The Color glass COndensate

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

2. 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

3. 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…

4. STRUCTURE OF HIGHER ORDER CONTRIBUTIONS IN DIS + higher twist (power suppressed) contributions… • 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

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

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

7. 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

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

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

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

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

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

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

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

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

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

17. 1 1/2 Evolution eqn. for the dipole cross-section BK: Rapidity: • From saturation condition,

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

19. 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

20. 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!

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

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

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

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

25. Breaks down at next order in Krasnitz,RV; Balitsky Systematic power counting-inclusive gluon production Adjoint dipole -includes all twists • K_t factorization seen “trivially” in p-p • Also holds for inclusive gluon production lowest order in but all orders in

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

27. 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

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

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

30. 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: Isotropizationtime ~ ~ 0.3 fm Mrowczynski; Arnold,Lenaghan,Moore,Yaffe Romatschke, Strickland; Jeon, RV, Weinstock

31. Open questions • 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?