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Quark Pair Production in the Color Glass Condensate

Quark Pair Production in the Color Glass Condensate. Raju Venugopalan Brookhaven National Laboratory. AGS users-Quarkonium workshop, June 6th, 2006. Work done in collaboration with J.-P. Blaizot, H. Fujii and F. Gelis. Based on, a) F. Gelis, RV, PRD 69 : 014019, (2004)

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Quark Pair Production in the Color Glass Condensate

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  1. Quark Pair Production in the Color Glass Condensate Raju Venugopalan Brookhaven National Laboratory AGS users-Quarkonium workshop, June 6th, 2006

  2. Work done in collaboration with J.-P. Blaizot, H. Fujii and F. Gelis. Based on, a) F. Gelis, RV, PRD 69: 014019, (2004) b) J.-P. Blaizot, F. Gelis, RV, NPA 743:57, (2004) c) H. Fujii, F. Gelis, RV, PRL 95:162002 (2005) d) H. Fujii, F. Gelis, RV, hep-ph/0603099 & in preparation. Related work by Kharzeev & Tuchin; Tuchin; Kovchegov & Tuchin; Gelis, Kajantie and Lappi

  3. Outline of Talk • The kt factorization formalism (and its breaking) for heavy quark production in the CGC • Isolating multiple scattering & quantum evolution effects -results in MV & BK models • Summary and outlook

  4. Universality: collinear versus k_t factorization Collinear factorization: Heavy quark production at colliders Collins,Soper,Sterman

  5. Leading twist shadowing “Higher twists” Novel regime of QCD at high energies A

  6. Kt factorization: Are these “un-integrated gluon distributions” universal? In CGC, “Dipoles”- with evolution a la JIMWLK / BK RG equations

  7. HADRONIC COLLISIONS IN THE CGC FRAMEWORK Solve Yang-Mills equations for two light cone sources: For observables average over

  8. Inclusive pair production in CGC framework Gelis, RV hep-ph/0310090 Abelian Non-Abelian Lipatov vertex To lowest order in sources:

  9. Identical to Collins-Ellis+ Catani-Ciafaloni-Hautmann k_t factorization result is the un-integrated gluon distribution in the Gaussian MV model K_t factorization compared to RHIC D-Au data by Kharzeev & Tuchin (hep-ph/0310358)

  10. Quark production to all orders in pA Blaizot, Gelis, RV Neither quark pair production nor single quark production is kt-factorizable

  11. … = Pair cross-section: Amputated time ordered quark propagator in classical background field

  12. Result can however still be “factorized” into novel multi-parton distributions These multi-parton distributions can be computed in closed form in the Gaussian (MV) approximation Quantum evolution of these distributions can be computed By solving the JIMWLK or BK renorm. group equations

  13. Blaizot, Gelis, RV; Tuchin Interpretation: Wilson line correlators - the last appears in pair production only Simplify greatly in large N_c limit x-evolution can be computed with Balitsky-Kovchegov eqn.

  14. Results I) Violation of k_t factorization in the MV model (multiple scattering only-no x evolution of target)

  15. Large N_c results - good approximation to exact result

  16. Cronin effect for quark production: (MV model- re-scattering but no evolution)

  17. Simple “Non-local” Gaussian model-simulates effects of (extreme) quantum evolution

  18. Results in the MV model: multiple-scattering effects

  19. Collinear logs: Relation to pQCD LO in pQCD Logs can be absorbed into structure functions

  20. Collinear logs: NLO in pQCD

  21. K_t factorization => pair scatters off medium like a gluon (is collinear) For small P_t (< Q_s) , and large M, re-scatterings are significant.

  22. R_pA: suppression Chudakov effect Frankfurt, Strikman; Matsui, Fujii

  23. Kharzeev-Tuchin, Hep-ph/0510358 x_F dependence Need to also consider color octet contributions if matrix elements are large

  24. II) Rapidity dependence • No rapidity dependence in the MV model-multiple scattering but no x-evolution • Y-dependence via JIMWLK RG equations-simplified large N_c & Large A limit is the BK equation • Compute ``dipole” correlators solving BK with MV initial conditions Important for forward physics at RHIC and at LHC energies

  25. PHENIX

  26. A) BK equation for the unintegrated distribution: Non-linear equation for dipole amplitude BFKL kernel U’s in fund. rep.

  27. Gelis, Stasto, RV Large Nc limit: Above equation F.T. of dipole amplitude

  28. Rapidity dist. of pairs from BK evolution Sensitive to Large x (> 0.01) extrapolation

  29. R_pA from BK: Dots denote region “uncontaminated” by large x extrapolation

  30. R_pA vs Y:

  31. Quark Production in A-A

  32. Solve Dirac equation in background field of two nuclei… Gelis,Kajantie,Lappi PRL 2005

  33. Ratio of quarks to glue roughly consistent with a chemically equilibrated QGP

  34. Outlook • We can compute both small x evolution (shadowing) and multiple scattering effects in quark production on same footing. • More detailed studies (in color octet and color evaporation framework for J/Psi) in progress for D-Au collisions • Quark production in AA collisions can be computed at the earliest stages. Same order as NLO gluon production. • Computationally intensive effort in progress.

  35. Quark mass dependence…

  36. Q_s dependence…

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