Evolution of higher point functions and

two-particle correlations in

CGC

Jamal Jalilian-Marian Baruch College, New York NY

based on AD-JJM, PRD82 (2010) 074023, PRD81 (2010) 094015

A hadron at small x

is the fraction of hadron energy carried by a parton

DIS:

there are a lot ofgluons at small x

Gluon saturation

“attractive” bremsstrahlung vs. “repulsive” recombination

Effective Action + RGEEffective Action + RGE

weight functional: probability distribution of color source

at longitudinal scale invariance under change of RGE for

Large x: color source small x: gluon field

QCD at High Energy: Wilsonian RG

Fields Sources

integrate out field fluctuations quadratically

resum

JIMWLK eq. describes x evolution of observables

CGC:QCD at high gluon density

multiple scatterings pt broadening

evolution with ln (1/x) suppression

“Leading twist” nuclear shadowing

effective degrees of freedom: Wilson line V (xt)

In CGC observables are expressed in terms of < tr V ....... V>

“Cronin” effect

Evolution of the 2-point function

Evolution of 2-point function depends on 4-point function

Infinitely many coupled equations!

Basic building block in DIS, pA processes

Evolution of the 2-point function

RW, NPA739 (2004) 183

saturation region

dilute region

pQCD region

Large Nc :BK eq.

higher point functions are expressed in terms of the 2-point function

extended scaling region:

IIM, NPA708 (2002) 327

NLO: B-KW-G-BC (2007-2008)

Running coupling BK

“dense”

Road Map of QCD Phase SpaceRoad Map of QCD Phase Space

A

“dilute”

ObservablesDIS:structure functions (inclusive and diffractive)single and double particle production

PA (dilute-dense):multiplicitiessingle and double inclusive spectra

AA, pp (dense-dense):multiplicities, spectralong range rapidity correlation

RIDGE

DISDIS

where JIMWLK/BK eqs. determine the x dependence of N

only the 2-pt function contributes

First successful application: DIS at HERA by G-BW PRD59 (1998) 014017 BG-BK: PRD66 (2002) 014001

CGC at HERA? Extended scaling

Collinear Fact.:

CGC:

S(G-B)K PRL86 (2001) 596

IIM (2002)

pA (dilute-dense) scattering

KM, DM, BGV

Single inclusive hadron production in pASingle inclusive hadron production in pA

2-point function only: same as in DIS and photon,dilepton production in pA (FG and JJM)

UNIVERSALITY

DJM,BMTS

Single inclusive hadron production

DHJNPA770 (2006) 57

deuteron-goldproton-protonBDH

PRD74 (2006) 074018true

prediction

Also, KKT, BUW, RS,........

dA at RHIC

Solution to the running coupling BK equationJ. Albacete + C. Marquet

PLB687 (2010) 174

dA at RHIC

Kinematics:projectile xis very large

how importantis cold matterenergy loss?

Kopeliovich, Frankfurt and Strikman, Neufeld-Vitev-Zhang, arXiv:1010.3708

Two-hadronCorrelations

Tevatron high pT data

in pQCD calculations based on collinear factorization, dijets are back-to-back

∼π

transverse view

peak narrower with higher pT

probing Λ QCD/pT <<1

power correctionsare negligible

Di-jet correlations in pp: pQCD

Di-hadron kinematics in CGC

11 , yk 22 , yks

ekekx

yy

p

21 21 +=s

ekekx

yy

A

21 21−− +=produced partons:

scanning the wave-functions

mid-mid correlations probe moderate x

forward-forward

mid-forward

D-jet correlations: pA

JJM and YK, PRD70 (2004), AK and ML, JHEP (2006), FGV, NPA (2006), CM, NPA796 (2007) , KT, NPA (2010)

two hadron production in pA probes higher point functions (up to 6-pt function)

dA: di-jet production

Dipole + large Nc approximation?

F2 in DIS, single hadron in pA

disappearance of back to back jets

CGC fit from Albacete + Marquet, PRL (2010)

using running coupling BK solution,Also by Tuchin, NPA846 (2010)

multiple soft scatterings de-correlate the hadrons

Beyond dipole + large Nc approximation

Dipole approximationJIMWLK

quadrupole dipole X dipole

and they evolve differently even at large Nc

Beyond dipole + large Nc

JIMWLK evolution equation

JIMWLK: Beyond dipole + large Nc

Recall evolution of O2 is sensitive to O4 only

DIS structure functions,single inclusive production in pA probe dipoles

JIMWLK: Beyond dipole + large Nc

these are the leading Nc pieces

JIMWLK: Beyond dipole + large Nc

these are the pieces

Di-jet correlations: DIS

JJM & YK, PRD70 (2004)AK & ML, JHEP (2006)

FG & JJM, PRD67 (2003)

di-jet production in DIS probes higher point functions

JIMWLK: Beyond dipole + large Nc

Dijet production probes quadrupoles

dipole approximation is not valid!

simplifies in some kinematicsdijet momentum imbalance: WW gluons

F. Dominguez et al.

JIMWLK: Beyond dipole + large Nc

Dijet production poses new challenges to CGCbut

every challenge can become an opportunity

How large are the Nc suppressed terms ?

What is their energy dependence ?

Evolution of higher point functions depends on lower point functions!

Can we solve JIMWLK please?

The Ridgein

CGC

Ridge in AA (long-range rapidity correlations)

DGMV: NPA810 (2008) 91 DGLV:NPA836 (2010) 159

GLASMA:gluon fields produced in collision of two sheets of color glass

Early on glasma fields (E and B) are longitudinal

Classical solutions are boost invariant

Transverse size of these flux tubes is

The CMS ridge at LHC

Ridge

The CMS ridge at LHC

Dumitru et al., Arxiv:1009:5295

Two-gluon correlation

dilute region: two-gluon correlation issensitive to 4-pt function

of gluon fields

Evolution of gluon 4-pt function

dipole approximation breaks down! AD-JJM, PRD81:094015 (2010)

The ridge

CMS data on high multiplicity events in pp are in qualitative agreement with CGC predictions

A quantitative description of two-hadron correlation requires going beyond dipole

approximation

High energy QCD: Color Glass Condensate

Evidence for CGC at HERA, RHIC soon (now) to be tested at LHC

Qs: a dynamical semi-hard scale

A systematic approach with controlled approximations

A new region of QCD phase space

2-hadron correlations probe the dynamics of CGC beyond dipoles