1. 9/17/20151 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 9/17/20152

3. QCD evolution drives the gluon distribution rising at small-x 9/17/20153

4. BFKL evolution becomes relevant at small-x Balitsky-Fadin-Lipatov-Kuraev, 1977-78 Balitsky-Kovchegov: Non-linear term, 98 9/17/20154

5. 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 9/17/20156

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 9/17/20157

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 9/17/20158

9. DIS dijet probes WW gluons Hard interaction includes the gluon attachments to both quark and antiquark The q t dependence is the gluon distribution w/o gauge link contribution at this order 9/17/20159

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 9/17/201510 ab ab

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 9/17/201511

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 9/17/201512

13. Photon-jet correlation probes the dipole gluon distribution No difference for the Born diagram Naïve kt-factorization would predict the same q t - dependence 9/17/201513

14. Initial/final state interactions There is no color structure corresponding to this, We have to express the gluon Distribution in the Fundamental representation 9/17/201514 ab ab

15. Differential cross section Dominguez-Xiao-Yuan, 2010 This is the dipole gluon distribution, also called unintegrated gluon distribution 9/17/201515

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 9/17/201516

17. 17 Initial state and/or final state interactions Dijet-correlation at RHIC Boer-Vogelsang 03 Jet 1 Jet 2 P,S T 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, 9/17/201518

19. Hard partonic cross section 9/17/201519

20. Kt-dependent gluon distributions 9/17/201520

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 9/17/201521 Mueller, Xiao, Yuan, PRL110,082301 (2013)

22. Di-hadron correlations 9/17/201522

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 9/17/201523

24. Hadronization in cold nuclei vs hot matter 9/17/201524

25. Observables 9/17/201525

26. Intensity Frontier (EW Physics) 9/17/201526

27. Observables 9/17/201527

28. Diffractions 9/17/201528

29. EIC Proposals in US 9/17/201529

30. Small-x factorization eikonal approximation in high energy scattering 9/17/201530 Mueller, 1994

31. Splitting function Dipole amplitude At one-loop order 9/17/201531 Y~Log(1/x) BK-JIMWLK