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

Probing the Dense Medium in Cold Nuclei -- Gluon Saturation at small-x. Bowen Xiao (CCNU) Feng Yuan (LBNL). Gluon saturation inevitable at small-x. QCD evolution drives the gluon distribution rising at small-x. BFKL evolution becomes relevant at small-x.

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

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  1. Probing the Dense Medium in Cold Nuclei-- Gluon Saturation at small-x Bowen Xiao (CCNU) Feng Yuan (LBNL)

  2. Gluon saturation inevitable at small-x

  3. QCD evolution drives the gluon distribution rising at small-x

  4. BFKL evolution becomes relevant at small-x • Balitsky-Fadin-Lipatov-Kuraev, 1977-78 • Balitsky-Kovchegov: Non-linear term, 98

  5. 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)

  6. Conventional gluon distribution • Collins-Soper, 1981 • Gauge link in the adjoint representation

  7. 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 nucleus • McLerran-Venugopalan • Kovchegov-Mueller

  8. Classic YM theory • McLerran-Venugopalan • See also, Kovchegov-Mueller • We 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

  9. 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

  10. 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 a a b b

  11. 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

  12. Golden channel for an EIC • Directly probe the Weizsacker-Williams gluon distribution in nucleus • Factorization is very clear • Various channels within DIS processes • Heavy flavor • Real/virtual photon

  13. Photon-jet correlation probes the dipole gluon distribution • No difference for the Born diagram • Naïve kt-factorization would predict the same qt-dependence

  14. Initial/final state interactions There is no color structure corresponding to this, We have to express the gluon Distribution in the Fundamental representation a b a b

  15. Differential cross section Dominguez-Xiao-Yuan, 2010 • This is the dipole gluon distribution, also called unintegrated gluon distribution

  16. 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

  17. Dijet-correlation at RHIC • Initial state and/or final state interactions Jet 2 Jet 1 Boer-Vogelsang 03 P,ST Standard (naïve) Factorization breaks! Becchetta-Bomhof-Mulders-Pijlman, 04-06 Collins-Qiu 08; Vogelsang-Yuan 08 Rogers-Mulders 10; Xiao-Yuan, 10

  18. Modified factorization • Dilute system on a dense target, in the large Nc limit,

  19. Hard partonic cross section

  20. Kt-dependent gluon distributions

  21. 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, α0 • Rapidity divergence Mueller, Xiao, Yuan, PRL110,082301 (2013)

  22. Di-hadron correlations

  23. Conclusions: EIC • Great opportunities in nuclear science • Ultimate machine for nucleon spin physics • Unique place to investigate gluon saturation • Potential discovery in BSM physics

  24. Hadronization in cold nuclei vs hot matter

  25. Observables

  26. Intensity Frontier (EW Physics)

  27. Observables

  28. Diffractions

  29. EIC Proposals in US

  30. Small-x factorization Mueller, 1994 • eikonal approximation in high energy scattering

  31. Splitting function • Dipole amplitude • At one-loop order BK-JIMWLK Y~Log(1/x)

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