1. Charm production in neutrino-nuclei collisions within the color dipole formalism at very 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. Lepton-nucleon collision Neutrino-nucleon cross section Structure functions Color dipole formalism Charged Current (CC) process and Neutral Current (NC) process Neutrino-nuclei Interaction Results Conclusions Outline HEP 08

3. Color dipole approach (CDA) for lepton-hadron DIS Phenomenology using saturation models in CDA (GBW and IIM models) Neutrino DIS at small-x within the dipole formalism Analysis of charm production cross section in NC interactions Color dipole formalism arises as a robust theoretical approach to describe small-x structure functions 1 Motivations 1 GAY DUCATI, M. B., M. M. M., MACHADO, M. V. T. – PLB 644 (2007) 340 HEP 08

4. Neutrino-nucleon collision  M is the nucleon mass  E is the neutrino energy  p and q are the nucleon and boson four-momenta HEP 08 W, Z (q) pipi p’ j pjpj pkpk

5. 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 HEP 08

6. Neutrino-nucleon cross section  G F is the Fermi constant 1.166.10 -5 GeV -2  M i is the boson mass  F 2, F L and F 3 are the structure functions HEP 08

7. Structure functions Chiral coupling  sin 2 θ W = 0.23120  θ W is the Weinberg angle 2 3 2 ROBERTS, R. G., “The structure of the proton”, Cambridge University Press 1993 HEP 08

8. Color dipole phenomenology   are the wave functions of quarks  z is the momentum fraction of quark and (1-z) is the momentum fraction of the antiquark  1 and 2 are the helicity of the quarks (1/2 or -1/2)  r is the transversal size of the dipole   dip is parametrized and fitted to the experiment. HEP 08

9. Structure functions  Structure function for bosons transversally or longitudinally polarized K 0,1 are the McDonald functions m q (m q ) is the mass of the quarks (antiquarks) HEP 08

10. Neutrino-nuclei interaction  Dipole cross section for bosons transversally or longitudinally polarized are extended for nuclei using Glauber-Gribov formalism  Nuclear profile function T A (b)  b is the impact parameter and n(r) is the nuclear matter density normalized as HEP 08

11. Dipole cross section Golec-Biernat-Wusthoff (GBW) 3 Iancu-Itakura-Munier (IIM) 4 Parameters fitted by data comparison,  s = 0.63 anomalous dimension, a and b are constants,  0 = 23 mb, ~ 0.288, x 0 ~ 3.10 -4 m, m f = 0.14 GeV HEP 08 3 GOLEC-BIERNAT, K; WUSTHOFF, M. PRD 60, 1140231 (1998); 4 IANCU, ITAKURA, MUNIER,.PLB 590, 199 (2004)

12. Comparison IIM and GBW Total = valence + sea Gay Ducati, MMM, Magno Machado, PLB 644 (2007) 340 HEP 08

13. NC structure functions (Q 2 fixed) F2F2 FLFL F3F3 HEP 08

14. NC structure functions (x fixed) F2F2 FLFL F3F3 HEP 08

15. NC charm structure functions Q2Q2 x F2F2 F3F3 F2F2 F3F3 HEP 08

16. Neutral Current Cross Section Results  High energies  contribution of sea quarks dominates neutrino-proton interaction 5 KWIECINSKI, J; et al. PRD 59 (1999) 093002 Energy (GeV)σ charm (cm 2 )σ Charm / σ Total 275,4 x 10 -40 0,027 1541,9 x 10 -38 0,135 10007,1 x 10 -37 0,154 100003,0 x 10 -35 0,193 1000003,3 x 10 -34 0,225 5

17. Neutral Current Cross Section Results Energy (GeV)σ charm (cm 2 )σ Charm / σ Total 276,56 x 10 -44 3,25 x 10 -3 1542,33 x 10 -42 1,04x10 -2 10 8 5,8 x 10 -33 0,25 10 9 1,4 x 10 -33 0.41 10 3,21 x 10 -31 0,42 neutrino-nuclei interaction 0,23 fb

18. Conclusions  Description of small-x structure functions in neutrino-hadron and neutrino-nuclei interaction using color dipole formalism  GBW parametrization gives good result to proton structure functions  Extension to neutrino-nuclei interaction is suitable  Estimations gives good results in comparison to neutrino-nuclei (NuTeV and CHORUS) data for charm quark contribution  Important framework to perform estimations for future neutrino-nuclei experiments (MINERvA and Neutrino Factory)  Color dipole formalism is a good model do describes deep inelastic scattering HEP 08