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Probing the Dense Medium in Cold Nuclei-- Gluon Saturation at small-x

Bowen Xiao (CCNU)

Feng Yuan (LBNL)

Gluon saturation inevitable at small-x

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QCD evolution drives the gluon distribution rising at small-x

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BFKL evolution becomes relevant at small-x Balitsky-Fadin-Lipatov-Kuraev, 1977-

78

Balitsky-Kovchegov: Non-linear term, 98

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QCD Phase structure of cold nuclei

Hard processes probe the kt-dependent gluon distributions directly

Saturation phenomena manifest in the observables

Xiao,Yuan, et al, PRL106, 022301

(2011) PRL105, 062001

(2010)

Conventional gluon distribution Collins-Soper, 1981

Gauge link in the adjoint representation

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Physical interpretation Choosing light-cone gauge, with certain

boundary condition (either one, but not the principal value)

Gauge link contributions can be dropped

Number density interpretation, and can be calculated from the wave functions of nucleusMcLerran-VenugopalanKovchegov-Mueller

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Classic YM theory

McLerran-Venugopalan

See also, Kovchegov-MuellerWe can reproduce this gluon distribution

using the TMD definition with gauge link contribution, following BJY 02, BHPS 02

Weizsacker-Williams gluon distribution is the conventional one

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DIS dijet probes WW gluons

Hard interaction includes the gluon attachments to both quark and antiquark

The qt dependence is the gluon distribution w/o gauge link contribution at this order

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Final state interaction gauge link

Dominguez-Xiao-Yuan, 2010

This is exactly the leading order expansion of the gauge link contribution, checked at

three-gluon exchange order

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a b

a b

Differential cross section

Rigorous kt-factorization can be built for this process

Initial photon, not hadron Similar to e+e-, Collins-Soper, 81 It is also a clean place to study the

gluon Sivers function, Vogelsang-Yuan, 07

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Golden channel for an EIC Directly probe the Weizsacker-

Williams gluon distribution in nucleus Factorization is very clear

Various channels within DIS processesHeavy flavorReal/virtual photon

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Photon-jet correlation probes the dipole gluon distribution

No difference for the Born diagram Naïve kt-factorization would predict the same qt-

dependence

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Initial/final state interactions

There is no color structure corresponding to this, We have to express the gluon

Distribution in the Fundamental representation

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a b

a b

Differential cross section

Dominguez-Xiao-Yuan, 2010

This is the dipole gluon distribution, also called unintegrated gluon distribution

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Intuitive explanations Final state interactions in DIS can be

eliminated by choosing the light-cone gauge number density interpretation

Photon-jet correlation have both initial/final state interactions, can not be eliminated by choosing LC gauge there is no number density interpretation dipole gluon distribution

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Initial state and/or final state interactions

Dijet-correlation at RHIC

Boer-Vogelsang 03Jet 1

Jet 2

P,ST

Standard (naïve) Factorization breaks!Becchetta-Bomhof-Mulders-Pijlman, 04-06Collins-Qiu 08; Vogelsang-Yuan 08Rogers-Mulders 10; Xiao-Yuan, 10

Modified factorization Dilute system on a dense target, in

the large Nc limit,

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Hard partonic cross section

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Kt-dependent gluon distributions

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Sudakov (CSS) Resummation Sudakov double logs can be re-

summed in the small-x saturation formalism

Radiated gluon momentum

Soft gluon, α~β<<1 Collinear gluon, α~1, β<<1 Small-x collinear gluon, 1-β<<1, α0

Rapidity divergence04/21/23 21

Mueller, Xiao, Yuan, PRL110,082301 (2013)

Di-hadron correlations

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Conclusions: EIC

Great opportunities in nuclear science Ultimate machine for nucleon spin physics Unique place to investigate gluon

saturation Potential discovery in BSM physics

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Hadronization in cold nuclei vs hot matter

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Observables

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Intensity Frontier (EW Physics)

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Observables

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Diffractions

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EIC Proposals in US

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Small-x factorization

eikonal approximation in high energy scattering

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Mueller, 1994

Splitting function Dipole amplitude

At one-loop order

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Y~Log(1/x) BK-JIMWLK