06/11/22 1 Probing the Dense Medium in Cold Nuclei -- Gluon Saturation at small-x Bowen Xiao (CCNU) Feng Yuan (LBNL)
Feb 04, 2016
04/22/23 1
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 divergence04/22/23 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