Transverse Spin Physics: Recent Developments

1. Transverse Spin Physics: Recent Developments Feng Yuan Lawrence Berkeley National Laboratory RBRC, Brookhaven National Laboratory

2. Transverse spin physics • Goal • Quark transversity distributions • Orbital motion of quarks and gluons? • Single transverse spin asymmetry • Various transverse momentum dependent physics (additional information on nucleon structure) • Sivers function (PDF) • Collins function (FF) • …

3. Outline • Introduction: single transverse spin phenomena • Universality of the Collins Mechanism • Non-universality of the Sivers effects • Conclusion

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

5. Single Spin Asymmetry • Motivations: • Its strong tied with the quark orbital angular momentum • We have beautiful data • Nontrivial QCD dynamics, and fundamental test of the factorization, and the universality of PDFs, FFs,…

6. SSAs in Modern era : RHIC, JLab, HERMES, … STAR Central rapidity!! BRAHMS Large SSA continues at DIS ep and collider pp experiments!!

7. Why Does SSA Exist? • Single Spin Asymmetry requires • Helicity flip: one must have a reaction mechanism for the hadron to change its helicity (in a cut diagram) • A phase difference: the phase difference is needed because the structure S ·(p × k) violate the naïve time-reversal invariance

8. 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 byαSmq/Q • We have to go beyond this naïve picture

9. ST kT Two mechanisms in QCD • Spin-dependent transverse momentum dependent (TMD) function • Sivers 90 • Brodsky,Hwang,Schmidt, 02 (FSI) • Gauge Property: Collins 02;Belitsky-Ji-Yuan,NPB03 Boer-Mulders-Pijlman,03 • Factorization: Ji-Ma-Yuan,PRD04;Collins,Metz,04 • Twist-3 quark-gluon correlations (coll.) • Efremov-Teryaev, 82, 84 • Qiu-Sterman, 91,98 Sivers function ~ ST (PXkT) . P

10. ST kT Two major contributions • Sivers effect in the distribution • Collins effect in the fragmentation • Other contributions… ST (PXkT) P (zk+pT) (k,sT) ~pTXsT

11. Semi-Inclusive DIS • Transverse Momentum Dependent (TMD) Parton Distributions and Fragmentations • Novel Single Spin Asymmetries U: unpolarized beam T: transversely polarized target

12. Universality of the Collins Fragmentation

13. Collins effects in e+e- • Reliable place to extract the information on the Collins fragmentation function Belle Col., PRL 06

14. Collins asymmetry in pp collisions Collins Fragmentation function Quark transversity distribution FY, arXiv:0709.3272 [hep-ph]

15. e+e- annihilation Semi-inclusive DIS Hadron in a jet in pp Simple model a la Collins 93 Phase information in the vertex or the quark propagator Collins-93 Universality of the Collins Function!!

16. One-gluon exchange (gauge link)? Metz 02, Collins-Metz 02: Gamberg-Mukherjee-Mulders, 08 Universality of the Collins function!!

17. By using the Ward Identity: same Collins fun. Similar arguments for pp collisions Conjecture: the Collins function will be the same as e^+e^- and SIDIS

18. Extend to two-gluon exchange Universality preserved

19. Extract the quark transversity from e+e- and SIDIS expreiments [1] Soffer et al. PRD 65 (02) [2] Korotkov et al. EPJC 18 (01) [3] Schweitzer et al., PRD 64 (01) [4] Wakamatsu, PLB 509 (01) [5] Pasquini et al., PRD 72 (05) [6] Anselmino et al., PRD 75 (07)

20. Key observations • 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

21. Predictions at RHIC Quark transversity: Martin-Schafer-Stratmann-Vogelsang, 98 Collins function: fit to the HERMES data, Vogelsang-Yuan, 05

22. Collins contribution to SSA in inclusive hadron pp--> Pi X Add a soft contribution ~Pt • Leading jet fragmentation contribution • Lower cut for the jet (>1GeV), upper cut for the fragmentation (<1GeV)

23. Recent STAR data • May indicate the importance of the soft contribution

24. 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”

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

26. A unified picture for SSA • In DIS and Drell-Yan processes, SSA depends on Q and transverse-momentum P • At large P, SSA is dominated by twist-3 correlation effects • At moderate P, SSA is dominated by the transverse-momentum-dependent parton distribution/fragmentation functions • The two mechanisms at intermediate P generate the same physics! Ji-Qiu-Vogelsang-Yuan,Phys.Rev.Lett.97:082002,2006

27. A difficulty at next-leading-power (1/Q) • Mismatch at low and high transverse momentum SIDIS at 1/Q • Bacchetta-Boer-Diehl-Mulders, 0803.0227 • The factorization needs to be carefully examined at this order • Earlier works indicates possible problems • Afanasev-Carlson, PRD, 2006 • Gamberg-Hwang-Metz-Schlegel, PLB, 2006

28. Experiment SIDIS vs Drell Yan HERMES Sivers Results RHIC II Drell Yan Projections 0 Markus Diefenthaler DIS Workshop Munich, April 2007 0 0.1 0.2 0.3 x http://spin.riken.bnl.gov/rsc/

29. Non-universality: Dijet-correlation at RHIC • Proposed by Boer-Vogelsang • Pheno. studies: Vogelsang-Yuan 05; Bomhof-Mulders-Vogelsang-Yuan 07; Bacchetta, et al, photon-jet correlation, 07 • Initial state and/or final state interactions? • Bacchetta-Bomhof-Mulders-Pijlman: hep-ph/0406099, hep-ph/0505268, hep-ph/0601171, hep-ph/0609206 • Qiu-Vogelsang-Yuan, arXiv:0704.1153; 0706.1196 • Collins-Qiu, arXiv:0705.2141  • Voglesang-Yuan, arXiv:0708.4398 • Collins, arXiv:0708.4410 • Bomhof-Mulders, arXiv:0709.1390 • Factorization? Universality?

30. The simple picture does not hold for two-gluon exchanges Qiu,Collins, 0705.4121; Vogelang-Yuan, 0708.4398; Collins, 0708.4410 Integrated over transverse momentum Becchetta-Bomhof-Mulders-Pijlman, 04-06

31. Another example:Heavy flavor production • Heavy quarkonium production (gg channel) • ep scattering • No SSA in color-singlet model • Final state interaction in color-octet model • pp scattering • Only initial state interaction in color-singlet • ISI and FSI cancel out in color-octet • Open charm or beauty • Different SSAs for charm and anti-charm

32. Color-singlet model Final state interactions with quark and anti-quark cancel out each other, no SSA in color-singlet model

33. Color-octet model Final state interactions can be summarized into a gauge link to infinity, nonzero SSA

34. pp scattering • Color-singlet model: only initial state interaction, non-zero SSA • Color-octet model: initial and final state interactions cancel out, no SSA

36. J/Psi Production at lower energy (JPARC or FAIR) • Quark-channel dominates • Color-singlet: only initial state interaction contributes, -1/2Nc relative to Drell-Yan • Color-octet: both initial and final state interactions contribute, -(Nc^2+1)/2Nc relative to DY DPN Meeting 2007

37. JPARC prediction Final A_N depends on the weight of the quark-channel contribution • Proportional to the sum of u- and d- quark Sivers function: fitted to HERMES data, Vogelsang-Yuan 05 DPN Meeting 2007

38. Heavy quark SSA ISI: contribute to quark and anti-quark ~1/4Nc FSI: contribute to quark ~(Nc^2-2)/4Nc FSI: contribute to anti-quark ~2/4Nc DPN Meeting 2007

39. A factor ~4 difference between charm and anticharm At JPARC, the quark channel contributes ~60% for charm cross sections DPN Meeting 2007

40. FAIR at GSI DPN Meeting 2007

41. Summary • We are in the early stages of a very exciting era of transverse spin physics studies, where the future RHIC, JLAB, JPARC, FAIR, and EIC experiments will certainly play very important roles • We will learn more about QCD dynamics and nucleon structure from these studies, especially for the quark orbital motion

42. What can we learn from SSA • Quark Orbital Angular Momentum e.g, Sivers function ~ the wave function amplitude with nonzero orbital angular momentum! Vanishes if quarks only in s-state! Ji-Ma-Yuan, NPB03 Brodsky-Yuan, PRD06

43. Take Drell-Yan as an example(with non-zero transverse momentum q?) • We need a loop to generate a phase + + + + - - + + • Twist-three Correlations • Efremov-Teryaev, 82, 84 • Qiu-Sterman, 91,98 Kane et al., hard parton model

44. Further factorization (q?<<Q) • The collinear gluons dominate q?<<Q • Transverse Momentum Dependent distributions • Sivers, 90, Collins, 93,02 • Brodsky-Hwang-Schmidt,02 • Ji-Qiu-Vogelsang-Yuan,06 • Twist-three Correlations • Efremov-Teryaev, 82, 84 • Qiu-Sterman, 91,98

45. New challenge from STAR data (2006) Talks by Ogawa and Nogach in SPIN2006 Users Meeting, BNL

46. Extend to all other TMDs: large Pt power counting • kt-even distributions have the same dependence on kt • kt-odd distributions are suppressed at large kt • Power Counting Rule kt-even: 1/kt2 kt-odd: 1/kt4

47. SIDIS cross sections at large Pt 1/Pt2 1/Pt4 1/Pt3 1/Pt5

48. Transition from Perturbative region to Nonperturbative region? • Compare different region of PT Nonperturbative TMD Perturbative region

49. RHIC Twist-3 Fit to data STAR E704 BRAMHS Kouvaris,Qiu,Vogelsang,Yuan, 06

50. Compare to 2006 data from RHIC J.H. Lee, SPIN 2006