1. High-Energy QCD Spin Physics Xiangdong Ji Maryland Center for Fundamental Physics University of Maryland DIS 2008, April 7, 2008, London

2. Outline Why spin physics? Polarized parton distribution functions Spin structure of the proton, Orbital angular momentum and Generalized parton distributions (GPDs) Transverse single-spin asymmetries Conclusion

3. Why spin physics? Spin is a fundamental degree of freedom originated from the space-time symmetry. Spin plays a critical role in determining the basic structure of fundamental interactions. Test of a theory is not complete without a full test of spin-dependent decays and scattering. Spin provides a unique opportunity to probe the inner structure of a composite system (such as the proton) and hence testing our ability to understand the working of non-perturbative QCD.

4. Remarkable experimental progress in QCD spin physics in the last 20 years Inclusive spin-dependent DIS EMC, SMC, COMPASS E142,E143,E154,E156 HERMES Jlab-Hall A, B(CLAS) Semi-inclusive DIS SMC, COMPASS HERMES Polarized pp collisions RHIC PHENIX & STAR

5. Double-spin asymmetries in semi-inclusive processes from HERMES & COMPASS Recent experimental progress Talks by Korzenev, Robinet, Stolarski, Jackson

6. Double spin asymmetry for pion production from PHENIX and jet production from STAR (run 5+6) ( Recent experimental progress Talks by Gagliardi, Hoffman, Aoki, Ellinghaus

7. Polarized Parton Distributions

8. Polarized PDFs When the proton (or neutron) is polarized, the quarks and gluons are polarized as well, In the large N c limit, the mass of the nucleon is order N c and spin is of order 1. The polarized effect is relatively small, particularly for the gluons of order N c squared in the vacuum. Pol. PDF can be extracted from the experimental data through global fits.

9. (NLO) Global fits Make some generic assumptions about the functional form with a few parameters and fit them to data Many efforts in the past have been made Gluck, Reya, Stratmann, Vogelsang (2001) Blumlein and Bottcher (2003) Leader, Sidorov, Stamenov (2006) Hirai, Kumano, Saito (2006) ….. One of the most recent is the NLO fit by de Florian, Sassot, Stratmann and Vogelsang (hep-ph/0804.0422) in which pp collision jet data are first included. (Technically challenging!)

10. DSSV PDF Polarized sea distributions RHIC spin asymmetries

11. DSSV spin content The gluon pol. is small, but the uncertainty is large (E. Leader’s talk). Future data will improve this

12. Gluon polarization and chi-squared

13. Future improvement Sea-quark polarization W production at RHIC EIC Gluon pol. Direct photon production Higher precision in jet and pion

14. Spin Structure of the Nucleon

15. The nucleon spin The driving question for QCD spin physics is where the nucleon spin come from? Total proton spin = 1/2 Quark spin measured In DIS “Dark” angular momentum?

16. Spin of the proton in QCD The spin of the nucleon can be decomposed into contributions from quarks and gluons Further decomposition of quark contribution Further decomposition of gluon contribution Infinite momentum frame There is no analogous sum rule involving transversity!

17. Spin in asymptotic limit Scale evolution equation Asymptotic solution Roughly half of the angular momentum is carried by gluons! OAM must be important

18. Argument for large orbital motion Quarks are essentially massless. A relativistic quark moving in a small region of space must have non-zero orbital angular momentum. (MIT bag model) Finite orbital angular momentum is essential for Magnetic moment of the proton. g 2 structure function Asymmetric momentum-dependent parton distribution in a transversely polarized nucleon …

19. Total quark angular momentum The total angular momentum is related to the GPDs by the following sum rule Where E and H are GPDs defined for unpolarized quarks. Contribution from H is related to the momentum fraction carried by quarks. E is similar to Pauli form factor F 2, can best be determined with a trans. pol. target. Talk by D. Mueller

20. DVCS with transversely polarized target from HERMES & Jlab

21. Talk by P. Haegler

22. Looking forward Jlab 12 GeV upgrade A comprehensive program to study GPDs EIC Vanderhaeghen et al. EIC: 5 GeV e on 50 GeV proton: Much large range possible…. D. Hasell, R. Milner et al. Vanderheaghen et al

23. Transverse Single-Spin Asymmetries Session talks by F. Yuan, Radici, Lu, Mulders Goldstein, Sozzi, Ogawa, Videbaek, Fields, Melis, Tanaka

24. Transverse-Spin Related Distributions Transversity distribution  q(x) or h(x) (twist-2) the density of transversely polarized quarks in a transversely polarized nucleon chirally-odd Sivers function q T (x, k T ) (twist-2 at small k) Asymmetric distribution of quarks with T-momentum k T in a transversely polarized nucleon T-odd, depends on ISI/FSI Twist-3 quark-gluon correlation functions Polarized gluons! Related Fragmentation functions

25. What have we learned from data? SSA in PP scattering is large, even at RHIC energy. Consistent with twist-3 expectation. SSA in eP scattering is large at HERMES, becomes small at COMPASS. The Collins function is consistent with e+e- data, but with interesting/strange charge dependence. (Ogawa) Siver’s function has interesting flavor dependence. Talk by Ogawa

26. First extraction of transversity From semi-inclusive DIS asymmetry measured by HERMES &COMPASS (Anselmino et al, 2007)

27. A unified picture for SSA In DIS and Drell-Yan processes, SSA depends on Q and transverse-momentum P T At large P T, SSA is dominated by twist-3 correlation effects (Afremov& Teryaev, Qiu & Sterman) At moderate P T, SSA is dominated by the k T - dependent parton distribution/fragmentation functions Ji, Qiu, Vogelsang, & Yuan, Phys.Rev.Lett.97:082002,2006 The two mechanisms at intermediate P T generate the same physics! However, this does not generalize to higher order in 1/Q (Bacchetta et al, 0803.0227) Baccetta’s talk

28. Future Challenge? PQCD & Factorization? Is P T =1-2 GeV high enough to use pQCD ? (a twist-3 effect, scaling, maybe ok for total cross section.) Is the peculiar flavor dependence in HERMES data due to non-perturbative physics? Or imprecise data? (g 2 ) Transverse-spin effort small at high energy? Jaffe & Saito, QCD selection rule (1996) Vogelsang & others, small double asymmetry for Drell-Yan PAX collaboration at GSI, PP-bar scattering at lower energy The ultimate goal? Can one extract transversity to a good precision? Can one calculate TMD & Twist-3 correlations?

29. Conclusion We have learned a lot about pol. PDF in the last 20 years. The quantitative gluon and sea quark polarizations need high-precision measurement. Significant orbital angular momentum contribution to the spin of the proton. Must find way to expose them. DVCS and other related process are unique way to do this (GPDs). Much theoretical progress has been made in understanding the physical mechanisms of single spin asymmetries. It yet becomes the useful tool to learn about the spin structure of the nucleon.