Color Glass Condensate in High Energy QCD

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

2. Proton’s gluon density  high energy Color Glass Condensate A new form of matter made of gluons ColorGlass Condensate gluons arecreated from “frozen” random dense! colored color source, evolve slowly high occupation number compared to natural time scale ~ 1/as at saturation What is it ? Where and when can we see it ? Why is it important ? Anywhere if scatt. energy is high enough  hadrons, nuclei (strong interaction) ex) DIS at small x (proton), relativistic heavy ion collision (nucleus) Necessary for unitarization of scattering amplitude

3. Low energy BFKL eq.[Balitsky, Fadin,Kraev,Lipatov ‘78] dilute N :scattering amp. ~ gluon number t : rapidity t = ln 1/x ~ ln s exponential growth of gluon number  violation of unitarity [Balitsky ‘96, Kovchegov ’99] Balitsky-Kovchegov eq. dense, saturated, random Gluon recombination  nonlinearity saturation, unitarization, universality High energy Gluon Saturation & Quantum Evolution

4. T.R.Malthus (1798) N:polulation density Growth rate is proportional to the population at that time.  Solution population explosion! P.F.Verhulst (1838) Growth constant k decreases as N increases. (due to lack of food, limit of area, etc) Logistic equation -- ignoring transverse dynamics -- Population growth linear regime non-linear exp growth saturation universal 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 t , Logistic eq.  BK eq.  Time (energy)

5. - Energy and nuclear A dependences LO BFKL NLO BFKL R [Gribov,Levin,Ryskin 83, Mueller 99 ,Iancu,Itakura,McLerran’02] [Triantafyllopoulos, ’03] A dependence gets modified in running coupling[Al Mueller ’03] Saturation scale 1/QS(x) : transverse size of gluons when the transverse plane of a hadron/nucleus is filled by gluons - Boundary between CGC and non-saturated regimes - Similarity between HERA (x~10-4, A=1) and RHIC (x~10-2, A=200) QS(HERA) ~ QS(RHIC)

6. = Q/Qs(x)=1 Total cross section Saturation scale from the data consistent with theoretical results Geometric scaling DIS cross section s(x,Q) depends only on Q/Qs(x) at small x [Stasto,Golec-Biernat,Kwiecinski,’01] • Natural interpretation in CGC • Qs(x)/Q=(1/Q)/(1/Qs) : number of overlapping • 1/Q: gluon sizetimes Once transverse area is filled with gluons, the only relevant variable is “number of covering times”.  Geometric scaling Geometric scaling persists even outside of CGC!!  “Scaling window”[Iancu,Itakura,McLerran,’02] Scaling window = BFKL window

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

8. ColorGlassCondensateconfrontsexperiments

9. A CGC fit to the HERA data [Iancu, Itakura, Munier,’03] Fit performed to F2 data in x < 0.01 & 0.045 < Q2<45 GeV2 • Based on analytic solutions • to the BK equation Including • geometric scaling and its • violation, saturation effects. • Only 3 parameters • [proton radius, x0and l=0.25 • for Qs2(x)=(x0/x)lGeV2] • Good agreement with data • The same fit works well for • vector meson production, • diffractive F2, [Forshaw et al ’04 ] • FL[Goncalves,Machado’04]

10. CGC at RHIC (Au-Au) Most of the produced particles have small momenta less than 1 GeV ~ QS(RHIC)  Effects of saturationmay be visible in bulk quantities Multiplicity : pseudo-rapidity & centrality dependences  in good agreement with the data [Kharzeev,Levin,’01]

11. Nuclear modification factor for dAu collisions at RHIC [Brahms] CGC at RHIC (d-Au) if RdAu=1,dAu is just a sum of pp Cronin peak at h=0, suppression at h=3.2 (high energy) 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 [Albacete, Armesto, Kovner, Salgado, Wiedemann 03] [Gelis,Jalilian-Marian 03, Kharzeev-Kovchegov-Tuchin 03] [Kharzeev,Levin,McLerran 02, Iancu,Itakura,Triantafyllopoulos 04]

12. Summary ColorGlassCondensate - 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 ColorGlassCondensate - 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]