1. Quark Pair Production in the Color Glass Condensate Raju Venugopalan Brookhaven National Laboratory RBRC Heavy Flavor Workshop, Dec. 12th-14th, 2005

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

3. Outline of Talk The kt factorization formalism for heavy quark production in the CGC The breaking of kt factorization by higher twist effects in pA and AA scattering Isolating multiple scattering & quantum evolution effects -results in MV & BK models Summary and outlook

4. McLerran, Ludlam

5. Universality: collinear versus k_t factorization Heavy quark production at colliders Collinear factorization:

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

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

8. Inclusive gluon production in pp & p-A :  K_t factorization seen “trivially” in p-p  Also holds for inclusive gluon production lowest order in but all orders in Adjoint dipole -includes all twists Breaks down at next order in Krasnitz,RV; Balitsky (Kovchegov, Mueller)

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

10. 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)

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

13. 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

14. 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. Blaizot, Gelis, RV; Tuchin

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

16. Large N_c results - good approximation to exact result

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

22. Simple “Non-local” Gaussian model-simulates effects of quantum evolution

23. Quark mass dependence…

24. Q_s dependence…

25. Pair cross-sections:

26. R_pA: suppression Frankfurt, Strikman; Matsui, Fujii

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

28. 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  The 3-point and 4-point functions can also be computed at large N_c -factorize into products of 2-point functions

30. Quark Production in A-A

31. 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. Quark production in AA collisions can be computed at the earliest stages. Energy loss? Is NLO in this picture but recent theoretical developments suggest it can be computed consistently. Outlook We can compute both small x evolution (shadowing) and multiple scattering effects in quark production on same footing. More detailed studies in progress for D-Au collisions