1. 2/10/20161 What can we learn with Drell-Yan in p(d)-nucleus collisions Feng Yuan Lawrence Berkeley National Laboratory RBRC, Brookhaven National Laboratory Collaborations with Dominguez, Kang, Marquet, Xiao

2. Outline Drell-Yan lepton pair production at small-x Universality of the Quark distribution between DIS and Drell-Yan Unique opportunity for Drell-Yan process in p(d)-nucleus collisions 2/10/20162

3. Beautiful data from HERA Both Parton Model with DGLAP and Dipole can describe the data 2/10/20163 GBW 98’

4. Twist expansion Leading twist expansion of the dipole formalism contains large Log(Q 2 )  Bartels et al, 2009  Stasto et al, 2010, Anna’s talk Saturation scale in proton is small at HERA energy, both DGLAP and dipole (CGC) can describe the DIS data 2/10/20164

5. Equivalently, quark distribution in dipole Integrated quark distribution has Ultraviolet divergence 2/10/20165 GBW model McLerran-Venugopalan 99 Mueller 1999 Xiao-Yuan, 2010

6. Parton distributions contain the non- perturbative (saturation) physics  As an input in the DGLAP fit  Model in the dipole formalism Saturation will be manifest when hard scale Q in order of Qs  Inclusive observables Or the processes which are sensitive to kt-dependent parton distributions  Semi-inclusive observables 2/10/20166

7. Inclusive observables Q in the same order of Qs, and both have to be large Dipole (CGC) formalism Taking Q->0 limit will lead to infrared divergence 2/10/20167 GBW model

8. Sensitive to the quark mass when Q=0  GBW 98, Log(mq^2) Associated with the real photon splitting to quark pair  Can be absorbed into the quark distribution in real photon (resolved photon) Small Q prediction is strongly model- dependent (wrong practice)  It works amazing well though, which might have nothing to do with saturation physics 2/10/20168

9. Pt dependent observables Inclusive pt spectrum in pA collisions  Requires large transverse momentum, probes the perturbative region of unintegrated gluon distributions Semi-inclusive processes, additional hard scale  Probe the broader range of UGD  However, Couple with other pt-dependent quantities 2/10/20169 Al’s talk

10. Inclusive cross section  Invariant mass not so large compared to the saturation scale Pt dependent observables  Directly probe the unintegrated gluon distributions  Correlation of DY-hadron Al’s, Bowen’s talks 2/10/201610

11. How relevant is the saturation scale at RHIC 2/10/201611 A 1/3 For typical Range of lepton Pair mass at RHIC, Saturation Is going to Be important DGLAP shadowing Will not be enough Jamal’s talk Anna’s talk

12. Advantage of Low Pt Drell-Yan Direct probe for the transverse momentum dependence of partons  Saturation effects explicitly show up in the transverse momentum distribution Factorization can be argued for large Q Related to the TMD factorization Complementary study in SIDIS 2/10/201612

13. Drell-Yan Process at small-x What are the relevant scales  Q, virtuality of the photon  Pt, transverse momentum of hadron  Qs, saturation scale We are interested in the region of Q>>Qs, Pt  TMD factorization makes sense 2/10/201613

14. Color-dipole, CGC formalism 2/10/201614 Al and Jamal’s talks

15. Keep the leading power contribution, transverse momentum decouples from the mass of the lepton pair M Small kt limit: M>>p T 2/10/201615

16. Quark distribution can be calculated The same quark distribution appears in SIDIS cross section, Marquet-Xiao-Yuan 08 It’s Universal 2/10/201616 McLerran-Venugopalan 98

17. TMD factorization 2/10/201617

18. Up to this order Trivial factors from  Soft factor  Fragmentation function  Hard factor These effects and the Sudakov form factor will be important when go beyond this order 2/10/201618

19. Interesting properties 2/10/201619 Mueller 99; McLerran-Venugopalan 99

20. Quark distribution at different x 20 Ratio relative to that at 10 -2

21. Applications: simple TMD 2/10/201621 Spin-average one: Spin-dependent one: Calculated from CGC

22. Pt dependence of the Nuclear suppression 2/10/201622 With smearing effects See also, Guo,Qiu,Zhang, 00

23. SSA at low P T Cross section dominated by low transverse momentum UGD 2/10/201623

24. SSA at high P T Cross section is dominated by large pt UGD Ratios 2/10/201624

25. Pt dependence for A N 2/10/201625 pp pA Illustration purpose Trivial assumption For the Sivers Function Full calculations Underway Similar analysis for Pion A N

26. 26 Summary Drell-Yan lepton pair production in p(d)nucleus collisions provide opportunities to detailed studying saturation physics, in particular, the pt dependence in  Very clean place to test the Nuclear shadowing  Spin asymmetries

27. Scaling in Forward hadron production 2/10/201627 H Quark distribution From the projectile Dense medium Dumitru-Jalilian-Marian, 02 Dumitru-Hayashigaki-Jalilian-Marian, 06

28. Simple power counting Forward region is dominated by the valence quark distribution (1-x) 3 Similar power behavior for the fragmentation function, (1-z) 1~2, 1009.2481 Pt-dependent-Geometric scaling, Similar study by McLerran- Praszalowicz, 10 2/10/201628

29. Scaling in pp collisions 2/10/201629 BRAHMS: 2 rapidity bins STAR: 3 rapidity bins

30. Geometric Scaling for R pA ? 2/10/201630 R ratio depends on the difference in the saturation scales More data are needed to draw conclusion

31. Phenomenology: quark distributions ratios 31 Transverse Mometum Broading with Q GBW model for dipole Cross section

32. Dipole picture for DIS 2/10/201632 Fragmentation function

33. Dipole picture for DIS 2/10/201633 Fragmentation function

34. SIDIS Differential Cross section 2/10/201634 Unintegrated gluon dis.

35. TMD limit: Q>>p T Keep the leading power contribution, neglect all higher power corrections 2/10/201635