The Color glass COndensate A classical effective theory of high energy QCD Raju Venugopalan Brookhaven National Laboratory ICPAQGP, Feb. 8th-12th, 2005

Outline of talk:  Introduction  A classical effective theory (and its quantum evolution) for high energy QCD  Hadronic scattering and k_t factorization in the Color Glass Condensate  What the CGC tells us about the matter produced in dA and AA collisions at RHIC.  Open issues

Much of the discussion in pQCD has focused on the Bjorken limit: Asymptotic freedom, the Operator Product Expansion (OPE) & Factorization Theorems: machinery of precision physics in QCD…

 Coefficient functions - C - computed to NNLO for many processes, e.g., gg -> H Harlander, Kilgore; Ravindran,Van Neerven,Smith; …  Splitting functions -P - computed to 3-loops recently! Moch, Vermaseren, Vogt + higher twist (power suppressed) contributions… STRUCTURE OF HIGHER ORDER CONTRIBUTIONS IN DIS

DGLAP evolution: Linear RG in Q^2 Dokshitzer-Gribov-Lipatov-Altarelli-Parisi # of gluons grows rapidly at small x…

increasing But… the phase space density decreases -the proton becomes more dilute Resolving the hadron -DGLAP evolution

The other interesting limit-is the Regge limit of QCD: Physics of strong fields in QCD, multi-particle production- possibly discover novel universal properties of theory in this limit

- Large x - Small x Gluon density saturates at f= BFKL evolution: Linear RG in x Balitsky-Fadin-Kuraev-Lipatov

Proton Proton is a dense many body system at high energies QCD Bremsstrahlung Non-linear evolution: Gluon recombination

Mechanism for parton saturation: Competition between “attractive” bremsstrahlung and “repulsive” recombination effects. Maximal phase space density => Saturated for Gribov,Levin,Ryskin Mueller, Qiu Blaizot, Mueller

Need a new organizing principle- beyond the OPE- at small x.  Higher twists (power suppressed-in ) are important when :  Leading twist “shadowing’’ of these contributions can extend up to at small x.

Born-Oppenheimer: separation of large x and small x modes Dynamical Wee modes Valence modes-are static sources for wee modes McLerran, RV; Kovchegov; Jalilian-Marian,Kovner,McLerran, Weigert In large nuclei, sources are Gaussian random sources MV, Kovchegov, Jeon, RV

Hadron at high energies is a Color Glass Condensate Random sources evolving on time scales much larger than natural time scales-very similar to spin glasses Typical momentum of gluons is Bosons with large occupation # ~ - form a condensate Gluons are colored

Quantum evolution of classical theory: Wilsonian RG Fields Sources Integrate out Small fluctuations => Increase color charge of sources JIMWLK (Jalilian-Marian, Iancu, McLerran, Weigert, Leonidov, Kovner)

JIMWLK RG Eqns. Are master equations-a la BBGKY hierarchy in Stat. Mech. -difficult to solve  Preliminary numerical studies.  Mean field approximation of hierarchy in large N_c and large A limit- the BK equation. Rummukainen, Weigert Balitsky; Kovchegov

The hadron at high energies Mean field solution of JIMWLK = B-K equation Balitsky-Kovchegov DIS: Dipole amplitude N satisfies BFKL kernel

BK: Evolution eqn. for the dipole cross-section  From saturation condition, 1 1/2 Rapidit y:

How does Q_s behave as function of Y? Fixed coupling LO BFKL: LO BFKL+ running coupling: Re-summed NLO BFKL + CGC: Triantafyllopolous Very close to HERA result!

Remarkable observation: Munier-Peschanski B-K same universality class as FKPP equation FKPP = Fisher-Kolmogorov-Petrovsky-Piscunov FKPP-describes travelling wave fronts - B-K “anomalous dimensions” correspond to spin glass phase of FKPP

Stochastic properties of wave fronts => sFKPP equation W. Saarlos D. Panja Exciting recent development: Can be imported from Stat. Mech to describe fluctuations (beyond B-K) in high energy QCD. Tremendous ramifications for event-by-event studies At LHC and eRHIC colliders!

Novel regime of QCD evolution at high energies “Higher twists” Leading twist shadowing

Universality: collinear versus k_t factorization Collinear factorization: Di-jet production at colliders

k_t factorization: Are these “un-integrated gluon distributions” universal? “Dipoles”-with evolution a la JIMWLK / BK

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

 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 Systematic power counting-inclusive gluon production

Quark production to all orders in pA Blaizot, Gelis, RV Two point-dipole operator in nucleus 3- & 4- point operators More non-trivial evolution with rapidity…

The demise of the Structure function  Dipoles (and multipole) operators may be more relevant observables at high energies  Are universal-process independent.  RG running of these operators - detailed tests of high energy QCD. Jalilian-Marian, Gelis; Kovner, Wiedemann Blaizot, Gelis, RV

Strong hints of the CGC from Deuteron-Gold data at RHIC

Colliding Sheets of Colored Glass at High Energies Classical Fields with occupation # f= Initial energy and multiplicity of produced gluons depends on Q_s Krasnitz,Nara,RV; Lappi Straight forward extrapolation from HERA: Q_s = 1.4 GeV

McLerran, Ludlam In bottom up scenario, ~ 2-3 fm at RHIC Baier,Mueller,Schiff,Son Exciting possibility - non-Abelian “Weibel” instabilities speed up thermalization - estimates: Isotropization time ~ ~ 0.3 fm Mrowczynski; Arnold,Lenaghan,Moore,Yaffe Romatschke, Strickland; Jeon, RV, Weinstock

 Are there contributions in high energy QCD beyond JIMWLK?  Are “dipoles” the correct degrees of freedom at high energies?  Do we have a consistent phenomenological picture?  Can we understand thermalization from first principles?