High energy hadronic/nuclear High energy hadronic/nuclear scatterings in QCDscatterings in QCD

Kazunori ItakuraKazunori ItakuraIPNS, KEKIPNS, KEK

““Towards precision QCD physics”Towards precision QCD physics”March 10th, 2007March 10th, 2007

Personal memories about Kodaira-saPersonal memories about Kodaira-sann

~ 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.

Kodaira-san’s concern about LHCKodaira-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.a

c.jp/ppp06/

August 3rd J. Kodaira, “Perturbative QCD: present status and problems” A pessimistic (but honest) talk emphasizing our poor understandin

g 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 t

here 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)

“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)

What happens at RHIC ?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

Color Glass Condensate Color Glass Condensate (CGC)(CGC)

higher energy

Dilute gas

COLOR : A state made of gluons with colors. GLASS : Almost frozen “random” color source creates gluon fieldsCONDENSATE: High density. Occupation number ~ O( 1/s )

CGC: high density gluons

Multiple gluonMultiple gluonproductionproduction

A new “semi-hard” scale: “saturation scale” QS > QCD

= typical transverse size of gluons at saturation

weak coupling S(QS) << 1

Weakly interacting many body system of gluonsWeakly 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)　 QS(HERA) ~ QS(RHIC) ~ 1 GeV

LO BFKL

NLO BFKL

CGC “observed” at RHICCGC “observed” at RHICDeuteron Au collisions 21 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

ffqqDDq /h q /h

)(),()(~ /212 zDrxxfrddz hqdipole

dq

: Dipole cross section saturation

Valence quark distrib. Fragmentation fnc.

e1s

px t

e2s

px t

dd

AuAu

q, g

g

Going forward = probing nuclear wavefunction at smaller x

h-

(h-+h+)/2

Nuclear modification factor

Suppression at moderate pt is due to saturation of the nuclear wavefunction. analytical investigation Iancu,KI,Triantafyllopoulos

mid rapidity forward rapidity

Towards more precise Towards more precise physics?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 F2 (x,Q2)

Geometric scaling in DIS as an Geometric scaling in DIS as an evidenceevidence

*p total cross section

[Stasto,Kwiecinski,Golec-Biernat 2001]

The*-proton total cross section (Q2 , x) becomes a function of only one variable Q2/Qs

2(x) at small x : (Q2 ,x)=f() , with Qs

2(x) ~1/x

determined by the fit.

• x-dependence of Qs is consistent with CGC

• A scaling window exists outside of CGC Qs2 < Q2 < Qs4/2 [Iancu,KI,McLerran]

Existence of saturation scale: Qs

DIS at HERA: the CGC fitDIS at HERA: the CGC fit

- Fit for the data with small x and moderate Q2

x < 0.01 & 0.045 < Q2 <45 GeV2

- Analytic solutions to Balitsky-Kovchegov equation built in: geometric scaling & its violation, saturation.

- Only 3 parameters: proton radius R, x0 (nonpert.) and for QS

2(x)=(x0/x)GeV2

- Good agreement with the data x0 = 0.26 x 10-4, = 0.25

- Also works well for vector meson () production, diffractive F2, FL [Forshaw et al, Goncalves, Machado ’04]

Red lineRed line : the CGC fitBlue lineBlue line : BFKL w/o saturation

),( 22 QxF

[Iancu,KI,Munier ‘04]

Emerging picture*Emerging picture*

No

n-p

ert

urb

ativ

e (

Reg

ge

)

1/x inlog scale

Q2 in log scale

Parton gas

Extended scaling regimeCGC

Hig

her

en

erg

ies

Fine transverse resolution

BFKL BK

DGLAPQCD

2

QS2(x) ~ 1/x: grows as x 0

QS4(x)/QCD

2

*Based on mean-field analysis

SummarySummary

• 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.

How important is CGC at How important is CGC at LHC?LHC?

MRST(Martin,Roberts,Stirling,Thorne) hep-ph/0507015

J. Ellis, “From HERA to the LHC” hep-ph/0512070