Transverse Spin Physics: Recent Developments

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

2. Outline • Introduction • Great progress in the last few years • Underlying physics unrevealed • Connections to other phenomena • Higher-twist effects • Generalized Parton Distributions • QCD dynamics: Factorization, Universality, … • Future: Puzzle and Challenges remain

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

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

5. 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

6. 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 • See also, Ma-Sang, arXive: 0809.1791 • We have to go beyond this naïve picture

7. 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,03 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

8. Polarized TMD Quark Distributions Nucleon Unpol. Long. Trans. Quark Unpol. Long. Trans. Boer, Mulders, Tangerman (96&98)

9. Three classes in the view of a quark model • S-wave • Unpolarized, helicity, transversity • S-P interference • g_1T,h_1L • f_1T^\perp, h_1^\perp • P-P or S-D interference • h_1T^\perp • Miller 07, Burkardt 07, Avakian et al 08, Pasquini et al 08, … Pasquini’s talk

10. Lz≠0 Amplitude and Sivers Function • All distributions can be calculated using the wave function. Sivers function: • Similar expressions for others Lz=1 Lz=0 Ji, Ma, Yuan, Nucl. Phys. B (2003)

11. Where can we learn TMDs • Semi-inclusive hadron production in deep inelastic scattering (SIDIS) • Drell-Yan lepton pair production in pp scattering • Relevant e+e- annihilation processes • …

12. Quark-gluon correlations (twist-three) • Have long been studied • F-type and D-type are related to each other, Eguchi-Koike-Tanaka 06

13. TMDs and Quark-gluon Correlations (twist-3) • Kt-odd distribution

14. 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

15. Initial vs Final State Interactions • Double Initial State Interactions in Drell-Yan Azimuthal asymmetry • Jian Zhou’s talk on Friday Drell-Yan DIS

16. TMDs vs GPDs • See Burkardt’s talk

17. Nontrivial feature for the TMDs: Universality • Universality of the Collins Mechanism • Non-universality of the Sivers effects

18. Universality of the Collins Fragmentation

19. 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!!

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

21. 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

22. Extend to two-gluon exchange Universality preserved

23. 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

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. 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/

27. 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?

28. 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

29. Another example:Heavy flavor production ISI: contribute to quark and anti-quark ~1/4Nc FSI: contribute to quark ~(Nc^2-2)/4Nc FSI: contribute to anti-quark ~2/4Nc Kang’s talk

30. Puzzles Continue • Experiment side • Pt-dependence A_N from STAR • Sivers effect: COMPASS vs HERMES • SSA for Keons, antiproton

31. Future: Theory challenges • Quantitative connection to the OAM • QCD corrections • Soft gluon resummation at small pt • …

32. Transverse Spin Wish (to do) List Experiment Theory Relation to OAM Evolution Soft gluon resummation Robust separation of Sivers and Collins in pp P_t behavior Explore More functional dependence (kt,x) • Drell-Yan • Photon-jet • Tensor charge (h_1) • Large P_t SSA (1/P_t) • Double spin asymmetry P_t depdence • W and z production (reconstruction low pt) • Flavor separation via He3 at RHIC • large-x Sivers/Collins • Polarized nucleon-nucleus experiments (nuclear effects in B-M function) • What if we don’t see DY=-DIS • Can we determine the sign of the transversity function? PKU-RBRC Workshop on Transverse Spin

33. 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

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

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

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