
presented in Table 3.2. Figure 3.8 presents spectra of lambda baryons and their relative
contribution to all negatively charged particles. As one can notice the highest yield of the
secondary pions is for the low energies, with the maximum at low transverse momenta.
This indicates that the inclusion of the feed-down is the most important at the energies
where the discrepancies between the models and experiment are the largest.
In Figure 3.9 there are presented the spectra of pions produced from the decays of
neutral kaons which were produced and reconstructed from MC models. The adjustment
was constructed in the same way in the case of lambda hyperons, by rescaling of the whole
spectra by the ratio of total multiplicities (see Table 3.2). The spectra obtained with both
models are in quite good agreement, VENUS spectra are slightly wider in rapidity than
EPOS. The secondary pions from neutral kaons decay, similarly as from lambda decays,
33
-
EPOS:
VENUS:
Figure 3.6: The reconstructed spectra of primary negative pions obtained with MonteCarlo models for interaction energy 20 and 158 GeV (left figures) and the correspondingratios of primary π− to all negative particles presented in percent (right figures).
contribute to negatively charged particles spectra mainly in low transverse momentum
spectra. The difference is that the yield of π−(K0s ) grows with the interaction energy,
opposite to the lambda’s case.
Other particles contributing to the h− correction are primary negative hadrons which
34
-
EPOS:
VENUS:
Figure 3.7: The adjustment of the negative pions obtained using preliminary NA61/SHINEspectra and total multiplicity from the world results compilation.
may be misassigned in h− analysis: the negative kaons and antiprotons. Figures 3.10
and 3.11 present the steps of construction of the bi-linear adjustment, as described in the
Analysis section. The histograms presented in the bottom rows of Figures show how well
the parameterization describes the ratio of the experimental and MC spectra. As can be
seen, in case of antiprotons the ratio between the spectra’s ratio and fitted function is
between 0.8-1.2, thus in satisfactory accordance, and in case of kaons accordance is even
35
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Energy [GeV] cΛ [EPOS] cΛ [VENUS]
158 0.948 0.88080 1.009 0.76240 0.808 0.57631 0.766 0.52620 0.656 0.459
Energy [GeV] cK0s [EPOS] cK0s [VENUS]
158 0.874 0.96480 0.840 0.74840 0.740 0.61231 0.738 0.57320 0.815 0.518
Table 3.2: The adjustment factor by which the spectra of secondary pions from neutralparticles decays are scaled.
better (between 0.9-1.2). The adjustment shows that the models underestimate the yield
of particles for high transverse momentum and overestimate for the low transverse mo-
mentum and high rapidity. Table 3.3 collects the values of the parameters of the fitted
function.
A B C
p̄ EPOS -0.124 0.766 0.674p̄ VENUS -0.469 0.290 0.972K− EPOS -0.252 0.281 0.995K− VENUS -0.299 0.710 0.851
Table 3.3: The parameters of the fitted plane from Figures 3.10 and 3.11, as marked inequation (2.7).
The Figures 3.12 and 3.13 present the spectra of antiprotons and negative kaons re-
spectively. The shape of both spectra is similar, but the kaon yield is around three times
larger. The most of the particles are in the region of low transverse momentum and middle
rapidity. The maximum region is shifted from the position y = 0 because of the change of
the rapidity variable: from the rapidity calculated with antiproton or kaon mass to rapid-
ity calculated with the pion mass. In Figures 3.10 and 3.11, where rapidity is calculated
with the corresponding particle mass, the maximum is in the position of low pT and y = 0.
The adjustment was calculated only for the proton beam of energy 158 GeV. Ac-
cordingly to Figure 3.1 the models describe well the experimental data for 20 GeV and
discrepancies grow with the energy, thus linear scaling of the adjustment was proposed as
described in the Analysis section (see eq.(2.8)). The spectra of antiprotons (Figure 3.12)
and negative kaons (Figure 3.13) are presented in coordinates with rapidity calculated with
36
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pion mass assumption, and thus the adjustments are asymmetric with respect to y = 0
as can be viewed in Figures 3.14 and 3.15. The tuning reduces the number of particles in
the low pT region and increases it in the high pT region. It can be noted, accordingly to
Figures with relative spectra, that the corrections from secondary pions of neutral parti-
cles and misassigned negative particles are complementary: they are important for other
energies and other regions of spectra.
Figure 3.16 presents of spectra called as ”others”, as defined in Analysis section. They
originate from various sources, mainly from the secondary interaction vertices in the de-
tector material. They originate from various primary particles, thus it is difficult to define
well the adjustment and it was not included in scope of the project. The contribution of
such particles to the spectra of all negative particles is luckily quite low, on the level of
2-5 %, and it is the most important in the low pT -low y region and very high pT region.
37
-
EPOS:
VENUS:
Figure 3.8: Spectra of secondary pions from lambda decays, reconstructed as primaryparticles obtained with Monte Carlo models for interaction energies 20 and 158 GeV (leftfigures) and the corresponding ratios of π−(Λ) to all negative particles presented in percent(right figures).
38
-
EPOS:
VENUS:
Figure 3.9: Spectra of secondary pions from neutral kaons decays, reconstructed as primaryparticles obtained with Monte Carlo models for interaction energies 20 and 158 GeV (leftfigures) and the corresponding ratios of π−(K0s ) to all negative particles presented inpercent (right figures).
39
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(1) VENUS EPOS Data
(2) Data/VENUS Data/EPOS
(3) fitted function:VENUS EPOS
(4) fitted function/(Data/MC):VENUS EPOS
y is a rapidity obtained with antiproton mass
Figure 3.10: The steps of construction of the antiproton adjustment for interaction energy158 GeV: (1) the generated MC spectra and preliminary NA61/SHINE spectra; (2) theNA61/SHINE spectra divided by MC spectra; (3) the bi-linear function fitted to thedivided spectra from (2); (4) the fitted function from (3) divided by spectra from (2),showing the quality of the fit.
40
-
(1) VENUS EPOS Data
(2) Data/VENUS Data/EPOS
(3) fitted function:VENUS EPOS
(4) fitted function/(Data/MC):VENUS EPOS
y is a rapidity obtained with kaon mass
Figure 3.11: The steps of construction of the negative kaon adjustment for interactionenergy 158 GeV: (1) the generated MC spectra and preliminary NA61/SHINE spectra forinteraction energy 158 GeV; (2) the NA61/SHINE spectra divided by MC spectra; (3) thebi-linear function fitted to the divided spectra from (2); (4) the fitted function from (3)divided by spectra from (2), showing the quality of the fit.
41
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EPOS:
VENUS:
Figure 3.12: Spectra of antiprotons obtained with Monte Carlo models for interactionenergies 20 and 158 GeV (left figures) and the corresponding ratios of p̄ to all negativeparticles presented in percent (right figures). Rapidity was calculated with pion massassumption.
42
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EPOS:
VENUS:
Figure 3.13: Spectra of negatively charged kaons obtained with Monte Carlo models forinteraction energies 20 and 158 GeV (left figures) and the corresponding ratios of K− toall negative particles presented in percent (right figures). Rapidity was calculated withpion mass assumption.
43
-
EPOS:
VENUS:
Figure 3.14: The adjustment to the antiprotons obtained in Figure 3.10 and scaled withthe interaction energy.
EPOS:
VENUS:
Figure 3.15: The adjustment to the negative kaons obtained in Figure 3.10 and scaledwith the interaction energy.
44
-
EPOS:
VENUS:
Figure 3.16: Spectra of other negative particles obtained with Monte Carlo models forinteraction energies 20 and 158 GeV (left figures) and the corresponding ratios of others toall negative particles (right figures). Rapidity was calculated with pion mass assumption.
45
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3.4. The h− Corrections: Methods of Application and Inclu-
sion of Particle Adjustments
To obtain the spectra of negative pions from the spectra of all negative particles, one need
to apply the h− correction, responsible for eliminating from the spectra particles different
than primary negative pions. In the Analysis chapter there were proposed three methods of
application of this correction. The previous sections clearly indicates that EPOS model is
in better agreement with the experimental data, thus in here mainly results for this model
are presented. The mixed correction will be treated as reference, and other corrections
will be presented relative to it. This method was chosen as the best way of application the
h− correction and used in final h− analysis [24]. This was based on the assumption that
the MC model may deform the spectra of the different particle (negative pions and kaons,
antiprotons) in the similar way. Whereas, the feed-down have a different character, as it
represents not a spectra of particles produced in interaction, but the secondary pions from
decays of primary neutral particles and thus it may require different treatment. This is
important to keep in mind that the above reasoning is only the hypothesis, and it cannot
be confirmed by the comparison of corrections showed below. Actually, in ideal case, if
MC models will describe exactly the experiment, all the corrections should be the same.
On the other hand, the comparisons enables to view the size of the discrepancies between
the corrections, which is a very important feature, as it translates directly on the size of
discrepancies in the final spectra constructed with this corrections.
Figure 3.17 present the mixed corrections obtained from EPOS model. As can be
noticed, the correction generally decreases the number of particles, as it is usually below
1. At low energies, the correction is high in the region of low transverse momentum, what
corresponds to the secondary pions produced in the decay of neutral particles. The cor-
rection grows also on the edge of the spectra: at high rapidity region. The correction in
the area of high pT increases with the growth of the interaction energy.
Figure 3.18 presents the comparison of mixed correction with additive and multiplica-
tive correction. The ratio of additive to mixed correction is usually lower than 1, especially
in region of low transverse momentum. The additive correction is slightly bigger in the
region of high pT . The multiplicative correction has in the majority of the spectrum the
same values as the mixed one. The difference is only in low transverse momentum region,
where the ratio is over 1.2; it indicates that the correction decreasing the particle num-
ber in this region is higher for mixed method. This comparison shows that the additive
correction describes the region of low pT more intensively than the others. On the other
hand, it has a smaller correction in the region of high pT , which is described on the similar
level by the other two. Thus, in a way, the mixed correction can be seen as including both
46
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Figure 3.17: The mixed h− corrections from EPOS model.
the contributions, while the additive and multiplicative corrections focus only on one of
them. This comparison, however, do not enable the judgment whether this fact makes the
mixed correction better than either of the other two.
Figure 3.19 presents the ratio of correction obtained with EPOS model to the correc-
tion obtained with VENUS model. The discrepancies between the corrections are mainly
located in the region of low and high transverse momenta. The ratio in vast majority of
spectra is over 1, thus indicating that, as correction is usually below 1, the correction is
bigger for the VENUS model.
Figure 3.20 presents the ratio of mixed corrections without and with the particle ad-
justments presented in previous Section. It shows how the spectra change after application
of the adjustments. The ratio at 20 GeV reaches 0.9 for EPOS and 0.6 for VENUS in
low pT region. Additionally, in case of VENUS model, there is a significant contribution
in high rapidity-low pT region: with the factor up to 0.9, for the higher interaction ener-
gies. Concluding, it is visible, that the adjustments have more impact on the correction
constructed from VENUS model. It is consequence of the fact that this model described
worse the experimental data, and adjustments needed to be bigger.
In Figure 3.21 there are presented again the relative spectra of different methods of
application of h− correction, but with the inclusion of the adjustments. The distribution
of the discrepancies is similar as in Figure 3.18, but their values are 50% smaller.
47
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Additive/Mixed:
Multiplicative/Mixed:
Figure 3.18: Ratio of the additive and multiplicative to the mixed h− corrections fromEPOS model.
Figure 3.22 presents the comparison of both corrections obtained with both MC models
with adjustments. The main differences are in the region of high rapidity, near the edge of
spectra and for the high transverse momentum. Comparing Figure 3.22, where the ratio
of h− corrections obtained with EPOS and VENUS models with inclusion of adjustment,
with Figure 3.19, without adjustments, it is visible, that the adjustments result in the
48
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Figure 3.19: Ratio of the mixed h− corrections from EPOS model to the one from VENUSmodel.
decrease of discrepancies between h− corrections from other models. It suggests that the
adjustments were calculated and applied correctly, and the both models were corrected to
obtain nearly same final result.
49
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EPOS:
VENUS:
Figure 3.20: Ratio of h− mixed corrections from MC models without and with adjustment
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Additive/Mixed:
Multiplicative/Mixed:
Figure 3.21: Ratio of the additive and multiplicative to the mixed h− corrections fromEPOS model with adjustments.
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Figure 3.22: Ratio of the mixed h− corrections from EPOS and VENUS model withadjustments.
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Chapter 4
Conclusions and Outlook
In scope of this thesis was presented comparison of the particle multiplicity and spectra
obtained with Monte Carlo models EPOS and VENUS with available experimental data.
The comparison was then used as a basis for a construction of the adjustments to the
spectra of particles important in the h− analysis: primary negatively charged pions (π−),
secondary negatively charged pions from decays of neutral particles (π−(Λ) and π−(K0s ))
and primary negatively charged particles (p̄ and K−). Finally the methods of application
of the h− correction, responsible for eliminating from the all negative particles spectra
the contribution from the particles different than primary pions, were compared to find
the most effective one. The adjustments to the particle spectra were applied to the h−
correction.
The first important conclusion is that the EPOS model in vast majority of compared
records agrees better with experimental data than the VENUS model. Thus the adjust-
ments applied to the spectra obtained with the EPOS model are smaller than in VENUS
case. It suggests that the corrected EPOS model should be preferred in the h− analysis.
The analysis of the spectra of particles contributing to the h− correction showed that
the contributions come mainly:
from the secondary pions produced in the decay of Λ or K0s for low interaction
energies in the low transverse momentum region
from the negative hadrons like antiprotons and kaons for high interaction energies
in the high transverse momentum region.
The study of methods of application of the h− correction showed that the method includ-
ing both contributions is the mixed one: with the correction from the secondary pions
from weak decays applied additively, while the contribution from primary negative parti-
cles is applied multiplicatively. The additional inclusion of the adjustments to the particle
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spectra changes the h− correction by up to 20 %.
The h− correction and its adjustments obtained with use of the Monte Carlo models
is just one step in obtaining the final negative pion spectra obtained in the h− analysis
of NA61/SHINE experiment. The comparison of models was also the suggestion for the
choice of the model for the ongoing and future analysis. The description of the other steps
of h− analysis is provided more extensively elsewhere [24] and is connected with the MC
corrections on the reconstruction procedure and its efficiency.
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Acknowledgments
I would like to thank my supervisor, prof. Wojciech Dominik, for given me opportunities
and support.
My sincere thanks are in order to Antoni Aduszkiewicz, my daily supervisor, for the
support during the realization of the project and writing this thesis. Thank you for your
time, patience and useful advice.
Also I would like to thank all the people from the Particle Physics Group at the Uni-
versity of Warsaw and NA61/SHINE Collaboration for the welcoming me into their group,
friendly work environment and useful remarks on my research. It was a pleasure to work
with you.
Finally, warm thanks to all my close ones for motivating and supporting me.
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