1. 12/13/20151 Transverse Spin Overview: Theory Perspective Feng Yuan Lawrence Berkeley National Laboratory RBRC, Brookhaven National Laboratory

2. Feynman Parton Model Inclusive cross sections probe the momentum (longitudinal) distributions of partons inside nucleon 12/13/2015 2 Hadronic reactions

3. Extension to transverse direction… Momentum Space: Semi-inclusive measurements  Transverse momentum dependent (TMD) parton distributions Coordinate Space: Deeply Virtual Compton Scattering and Exclusive processes  Generalized parton distributions (GPD) 12/13/2015 3

4. Transverse momentum dependent parton distribution Straightforward extension  Spin average, helicity, and transversity distributions Transverse momentum-spin correlations  Nontrivial distributions, S T XP T  In quark model, depends on S- and P-wave interference, or p-p 12/13/2015 4

5. 5  Nucleon Structure, spin correlation, orbital motion of quarks and gluon  Nontrivial QCD dynamics, and fundamental test of the factorization, and the universality of PDFs, FFs,…  Single spin asymmetry phenomena Motivations…

6. 6 What’s Single spin asymmetry? Single Transverse Spin Asymmetry (SSA) Final state particle is Azimuthal symmetric Transverse plane

7. 7 Naïve parton model fails If the underlying scattering mechanism is hard, the naïve parton model generates a very small SSA: (G. Kane et al, 1978),  It is in general suppressed by α S m q /Q See also, Ma-Sang, arXive: 0809.1791 We have to go beyond this naïve picture

8. 8 Two mechanisms in QCD Spin-dependent transverse momentum dependent (TMD) function  Sivers 90  Colllins 93  Brodsky-Hwang-Schmidt, 02 Twist-3 quark-gluon correlations (coll.)  Efremov-Teryaev, 82, 84  Qiu-Sterman, 91,98 P kTkT STST Sivers function ~ S T (P X k T ).

9. 912/13/2015 Two contributions, e.g., in DIS  Fragmentation : Collins Function STXkTSTXkT STST sTsT pTXsTpTXsT  Distribution: Sivers Function

10. Universality Property Collins fragmentation function is universal  DIS, e+e-, and hadron in jet in pp Sivers distribution functions are not  Change sign between DIS and Drell-Yan  More complicated structure for the dijet correlation pp collisions 12/13/201510

11. A unified picture between TMD and twist-three (leading pt/Q) 12/13/201511 Q  QCD PTPT Collinear/ longitudinal << Transverse momentum dependent Ji-Qiu-Vogelsang-Yuan,2006 Yuan-Zhou, 2009 PTPT

12. NLO corrections to SSA SSA in Drell-Yan as an example, Collinear factorization 12/13/201512 Vogelsang-Yuan, arXiv:0904.0410 Collinear functions, evolution: Kang-Qiu, 08; Zhou-Yuan-Liang, 08 Braun et al., 0909.3410

13. Universality of the Collins Fragmentation 12/13/2015 13 ep--> e Pi X e+e--> Pi Pi X pp--> jet(->Pi) X Metz 02, Collins-Metz 02, Yuan 07, Gamberg-Mukherjee-Mulders 08 Meissner-Metz 0812.3783 Yuan-Zhou, 0903.4680 JLab HERMES, COMPASS, JLab, (?) BELLE (KEK), BARBAR, BESIII(?)

14. The reason is Final state interactions DO NOT provide a phase for a nonzero SSA Eikonal propagators DO NOT contribute to a pole Ward identity is applicable to warrant the universality arguments 12/13/2015 14

15. Sivers effect is different It is the final state interaction providing the phase to a nonzero SSA Ward identity is not easy to apply Non-universality in general Only in special case, we have “Special Universality” Brodsky,Hwang,Schmidt 02 Collins, 02; Ji,Yuan,02; Belitsky,Ji,Yuan,02

16. 16 DIS and Drell-Yan Initial state vs. final state interactions “Universality”: QCD prediction HERMES ** ** Drell-Yan DIS

17. 12/13/2015 0.1 0.2 0.3 x 0 0 Experiment SIDIS vs Drell Yan HERMES Sivers ResultsRHIC II Drell Yan Projections Markus Diefenthaler DIS Workshop Munich, April 2007 http://spin.riken.bnl.gov/rsc/

18. 18 Initial state and/or final state interactions Non-universality: Dijet-correlation at RHIC Boer-Vogelsang 03 Jet 1 Jet 2 P,S T Standard Factorization breaks, no universality! Bacchetta-Bomhof-Mulders-Pijlman, 04-06 Collins-Qiu 08 Vogelsang-Yuan 08

19. Indication from the experimental measurement? 12/13/2015 19 STAR,0705.4629  Theory calculations use one-gluon exchange formalism  Future photon-jet correlation measurement shall be able to help us to understand this issue

20. Highlights from recent measurements Pt dependence for single inclusive hadron SSA Eta SSA much larger than Pi0 Consistency between HERMES and COMPASS on Sivers in DIS SSA for heavy mesons consistent with zero 12/13/201520 Theory challenge!! Exp. Issue

21. Transverse spin is still in the exploration stage (my opinion) No confirmation from pp collisions for whatever observed in DIS and e+e- There is no decisive answer for the underlying mechanism for SSA of pp  Pi+X  Collins or Sivers  Pt dependence (in general) 12/13/201521

22. Theory wish list (personal bias) Test the non-universality for the Sivers mechanism  Drell-Yan, ideal place  photo-jet could be used as well Separate Sivers and Collins contributions  Hadron in jet  Di-hadron correlation Transversity  Two hadron fragmentation 12/13/201522

23. 23 12/13/2015 Azimuthal distribution of hadrons inside a jet (large P T ) Collins Fragmentation function Quark transversity distribution

24. 24 12/13/2015 Extend the Collins measurement in e + e - to pp collisions? Dilution factor to select the quark-antiquark jets Looking for dihadrons’ cos2phi correlation Belle Coll., PRL 06 p p

25. Isolate Sivers effects Drell-Yan/W Direct photon production  Initial state interaction Jet production  Initial/final state interactions Dijet/photon-jet correlation  Both initial/final state interactions, factorization breaks down 12/13/201525 TMD TMD? Twist-3

26. 26 Summary and Outlook There has been great progress on both theory and experiment sides for (single) transverse spin phenomena  Next-to-leading order QCD corrections and scale evolutions have been carried out There are still challenges and puzzles!!

27. theo ry [by Naomi Makins] looking forward to new projects: Jlab12, EIC, JPARC, PAX@FAIR Global effort in Transverse Spin Physics: Intense Interactions between different collaborations and Theoreticians

28. 28 SPIN Workshop, JLab New challenge from STAR data (2006)  Anselmino et al.,  Kouvaris et al.,

29. 29 12/13/2015 Predictions at RHIC Quark transversity: Martin-Schafer-Stratmann-Vogelsang, 98 Collins function: fit to the HERMES data, Vogelsang-Yuan, 05

30. 30 Transition from Perturbative region to Nonperturbative region Compare different region of P T Nonperturbative TMDPerturbative region

31. Perturbative tail is calculable Transverse momentum dependence 12/13/201531 Power counting, Brodsky-Farrar, 1973 Integrated Parton Distributions Twist-three functions

32. 3212/13/2015 Model calculations Metz 02, Collins-Metz 02: Gamberg-Mukherjee-Mulders, 08 Universality of the Collins function!!

33. 3312/13/2015 Similar arguments for pp collisions Conjecture: the Collins function will be the same as e^+e^- and SIDIS By using the Ward Identity: same Collins fun. Yuan, PRL08,PRD08

34. Collinear factorization verified at one-loop order Soft-collinear divergence cancelled out between virtual and real diagrams Collinear divergence identified as the splitting functions for the antiquark and twist-three correlation functions 12/13/201534

35. Finite terms +... 12/13/201535

36. Threshold limits Large-z, The asymmetry should not change dramatically with energy in the forward region 12/13/201536

37. 37 Twist-3 Fit (LO) to data: E704 STAR Kouvaris,Qiu,Vogelsang,Yuan, 06 RHIC BRAMHS

38. 38