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Quark pair production using dipole formalism in neutrino-proton scattering at high energies *

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.

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Quark pair production using dipole formalism in neutrino-proton scattering at high energies *

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  1. 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

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

  3. 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)

  4. 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

  5. 2 Neutrino-nucleon cross section • 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);

  6. 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.

  7. Structure functions sin 2θW = 0.23120 Chiral coupling K0,1 are the McDonald functions

  8. 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

  9. 3 GOLEC-BIERNAT, K; WUSTHOFF, M. PRD 60, 1140231 (1998); 4 IANCU, ITAKURA, MUNIER, PLB 590, 199 (2004); 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 Y=ln(1/x), BCGC = 5.5 GeV-2 HEP 08

  10. 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

  11. 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%

  12. 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

  13. 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

  14. NC charm structure functions F2 Q2 x F2 F3 F3

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

  16. Neutral Current Cross Section Results neutrino-nuclei interaction 0.23 fb

  17. 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

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