2. Outline of Lectures Lecture I: EFT approach to high energy QCD-The Color Glass Condensate; multi-particle production in the CGC Lecture II: Hadronic scattering in the CGC - multiple scattering & quantum evolution effects in limiting fragmentation & quark pair production Lecture III: Plasma instabilities & thermalization in the CGC; computing particle production in Heavy Ion collisions to next-to-leading order (NLO)

3. Limiting fragmentation: Benecke, Chou, Yang, Yen PHOBOS Work motivated by A. Bialas and M. Jezabek

4. Proton-Nucleus collisions in the Color Glass Condensate Power counting may also be applicable in AA collisions in the fragmentation regions

5. Solve classical Yang-Mills equations: with two light cone sources Proton sourceNuclear source Dumitru, McLerran; Blaizot, Gelis, RV Lorentz gauge:

6. Systematically truncate equations to lowest order in and all orders into obtain gauge field Compute the k_perp factorized inclusive multiplicity: M. Braun; Kharzeev, Kovchegov, Tuchin; Blaizot, Gelis, RV

7. Unintegrated distribution: with the path ordered exponentials in the adjoint representation = Compute in CGC EFT

8. Normalization:

9. First, a qualitative explanation of LF: Large x-dilute projectile Small x-black disc-unitary limit- No dependence on x_2 = y+ y_beam When From unitarity of the U matrices ~ Bj. Scaling => independent of x_2 J. Jalilian-Marian

10. Detailed analysis: A) Solve RG (in x) equations for unintegrated gluon distributions- consider the Balitsky-Kovchegov (BK) “mean field” equation (large Nc and large A limit of general expression in the CGC) B) Compute inclusive distributions and compare to data from pp, D-A and AA collisions for different initial conditions Similar in spirit to previous work of Kharzeev, Levin, Nardi Gelis, Stasto, RV

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

12. Large Nc limit: F.T. of dipole amplitude Above equation

13. Initial conditions for BK evolution:

14. Parameters: From quark counting rules Regulates log. Infrared divergence (same value in \eta -> y conversion) Take zero for AA-may need finite value for pp

15. B) Results: Note: assume Parton-Hadron duality initially - shall discuss effects of fragmentation later i) PP collisions: UA5 data: PHOBOS data:

16. Limiting fragmentation in pp from MV/GBW + BK

17. Extrapolation to LHC Extrapolation with GBW initial conditions -MV is much flatter

18. Cut-off dependence:

19. P_t distribution-effect of fragmentation functions: MV GBW MV+frag.function UA1 data averaged over y=0.0-2.5

20. ii) AA collisions: PHOBOS Data at c.m energies Of 19.6, 130, 200 GeV/n Filled triangles, squares & circles BRAHMS Open triangles, squares & circles STAR Data at 62.4 GeV/n

21. Extrapolation to LHC: Estimated charged particle multiplicity ~ 1000-1500

22. dN/deta extrapolations to LHC Central Pb+Pb collisions at LHC energy Assuming: dN/d  grows  log(s) and linear scaling at high  holds Acta Phys.Polon.B35 2873 (2004 ) M. Nardi W. Busza ALICE Tech. Proposal, M. Nardi, various models and fits Gabor Veres, QM2005

23. MV MV + frag. func. Pt distribution:

24. iii) D-Au collisions: PHOBOS

25. Summary of LF discussion:  In the kt factorization framework, LF follows from Saturation of unitarity constraint in the target wavefunction-``black disc” limit. Bjorken scaling at large x  Deviations from LF test QCD evolution equations (caveat: large x extrapolations matter)  Fragmentation function effects important for better agreement with data at higher energies (study in progress). Need to quantify deviations from kt factorization as well.

26. Quark pair production in pA collisions

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

28. Result not kt factorizable in general -can however be “factorized” into novel multi-parton distributions These multi-parton distributions can be computed: a)in closed form in Gaussian (MV) approximation - study multiple scattering effects b) Quantum evolution of distributions determined by JIMWLK or BK RG eqns. - study shadowing effects as well Blaizot, Gelis, RV

29. 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

30. Results in the MV model: multi-scattering effects

31. Collinear logs: Relation to pQCD LO in pQCD NLO in pQCD

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

33. Rapidity dist. of pairs from BK evolution

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

35. R_pA vs Y:

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

37. Ratio of quarks to glue roughly consistent with a chemically equilibrated QGP at early times

38. Quark production in AA collisions can be computed at the earliest stages. 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