1. Color Glass Condensate in High Energy QCD Kazunori Itakura SPhT, CEA/Saclay 32 nd ICHEP at Beijing China 16 Aug. 2004

2. 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

3. 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]

4. 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 --

5. 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

6. 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

7. “Phase diagram” Energy (low  high) Transverse resolution (low  high) BFKL Parton gas BFKL, BK DGLAP

8. Color Glass Condensate confronts experiments

9. A CGC fit to the HERA data Fit performed to F 2 data in x < 0.01 & 0.045 < 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]

10. 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]

11. 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]

12. 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.

13. 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]