1. Transverse Spin and TMDs Jian-ping Chen, Jefferson Lab EIC Workshop at INT09, Oct.19-23, 2009  Introduction: why do we care about transverse structure?  Current status: What have we learned?  Near-future perspective: What do we expect before EIC?  Ultimate goal: What can EIC contribute? Acknowledgement: Some plots from H. Avagyan, H. Gao, X. Jiang, X. Qian, …

2. Introduction Why do we care about transverse structure?

3. Strong Interaction and QCD Strong interaction, running coupling ~1 -- QCD: accepted theory for strong interaction -- asymptotic freedom (2004 Nobel) perturbation calculation works at high energy -- interaction significant at intermediate energy quark-gluon correlations -- interaction strong at low energy (nucleon size) confinement  theoretical tools: pQCD (co-linear factorization), OPE, Lattice QCD, AdS/CFT, … A major challenge in fundamental physics: Understand QCD in all regions, including strong (confinement) region E ss

4. Nucleon (Hadron) Structure Colors are confined in hadronic system Hadron: ideal lab to study QCD Nucleon = u u d + sea + gluons Mass, charge, magnetic moment, spin, axial charge, tensor charge Decomposition of each of the above fundamental quantities Mass: ~1 GeV, but u/d quark mass only a few MeV each! Momentum: total quarks only carry ~ 50% Spin: ½, total quarks contribution only ~30% Spin Sum Rule Orbital Angular Momentum Relations to GPDs and TMDs Tensor charge Transverse sum rule? Partons and gluon field are in-separable Multi-parton correlations are important Beyond co-linear factorization Multi-dimensional structure and distributions Transverse dimension is crucial for complete understanding of nucleon structure and QCD, and help shed light in understanding confinement

5. Three Decades of Spin Structure Study 1980s: EMC (CERN) + early SLAC quark contribution to proton spin is very small  = (12+-9+-14)% ! ‘spin crisis’ ( Ellis-Jaffe sum rule violated) 1990s: SLAC, SMC (CERN), HERMES (DESY)  = 20-30% the rest: gluon and quark orbital angular momentum A + =0 (light-cone) gauge (½)  + L q +  G + L g =1/2 (Jaffe) gauge invariant (½)  + Lq + J G =1/2 (Ji) A new decomposition (X. Chen, et. al.) Bjorken Sum Rule verified to <10% level 2000s: COMPASS (CERN), HERMES, RHIC-Spin, JLab, … :  ~ 30%;  G probably small?, orbital angular momentum important?  Transversity and Transverse-Momentum Dependent Distributions  Generalized Parton Distributions  Orbital angular Momentum

6. Current Status What have we learned?

7. Transversity and TMDs Three twist-2 quark distributions: Momentum distributions: q(x,Q 2 ) = q ↑ (x) + q ↓ (x) Longitudinal spin distributions: Δq(x,Q 2 ) = q ↑ (x) - q ↓ (x) Transversity distributions: δq(x,Q 2 ) = q ┴ (x) - q ┬ (x) It takes two chiral-odd objects to measure transversity Semi-inclusive DIS Chiral-odd distributions function (transversity) Chiral-odd fragmentation function (Collins function) TMDs: (without integrating over P T ) Distribution functions depends on x, k ┴ and Q 2 : δq, f 1T ┴ (x, k ┴,Q 2 ), … Fragmentation functions depends on z, p ┴ and Q 2 : D, H 1 (x,p ┴,Q 2 ) Measured asymmetries depends on x, z, P ┴ and Q 2 : Collins, Sivers, … (k ┴, p ┴ and P ┴ are related)

8. “Leading-Twist” TMD Quark Distributions Quark Nucleon Unpol. Long. Trans. Unpol. Long. Trans.

9. Multi-dimension Distributions GPDs/IPDs H(x,r T ),E(x,r T ),.. d2kTd2kT d2kTd2kT TMD PDFs f 1 u (x,k T ),.. h 1 u (x,k T )  Gauge invariant definition (Belitsky,Ji,Yuan 2003)  Universality of k T -dependent PDFs (Collins,Metz 2003)  Factorization for small k T. (Ji,Ma,Yuan 2005) W p u (k,r T ) “Mother” Wigner distributions d2rTd2rT PDFs f 1 u (x),.. h 1 u (x) quark polarization

10. Access TMDs through Hard Processes Partonic scattering amplitude Fragmentation amplitude Distribution amplitude proton lepton pion proton lepton antilepton Drell-Yan BNL JPARC FNAL EIC SIDIS electron positron pion e – e + to pions

11.  s=20 GeV, p T =0.5-2.0 GeV/c   0 – E704, PLB261 (1991) 201.   +/- - E704, PLB264 (1991) 462. Single Spin Asymmetries in Large transverse single-spin effects were observed at RHIC, at much higher CM energies. In collinear picture, the QCD predict small SSAs with transversely polarized protons colliding at high energies. Kane, Pumplin, Repko ‘78 FermiLab E-704 FNAL

12. BELLE: Collins function measurements BELLE: Asymmetries in e + e - →h 1 h 2 X (H ┴ 1 H ┴ 1 ) _ Efremov et al. Phys.Rev.D. 73,094025 (2006) positivity limit 11 Belle detector KEKB Asymmetric collider 8GeV e- + 3.5GeV e+ Direct indication of non-0 Collins fragmentation !

13. Separation of Collins, Sivers and pretzelocity effects through angular dependence in SIDIS

14. A UT sin(  ) from transv. pol. H target `Collins‘ moments Non-zero Collins asymmetry Assume  q(x) from model, then H 1 _unfav ~ -H 1 _fav H 1 from Belle (arXiv:0805:2975) `Sivers‘ moments Sivers function nonzero (  + )  orbital angular momentum of quarks Regular flagmentation functions

15. Collins Moments for Kaon S. Gliske’s talk at DNP09

16. Sivers Moments for Kaon

17. Collins asymmetries from COMPASS deuteron Phys. Lett. B 673 (2009) 127-135 u and d cancellation?

18. Sivers asymmetries from COMPASS deuteron

19. Transversity Distributions A global fit to the HERMES p, COMPASS d and BELLE e+e- data by the Torino group (Anselmino et al.). PRD 75, 054032 (2007)

20. PKU-RBRC Workshop on Transverse Spin Physics, June 30, 2008 F. Bradamante Collins asymmetry – proton data comparison with M. Anselmino et al. predictions PRD 75, 054032 (2007) Franco Bradamante Transverse2008, Beijing

21. PKU-RBRC Workshop on Transverse Spin Physics, June 30, 2008 F. Bradamante Sivers asymmetry – proton data comparison with the most recent predictions from M. Anselmino et al. (arXiv 0805.2677) Franco Bradamante Transverse2008, Beijing

22. 2-d (x-P T ) Collins Moments S. Gliske’s talk at DNP09

23. 2-d (x-P T ) Sivers Moments

24. Other TMDs xBxB COMPASS 2002-2004 arXiv:0705.2402 Pretzelocity g1Tg1T

25. E06-010 Single Target-Spin Asymmetry in Semi-Inclusive n ↑ (e,e′π +/- ) Reaction on a Transversely Polarized 3 He Target Collins Sivers First measurement on the neutron with polarized 3 He With good PID, Kaon data for free Collins, Sivers, Pretzelocity and g 1 T 7 PhD Students Completed data taking 2/09 Exceeded PAC approved goal

26. Summary of Current Status Large single spin asymmetry in pp->  X Collins Asymmetries - sizable for the proton (HERMES and COMPASS ) large at high x,  - and  has opposite sign  unfavored Collins fragmentation as large as favored (opposite sign)? - consistent with 0 for the deuteron (COMPASS) Sivers Asymmetries - non-zero for  + from proton (HERMES), consistent with zero (COMPASS)? - consistent with zero for  - from proton and for all channels from deuteron - large for K + ? Collins Fragmentation from Belle Global Fits/models by Anselmino et al., Yuan et al. and … First neutron measurement from Hall A 6 GeV (E06-010) Very active theoretical and experimental study RHIC-spin, JLab (6 GeV and 12 GeV), Belle, FAIR, J-PARC, … EIC

27. Near-future Perspective What do we expect before EIC?

28. Collins and Sivers SSAs with CLAS @ 6 GeV JLab CLAS with a transversely polarized proton target will allow measurements of Collins and Sivers asymmetries in the large-x region Anselmino et al Vogelsang & Yuan Schweitzer et al

29. Precision Study of Transversity and TMDs From exploration to precision study Transversity: fundamental PDFs, tensor charge TMDs provide 3-d structure information of the nucleon Learn about quark orbital angular momentum Multi-dimensional mapping of TMDs 3-d (x,z,P ┴ ) Q 2 dependence Multi-facilities, global effort Precision  high statistics high luminosity and large acceptance

30. CHL-2 Upgrade magnets and power supplies Enhance equipment in existing halls 6 GeV CEBAF 11 12 Add new hall

31. 12 GeV Upgrade Kinematical Reach Reach a broad DIS region Precision SIDIS for transversity and TMDs Experimental study/test of factorization Decisive inclusive DIS measurements at high-x Study GPDs

32. Solenoid detector for SIDIS at 11 GeV Proposed for PVDIS at 11 GeV FGEMx4 LGEMx4 LS Gas Cherenkov HG Aerogel GEMx2 SH PS Z[cm] Y[cm] Yoke Coil 3 He Target

33. 3-d Mapping of Collins/Sivers Asymmetries at JLab 12 GeV With A Large Acceptance Solenoid Detector (L=10 36 ) Both  + and  - For one z bin (0.5-0.55) Will obtain 8 z bins (0.3- 0.7) Upgraded PID for K+ and K-

34. Power of SOLid

35. Discussion Unprecedented precision 3-d mapping of SSA Collins and Sivers  +,  - and K +, K - Study factorization with x and z-dependences Study P T dependence With similar quality SIDIS data on the proton and data from e+e- extract transversity and fragmentation functions for both u and d quarks determine tensor charge study TMDs for valence quarks study quark orbital angular momentum Combining with world data, especially data from high energy facilities (future EIC) study Q 2 evolution (need theoretical development) sea and gluon TMDs (more surprises are waiting?) Global efforts (experimentalists and theorists), global analysis Precision information on multi-dimension nucleon structure

36. Ultimate Goal What can EIC contribute?

37. Transverse Structure Study with EIC Much large kinematical reach  Much higher Q 2 range, clearly into hard scattering region Wide Q 2 range, study Q 2 evolution and high-twist effects  Much higher PT range, into high PT region and overlap region  Much lower x range, study sea TMDs  Reach current fragmentation region for flavor study (pions, Kaons, nucleons, …) Ultimate understanding of nucleon structure with complete 4-d (x,z,P T,Q 2 ) mapping  Model independent extractions of transversity and TMDs through global analysis  Determination of tensor charge Study, test and understand QCD Special universality: Sivers(SIDIS) = - Sivers(Drell-Yan) Study QCD beyond co-linear approximation, study parton correlations Shed light on QCD in strong region (confinement)

38. Sivers effect: Pion electroproduction 100 days at L=10 33 MEIC (4x60 GeV) (Harut Avakian)

39. Sivers effect: Kaon electroproduction EIC CLAS12 (Harut Avakian)

40. Summary Why transverse dimension?  Complete understanding of nucleon structure  Transverse momentum dependence - strong quark-gluon correlations  Key to understanding QCD in all regions, including confinement region What have we learned?  Non-zero Collins and Sivers asymmetries for pions and Kaons  Non-favored Collins fragmentation functions as important as favored ones  HERMES and COMPASS Collins asymmetries consistent,  HERMES and COMPASS Sivers results on the proton might be different?  First measurements of Collins and Sivers asymmetry on the neutron  Explorations on other TMDs: Boer-Mulders, Pretzelocity and g 1 T  Model dependent extractions of transversity, Sivers and Collins functions What do we expect before EIC? Precision 3-d (x,z,P T ) mapping of TMDs What can EIC contribute? Ultimate coverage in kinematics, complete 4-d (x,z,P T,Q 2 ) mapping Lead to breakthrough in full understanding of nucleon structure and QCD