1. High energy hadronic/nuclear scatterings in QCD Kazunori Itakura IPNS, KEK “Towards precision QCD physics” March 10th, 2007

2. Personal memories about Kodaira-san ~ 1995 Got to know him as one of the audience of his review talks ~ 1998 First real acquaintance Visited Hiroshima University to give a seminar (on Light-Front field theory) Shared his vision about the future of hadron physics in Japan “Let’s form a hadron community in Japan ! ” (for the communication between particle and nuclear theorists) 2000~ Rendezvous abroad I moved to BNL in NY. Kodaira-san was a frequent visitor. Every time we met, I was greatly encouraged by him. “You are proceeding in the right direction ! ” 2005 In KEK I came back to Japan (KEK) just after Kodaira-san moved to KEK. Asked him to give a review talk in the workshop I organized. He has been watching our progress about high energy nuclear scatterings.

3. Kodaira-san’s concern about LHC Domestic workshop “Progress in Particle Physics 2006” at YITP Audio file (in Japanese) available from http://higgs.phys.kyushu-u.ac.jp/ppp06/ August 3 rd J. Kodaira, “Perturbative QCD: present status and problems” A pessimistic (but honest) talk emphasizing our poor understanding of the “QCD-background” at LHC energies After explaining the standard parton picture in pp collisions at LHC, he said without showing any slides, “I don’t mention this so frequently because it will surely throw you into a panic, but there is one thing about which well-educated experts are seriously worried. At the LHC energies, we will see so many events involving small-x partons, and the density of small-x partons will become exceedingly high. This makes us worried about the possibility that the parton distribution functions obtained by simple extrapolation of those obtained from the HERA and Tevatron experiments could be useless. I mean, multiple scattering which is present in RHIC could occur even in LHC. If this is true, we have to determine the parton distribution functions from the LHC experiment itself. (…) We sometimes discuss such possibility in our community, but we don’t mention it in public so as not to make people panic. So, the present situation is very hard.” (translation by KI)

4. What happens at RHIC ? A hot and dense matter is created after the heavy ion collisions.  strongly interacting QGP(?) A dense gluonic state is formed in each nucleus before the collision.  Color Glass Condensate STAR

5. Color Glass Condensate (CGC) higher energy Dilute gas COLOR : A state made of gluons with colors. GLASS : Almost frozen “random” color source creates gluon fields CONDENSATE : High density. Occupation number ~ O ( 1 /  s ) CGC: high density gluons Multiple gluon production A new “semi-hard” scale: “saturation scale” Q S >  QCD = typical transverse size of gluons at saturation  weak coupling  S (Q S ) << 1 Weakly interacting many body system of gluons The universal state of matter which appears in the limit of large scattering energies. An accidental coincidence: HERA (x~10 -4, A=1) ~ RHIC (x~10 -2, A=200)  Q S (HERA) ~ Q S (RHIC) ~ 1 GeV LO BFKL NLO BFKL

6. CGC “observed” at RHIC Deuteron Au collisions 2  1 process is dominant when the target nucleus is saturated A~1/g [Kharzeev,Kovchegov,Tuchin, ’04, Dumitru,Hayashigaki,Jalilian-Marian, ’05, etc] h Au (CGC) d  dipole fqfqfqfq D q /h : Dipole cross section  saturation Valence quark distrib.Fragmentation fnc. d Au q, g g Going forward = probing nuclear wavefunction at smaller x h-h- (h - +h + )/2 Nuclear modification factor Suppression at moderate p t is due to saturation of the nuclear wavefunction. analytical investigation  Iancu,KI,Triantafyllopoulos mid rapidity forward rapidity

7. Towards more precise physics? DIS is the ideal (cleanest) laboratory for studying CGC, but we have to go to very small x to get a large Qs (A=1). Still, accidental coincidence btw Qs(RHIC) and Qs(HERA)  CGC should be observed in HERA 1. Geometric scaling 2. The CGC fit of F 2 (x,Q 2 )

8. Geometric scaling in DIS as an evidence  *p total cross section [Stasto,Kwiecinski,Golec-Biernat 2001] The  *-proton total cross section  (Q 2, x) becomes a function of only one variable  Q 2 /Q s 2 (x) at small x :  (Q 2,x)=f(  ), with Q s 2 (x) ~1/x    determined by the fit. x-dependence of Q s is consistent with CGC A scaling window exists outside of CGC Qs 2 < Q 2 < Qs 4 /  2 [Iancu,KI,McLerran]  Existence of saturation scale: Qs

9. DIS at HERA: the CGC fit - Fit for the data with small x and moderate Q 2 x < 0.01 & 0.045 < Q 2 <45 GeV 2 - Analytic solutions to Balitsky- Kovchegov equation built in: geometric scaling & its violation, saturation. - Only 3 parameters: proton radius R, x 0 (nonpert.) and for Q S 2 (x)=(x 0 /x) GeV 2 - Good agreement with the data x 0 = 0.26 x 10 -4,  = 0.25 - Also works well for vector meson (  ) production, diffractive F 2, F L [Forshaw et al, Goncalves, Machado ’04] Red line Red line : the CGC fit Blue line Blue line : BFKL w/o saturation [Iancu,KI,Munier ‘04]

10. Emerging picture* Non-perturbative (Regge) 1/x in log scale Q 2 in log scale Parton gas Extended scaling regime CGC Higher energies  Fine transverse resolution  BFKL BK DGLAP  QCD 2 Q S 2 (x) ~ 1/x : grows as x  0 Q S 4 (x)/  QCD 2 * Based on mean-field analysis

11. Summary High density gluonic state appears in the limit of high energy scattering  Color Glass Condensate In both RHIC and HERA, data at small-x are consistent with the picture of CGC Still, open question how CGC is important in LHC (especially in pp collision)  to be investigated This is the interdisciplinary field for particle and nuclear physics. An ideal field to enhance the communication btw two communities.

12. How important is CGC at LHC? MRST(Martin,Roberts,Stirling,Thorne) hep-ph/0507015 J. Ellis, “From HERA to the LHC” hep-ph/0512070