Transcript ppt
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… STRUCTURE OF HIGHER ORDER CONTRIBUTIONS IN DIS + higher twist (power suppressed) contributions… Coefficient functions - C - computed to NNLO for many pr e.g., gg -> H Harlander, Kilgore; Ravindran,Van Neerven,Smith; … Splitting functions -P - computed to 3-loops recently! Moch, Vermaseren, Vogt DGLAP evolution: Linear RG in Q^2 Dokshitzer-Gribov-Lipatov-Altarelli-Par # of gluons grows rapidly at small x… Resolving the hadron -DGLAP evolution increasing But… the phase space density decreases -the proton becomes more dilute The other interesting limit-is the Regge limit of QCD: Physics of strong fields in QCD, multi-particle productionpossibly discover novel universal properties of theory in this lim BFKL evolution: Linear RG in x Balitsky-Fadin-Kuraev-Lipatov - Large x - Small x Gluon density saturates at f= Non-linear evolution: Gluon recombination QCD Bremsstrahlung Proton Proton is a dense many body system at high energies Mechanism for parton saturation: Gribov,Levin,Ryskin Mueller, Qiu Blaizot, Mueller Competition between “attractive” bremsstrahlung and “repulsive” recombination effects. Maximal phase space density => Saturated for Higher twists (power suppressed-in ) are important when: Leading twist “shadowing’’ of these contributions c extend up to at small x. Need a new organizing principlebeyond the OPE- at small x. McLerran, RV; Kovchegov; Jalilian-Marian,Kovner,McLerran, Weige Born-Oppenheimer: separation of large x and small x modes Dynamical Wee modes Valence modes-are static sources for wee modes In large nuclei, sources are Gaussian random sources MV, Kovchegov, Jeon, 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 Bosons with large occupation # ~ Typical momentum of gluons is - form a condensate 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. Rummukainen, Weigert Mean field approximation of hierarchy in large N_c and large A limit- the BK equation. 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 Rapidit y: 1 1/2 From saturation condition, How does Q_s behave as function of Y? Fixed coupling LO BFKL: LO BFKL+ running coupling: Re-summed NLO BFKL + CGC: Triantafyllopolous QuickTime™ and a TIFF (LZW) decompressor are needed to see this picture. 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: QuickTime™ and a TIFF (LZW) decompressor are needed to see this picture. Di-jet production at colliders k_t factorization: QuickTime™ and a TIFF (LZW) decompressor are needed to see this picture. Are these “un-integrated gluon distributions” universal? “Dipoles”-with evolution a la JIMWLK / BK HADRONIC COLLISIONS IN THE CGC FRAMEWORK QuickTime™ and a TIFF (LZW) decompressor are needed to see this picture. Solve Yang-Mills equations for two light cone sources: For observables average over Systematic power counting-inclusive gluon production Breaks down at next order in Krasnitz,RV; Balitsky 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 Quark production to all orders in pA Blaizot, Gelis, RV 3- & 4- point operators Two point-dipole operator in nucleus More non-trivial evolution with rapidity… The demise of the Structure function Dipoles (and multipole) operators may be more relevant observables at high energies Jalilian-Marian, Gelis; Kovner, Wiedemann Blaizot, Gelis, RV Are universal-process independent. RG running of these operators - detailed tests of high energy QCD. Strong hints of the CGC from Deuteron-Gold data at RHIC 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 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, Are there contributions in high energy QCD beyond JIMWL Are “dipoles” the correct degrees of freedom at high energi Do we have a consistent phenomenological picture? Can we understand thermalization from first principles?