1. “Overview” of Nucleon Spin Structure Xiangdong Ji University of Maryland Workshop on Future Prospects on QCD at High-Enegy, BNL, July 19, 2006

2. Outline Introduction Quark sea polarization Gluon polarization Orbital angular momentum and generalized parton distribution Transverse spin physics Conclusion

3. Introduction The driving force behind the modern cosmology is The origin of energy density in the universe

4. Introduction The driving force for high-energy spin physics is Total proton spin = 1/2 Quark spin measured in inclusive pol. DIS “Dark” angular momentum?

5. Spin of the proton in QCD The spin of the nucleon can be decomposed into contributions from quarks and gluons Further decomposition of the quark contribution Further decomposition of the gluon contribution gauge invariant parton-physics motivated

6. Probing “dark” angular momentum Quark-sea polarization HERMES semi-inclusive DIS Polarized RHIC & EIC Gluon polarization COMPASS/HERMES semi-inclusive DIS Polarized RHIC & EIC Quark orbital angular momentum Proton tomography HERMES, JLab, COMPASS, & EIC

7. Sea quark Polarization

8. The sea quark contribution: an indirect approach using SU(3) flavor symmetry Quark spin contribution to the proton spin can be determined from the axial charges. The isovector axial charge (neutron decay const.) The octet axial charge (hyperon β -decays) Inclusive polarized DIS yields Together, they produce Explains “spin crisis?”

9. Measuring the sea quark spin in SIDIS: One can measure the sea quark contribution to the spin of the proton through fragmentation of the polarized quark into mesons (Close & Milner) A major motivation for HERMES

10. HERMES result Airapetian et al, PRL 92 (2004) 012005 Sea quark polarization The result for  s is very different from the inclusive DIS plus SU(3) symmetry analysis! Precision? Small x? QCD Factorization? SU(3) flavor symmetry?

11. Future possibilities Polarized RHIC Can measure through W boson production of polarized proton-proton collision at RHIC Center of mass energy must be high Neutrino elastic scattering Measuring the axial form factor in elastic scattering

12. Parity Violating Structure Functions g 5 Unique measurement with EIC Experimental Signature: missing (neutrino) momentum: huge asymmetry in detector Complementary measurement to RHIC SPIN For EIC kinematics

13. Measurement Accuracy PV g 5 with EIC Assume: 1) Input GS Polarized PDFs 2) xF 3 is measured well by that time 3) 4fb-1 luminosity If e+ and e- possible then one can have g5(+) as well. Separate flavors  u,  d etc.

14. Flavor decomposition EIC White Paper 2002 @10 33 luminosity (Stoesslein, Kinney) Small x!

15. Gluon polarization  g

16. Gluon polarization Thought to be large because of the possible role of axial anomaly –( α s / 2  )  g (Altarelli & Ross, 1988) 2-4 units of hbar! Of course, the gluon contribute the proton spin directly. 1/2 =  g + … One of the main motivations for COMPASS and RHIC spin experiments! Surprisingly-rapid progress, but the error bars remain large.

17. Experimental progress-I Two leading-hadron production in semi-inclusive DIS Q-evolution in inclusive spin structure function g 1 (x)

18. Experimental progress-II  production in polarized PP collision at RHIC Two jet production in polarized PP collision at RHIC

19. Fit to data  g = 0.31 ± 0.32 type-1 = 0.47 ± 1.0 type-2 = — 0.56 ± 2.16 type-3 Type-3 fit assumes gluon polarization is negative at small x. Hirai, Kumano,Saito, hep-ph/003213

20. Theoretical prejudices It shall be positive: There was a calculation by Jaffe ( PRB365, 1996 ), showing a negative result in NR quark and bag models. However, there are two type of contributions The contribution calculated by Jaffe is cancelled by the one-body contribution. Calculating x-dependence is in progress (P.Y. Chen) Barone et al., PRB431,1998

21. Theoretical prejudices It shall not be as large! The anomaly argument for large Δg is controversial There is also an anomaly contribution to the quark orbital motion. It is un-natural for heavy quarks. Naturalness Δ q + Δ g + L z = 1/2 if Δg is very large, there must be a large negative L z to cancel this---(fine tuning!) Model predictions are around 0.5 hbar.

22. More data from RHIC More precise measurement on pi production asymmetry as well as two-jet production Direct photon production, proportional to  g linearly STAR-jet

23. Gluon Distributions at EIC Deep Inelastic Scattering Kinematics with EIC: Perturbative QCD analysis of the g 1 spin structure of the data 2+1 Jet production in photon gluon fusion (PGF) process 2-high p T opposite charged hadron tracks (PGF) Photo-production (real-photon) Kinematics with EIC: Single jet production in PGF Di-Jet production in PGF Open charm production

24.  G(x)/G(x) EIC vs. Rest of the World EIC Di-Jet DATA 2fb -1 Good precision Clean measurement Range 0.01 <x< 0.3 Constrains shape!!

25. g 1 (x) at small x

26. Orbital angular momentum

27. 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 …

28. OAM and Wigner distribution To measure orbital motion, one must have information of a parton’s position and momentum simultaneously. A natural observable is the so-called Wigner distribution in Quantum Mechanics. When integrated over x (p), one gets the momentum (probability) density. Not positive definite in general (not strict density), but is in classical limit! Any dynamical variable can be calculated as

29. Harmonic oscillator & squeezed light n=0 Wiger distribution or squeezed light! n=5

30. Generalized parton distributions Off-forward matrix elements Reduces to ordinary parton distribution when t->0 x-moments yield electromagnetic, gravitational,…etc form factors P P'P' x1Px1P x2P'x2P'

31. 3D images of quarks at fixed-x GPDs as Wigner distribution can be used to picture quarks in the proton (A. Belitsky, X. Ji, and F. Yuan, PRD, 2004) The associated Winger distribution is a function of position r and Feynman momentum x: f(r,x) One can plot the Wigner distribution as a 3D function at fixed x A GPD model satisfying known constraint: x y z

32. Integrating over z  2D Impact parameter space Th. Feldman

33. 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. In the forward limit, H reduces to ordinary parton distribution q(x). E can best be determined with a trans. pol. target.

34. Measuring GPD Deeply virtual Compton scattering Deeply virtual meson production (replacing the photon by mesons) Measurements have been made at HERA & Jlab:

35. DVCS with transversely polarized target

36. Looking forward Jlab 12 GeV upgrade A comprehensive program to study GPDs HERMES & COMPASS ： rho production on transversely polarized target Vanderhaeghen et al.

37. Deeply Virtual Compton Scattering at EIC D. Hasell, R. Milner et al. EIC: 5 GeV e on 50 GeV proton: Could be measured with EIC with considerable x,Q 2 range.

38. DVCS at EIC (preliminary) 10 x 250 GeV Q 2 > 1 GeV 2 20<W<95 GeV 0.1<|t|<1.0 GeV 2 Full curve: all events Dashed curve: accepted events Q 2 >1 GeV 2 : 50K events/fb -1 A. Sandacz Acceptance enhanced ZEUS-like detector Add Roman pots a la PP2PP at RHIC

39. Transverse Spin Physics left right

40. Driving questions What effects can transverse spin produce in a high- energy collision process? What can one learn about the quark-gluon structure of the proton form these effects? Transversity distribution Quark-gluon correlations TMD quark distributions

41. Transverse spin asymmetries pp  epep ep  e+e-

42. Understanding the Asymmetries If a process does not involve hard momentum transfer, our understanding is very limited. pp  : SSA at small transverse momentum ep  : spin asymmetry at small Q 2 Hard processes: either a large transverse-momentum or a high Q QCD factorization theorems Asymmetries are related to underlying parton properties: i.e. parton distributions & fragmentations

43. Observable Asymmetries Single Spin Asymmetries pp  to semi-inclusive hadrons (twist-3)  pp  to  *, W, Z + X, small P  (twist-2) pp  to 2 jets, jet+ , small P  (twist-2) ep  to semi-inclusive hadrons, small P  (twist-2)  Double Spin Asymmetries p  p  to  *, W, Z + X (twist-2) p  p  to jets, heavy quarks (twist-2) e  p  inclusive g 2 (twist-3)  ep  to polarized  + X (twist-2)  ep  to semi-inclusive two hadrons (twist-2)  Angular Correlation: e+e- to hh’ + X (twist-2) 

44. 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  ) (twist-2 at small k) Asymmetric distribution of quarks with T-momentum k  in a transversely polarized nucleon T-odd, depends on ISI/FSI Twist-3 Quark-gluon correlation functions Polarized gluons! Related Fragmentation functions

45. 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 (Afremov& Teryaev, Qiu & Sterman) At moderate P , SSA is dominated by the k  - dependent parton distribution/fragmentation functions Ji, Qiu, Vogelsang, & Yuan (2006) The two mechanisms at intermediate P  generate the same physics!

46. 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 smaller at COMPASS. The Collins function is consistent with e+e- data, but with very striking charge behavior Siver’s function has striking flavor dependence

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

48. EIC with transverse spin Angular Momentum Transversity

49. Conclusion The proton spin structure is a fundamental question in QCD. Much work is need to identify the “dark” angular momentum! The field is active with COMPASS, Polarized RHIC underway Jlab 12 GeV on the horizon EIC can definitive contributions to all aspects of proton spin physics, and bring the field to its maturity.

50. Spin budget of the proton Quark spin ? Total proton spin = 1/2