High Energy Phenomenology Group, GFPAE IF – UFRGS, Porto Alegre 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 melo.machado@ufrgs.br www.if.ufrgs.br/gfpae * In collaboration with M. B. Gay Ducati and M. V. T. Machado Mairon Machado

Outline Lepton-nucleon collision Color dipole formalism Structure functions Neutral Current (NC) process Neutrino-nucleon cross section Results and conclusions Mairon Machado

1GAY DUCATI, M. B., MACHADO, M. M., MACHADO, M. V. T. – PLB 644 (2007) 340; 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) Mairon Machado

Neutrino-nucleon collision Z (q) p’j pi M is the nucleon mass E is the neutrino energy p and q are the nucleon and boson four-momenta pj pk Mairon Machado

Neutrino-nucleon cross section 2 GF is the Fermi constant 1.166.10-5 GeV-2 Mi is the boson mass F2, FL and F3 are the structure functions 2 ROBERTS, R. G., “The structure of the proton”, Cambridge University Press (1993); Mairon Machado

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 sin 2 θW = 0.23120 Chiral coupling K0,1 are the McDonald functions Mairon Machado

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 Mairon Machado

Dipole cross section Golec-Biernat-Wusthoff (GBW) 3 3 GOLEC-BIERNAT, K; WUSTHOFF, M. PRD 60, 1140231 (1998); 4 IANCU, ITAKURA, MUNIER, PLB 590, 199 (2004); Golec-Biernat-Wusthoff (GBW) 3 Iancu-Itakura-Munier (IIM) 4 , 0 = 23 mb,  ~ 0.288, x0 ~ 3.10-4 m, mf = 0.14 GeV Y=ln(1/x), BCGC = 5.5 GeV-2 HEP 08

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 5 WATT, G. KOWALSKI, H. PRD 78 (2008) 014016 HEP 08

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% Mairon Machado

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 Mairon Machado

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 Mairon Machado

NC charm structure functions Q2 x F2 F3 F3 Mairon Machado

Neutral Current Cross Section Results 6 neutrino-proton interaction Contribution of sea quarks dominates at high energies 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 6 KWIECINSKI, J. et al. PRD 59 (1999) 093002 Mairon Machado

Neutral Current Cross Section Results neutrino-nuclei interaction 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 0.23 fb Mairon Machado

Conclusions 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 Mairon Machado