Color Glass Condensate in High Energy QCD Kazunori Itakura SPhT, CEA/Saclay 32 nd ICHEP at Beijing China 16 Aug. 2004
Color Glass Condensate What is it ? Where and when can we see it ? Why is it important ? A new form of matter made of gluons Color Glass Condensate gluons are created from “frozen” random dense! colored color source, evolve slowly high occupation number compared to natural time scale ~ 1/ s at saturation Anywhere if scatt. energy is high enough hadrons, nuclei (strong interaction) ex) DIS at small x (proton), relativistic heavy ion collision (nucleus) Proton’s gluon density high energy Necessary for unitarization of scattering amplitude
Gluon Saturation & Quantum Evolution dilute Low energy BFKL eq. [Balitsky, Fadin,Kraev,Lipatov ‘78] N : scattering amp. ~ gluon number : rapidity = ln 1/x ~ ln s exponential growth of gluon number violation of unitarity High energy dense, saturated, random Balitsky-Kovchegov eq. Gluon recombination nonlinearity saturation, unitarization, universality [Balitsky ‘96, Kovchegov ’99]
Population growth Solution population explosion! N : polulation density T.R.Malthus (1798) Growth rate is proportional to the population at that time. P.F.Verhulst (1838) Growth constant decreases as N increases. (due to lack of food, limit of area, etc) 1. Exp-growth is tamed by nonlinear term saturation !! 2. Initial condition dependence disappears at late time dN/dt =0 universal ! 3. True if gluons had no momentum dependence… t rapidity , Logistic eq. BK eq. Logistic equation linear regime non-linear exp growth saturation universal Time (energy) -- ignoring transverse dynamics --
R Saturation scale - Boundary between CGC and non-saturated regimes - Similarity between HERA (x~10 -4, A=1) and RHIC (x~10 -2, A=200) Q S (HERA) ~ Q S (RHIC) - Energy and nuclear A dependences LO BFKL NLO BFKL [Gribov,Levin,Ryskin 83, Mueller 99,Iancu,Itakura,McLerran’02] [Triantafyllopoulos, ’03] A dependence gets modified in running coupling [Al Mueller ’03] 1/Q S (x) : transverse size of gluons when the transverse plane of a hadron/nucleus is filled by gluons
Geometric scaling Geometric scaling persists even outside of CGC!! “Scaling window” [Iancu,Itakura,McLerran,’02] DIS cross section x,Q) depends only on Q/Qs(x) at small x = Q/Qs(x)=1 [Stasto,Golec-Biernat,Kwiecinski,’01] Total cross section Once transverse area is filled with gluons, the only relevant variable is “number of covering times”. Geometric scaling Natural interpretation in CGC Qs(x)/Q=(1/Q)/(1/Qs) : number of overlapping 1/Q: gluon size times Scaling window = BFKL window consistent with theoretical results Saturation scale from the data
“Phase diagram” Energy (low high) Transverse resolution (low high) BFKL Parton gas BFKL, BK DGLAP
Color Glass Condensate confronts experiments
A CGC fit to the HERA data Fit performed to F 2 data in x < 0.01 & < Q 2 <45 GeV 2 - Based on analytic solutions to the BK equation Including geometric scaling and its violation, saturation effects. - Only 3 parameters [proton radius, x 0 and for Qs 2 (x)=(x 0 /x) GeV 2 ] - Good agreement with data - The same fit works well for vector meson production, diffractive F 2, [Forshaw et al ’04 ] F L [Goncalves,Machado’04] [Iancu, Itakura, Munier,’03]
CGC at RHIC (Au-Au) Most of the produced particles have small momenta less than 1 GeV ~ Q S (RHIC) Effects of saturation may be visible in bulk quantities Multiplicity : pseudo-rapidity & centrality dependences in good agreement with the data [Kharzeev,Levin,’01]
CGC at RHIC (d-Au) if R dAu =1, dAu is just a sum of pp Cronin peak at =0, suppression at =3.2 (high energy) Nuclear modification factor for dAu collisions at RHIC [Brahms] Consistent with CGC picture !! Numerical analysis Cronin peak = multiple scattering (McLerran-Venugopalan model) High pt suppression = due to mismatch between “evolution speed” of proton & nucleus [Kharzeev,Levin,McLerran 02, Iancu,Itakura,Triantafyllopoulos 04] [Gelis,Jalilian-Marian 03, Kharzeev-Kovchegov-Tuchin 03] [Albacete, Armesto, Kovner, Salgado, Wiedemann 03]
Summary Color Glass Condensate - high density gluonic matter, relevant for high energy scattering saturation of gluon distribution (non-linearity), unitarization of scattering amplitude, universal (insensitive to initial conditions) natural interpretation of geometric scaling - can be compared with experiments small x data in DIS at HERA bulk properties of AuAu at RHIC Cronin effect and high pt suppression in dAu at RHIC - will be more important at LHC or higher energy experiments.
Topics not covered… Very theoretical aspects of the Color Glass Condensate - JIMWLK equation = Renormalization group eq. for the weight function of random color source [Jalilian-Marian, Iancu, McLerran, Weigert, Leonidov, Kovner] can derive the Balitsky equation equivalent Langevin approach [Weigert, Blaizot, Iancu] classical simulation [Krasnitz,Nara,Venugopalan,Lappi] - Properties of the Balitsky-Kovchegov and Balitsky equations Numerical solutions [Motyka, Stasto, Golec-Biernat, Rummukainen, Weigert] Absence of diffusion, geometric scaling, impact parameter dependence Analytic solutions [Levin,Tuchin,Iancu,Itakura,McLerran,Ferreiro, Kovner,Wiedemann] Levin-Tuchin law, scaling solution with anomalous dimension, Froissart bound Analogy with traveling wave [Munier,Peschanski] Difference btw Balitsky-Kovchegov and Balitsky equations [Mueller,Shoshi,Janik,Peschanski,Rummukainen,Weigert] Computation of other observables at RHIC, predictions for LHC Azimuthal correlation of jets [Kharzeev,Levin,McLerran] dilepton, charm production [Blaizot,Gelis,Venugopalan,Baier,Shiff,Mueller,Kharzeev,Tuchin]