quark pair production using dipole formalism in neutrino-proton scattering at high energies *
DESCRIPTION
Quark pair production using dipole formalism in neutrino-proton scattering at high energies *. Mairon Melo Machado High Energy Phenomenology Group, GFPAE IF – UFRGS, Porto Alegre [email protected] www.if.ufrgs.br/gfpae. * In collaboration with M. B. Gay Ducati and M. V. T. Machado. - PowerPoint PPT PresentationTRANSCRIPT
Quark pair production using dipole formalism in neutrino-proton scattering
at high energies *
Mairon Melo Machado
High Energy Phenomenology Group, GFPAE IF – UFRGS, Porto Alegre
www.if.ufrgs.br/gfpae
* In collaboration with M. B. Gay Ducati and M. V. T. Machado
Outline• Lepton-nucleon collision
• Color dipole formalism
• Structure functions
• Neutral Current (NC) process
• Neutrino-nucleon cross section
• Results and conclusions
Motivations
• Interaction of high energy neutrinos on hadron targets are an important probe to test QCD and to understand the parton properties of hadron structure
• Combinations of neutrino and anti-neutrino scattering data used to determine the structure functions
• The structure function F2 is the singlet distribution
• Phenomenology using saturation models within the Color Dipole Approach successfully describes current small-x data 1
• Purpose of a new high-energy, ultra-high statistics neutrino scattering experiment (NuSOnG)
1GAY DUCATI, M. B., MACHADO, M. M., MACHADO, M. V. T.
– PLB 644 (2007) 340;
Neutrino-nucleon collision
M is the nucleon mass
E is the neutrino energy
p and q are the nucleon and boson four-momenta
Z (q)
pi
p’j
pj
pk
GF is the Fermi constant
1.166.10-5 GeV-2
Mi is the boson mass
F2, FL and F3 are the structure functions
Neutrino-nucleon cross section
)()1)(( 22)(
xqxyxxqEmG
dxdy
d NFN
22)(
)1)(()( yxqxxxqEmG
dxdy
d NFN
2 ROBERTS, R. G., “The structure of the proton”, Cambridge University Press (1993);
2
Color dipole phenomenology ’s are the wave functions for electroweak bosons
z is the momentum fraction of quark and (1-z) is the momentum fraction of the antiquark
1 and 2 are the helicities of the quarks (1/2 or -1/2)
r is the transversal size of the dipole
dip is parametrized and fitted to the experiment .
Structure functions
Chiral
coupling
sin 2 θW = 0.23120
K0,1 are the McDonald functions
Quark distribution
• Gluon emits a quark-antiquark pair changing the quark distribution in the nucleon
• These quarks are called sea quarks
• Quark content is given by the sum of valence quarks and sea quarks
Dipole cross section
• Golec-Biernat-Wusthoff (GBW) 3
• Iancu-Itakura-Munier (IIM) 4
, 0 = 23 mb, ~ 0.288, x0 ~ 3.10-4 m, mf = 0.14 GeV
4exp1),(
22
02 sat
dip
Qrrx
HEP 08
Y=ln(1/x), BCGC = 5.5 GeV-2
3 GOLEC-BIERNAT, K; WUSTHOFF, M. PRD 60, 1140231 (1998);
4 IANCU, ITAKURA, MUNIER, PLB 590, 199 (2004);
Neutrino-nuclei interaction 5
Dipole cross section for bosons transversally or longitudinally polarized are extended for nuclei using Glauber-Gribov formalism
Nuclear profile function TA (b)
b is the impact parameter and n(r) is the nuclear matter density normalized as
HEP 08
|),(|),( 2, rxQx ARL
21
21
,.
22,,
1
0
2 ),(),,(
rxQrzdzrd AdipRL
)()( 22 bzdznbTA
Arrnd )(3
5 WATT, G. KOWALSKI, H. PRD 78 (2008) 014016
Structure functions (x fixed)
Virtuality dependence for b-CGC and GBW models
Small deviation more sizable at large Q2
Quarks (d,s) dominat over u
Electroweak couplings
Charm contribution 13%
Structure functions (Q2 fixed b-CGC model)
Dependence approximatelly power-like with an effective power which growths on Q2
λ(Q2=1 GeV2) ~ 0.12
λ(Q2=M2Z) ~ 0.224
Unusual behavior in the limit of large Q2 and large x
Structure functions (Q2 fixed GBW model) Estimates the uncertainty from the theoretical side
GBW model does not include the QCD evolution in the dipole cross sectin
Effective power is similar to the b-CGC model
FL being distinct at Q2=M2Z
Flattening in FL is stronger in b-CGC than in GBW
NC charm structure functions
Q2 xF2
F3
F2
F3
Neutral Current Cross Section Results
Energy (GeV) σcharm (cm2) σCharm/ σTotal
27 5,4 x 10-40 0,027
154 1,9 x 10-38 0,135
1000 7,1 x 10-37 0,154
10000 3,0 x 10-35 0,193
100000 3,3 x 10-34 0,225
Contribution of sea quarks dominates at high energies
neutrino-proton interaction
6 KWIECINSKI, J. et al. PRD 59 (1999) 093002
6
Neutral Current Cross Section Results
Energy (GeV) σcharm (cm2) σCharm/ σTotal
27 6,56 x 10-44 3,25 x 10-3
154 2,33 x 10-42 1,04 x 10-2
108 5,8 x 10-33 0,25
109 1,4 x 10-33 0.41
neutrino-nuclei interaction
0.23 fb
Analysis of small-x neutral current neutrino-nucleus is performed within the color dipole formalism
Structure functions F2 and FL are investigated
Employement of two phenomenological parametrizations for the dipole cross sections which succesfully describe small-x data
Deviations among the models at very small-x data
Further investigations are requested
Computation of the charm content to the total NC neutrino cross section consistent with current experimental measurements
Conclusions