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)

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

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

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

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

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

Normalization:

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

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

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

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

Initial conditions for BK evolution:

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

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

Limiting fragmentation in pp from MV/GBW + BK

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

Cut-off dependence:

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

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

Extrapolation to LHC: Estimated charged particle multiplicity ~

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.B (2004 ) M. Nardi W. Busza ALICE Tech. Proposal, M. Nardi, various models and fits Gabor Veres, QM2005

MV MV + frag. func. Pt distribution:

iii) D-Au collisions: PHOBOS

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.

Quark pair production in pA collisions

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

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

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

Results in the MV model: multi-scattering effects

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

R_pA: suppression Frankfurt, Strikman; Matsui, Fujii

Rapidity dist. of pairs from BK evolution

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

R_pA vs Y:

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

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

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