1. 9/19/20151 Nucleon Spin: Final Solution at the EIC Feng Yuan Lawrence Berkeley National Laboratory

2. Next Big Thing in QCD 9/19/20152

3. References: INT-Write-Up, “Gluons and the quark sea at high energies: distributions, polarization, tomography”, 500 pages, e-Print: arXiv:1108.1713 [nucl-th]. EIC-White Paper, “Electron-Ion Collider: Next QCD Frontier”,150 pages, e-Print: arXiv:1212.1701 [nucl-ex] 3

4. 4 9/19/2015 QCD and Strong-Interactions QCD: Non-Abelian gauge theory  Building blocks: quarks (spin ½, m q, 3 colors; gluons: spin 1, massless, 3 2 -1 colors) Asymptotic freedom and confinement Clay Mathematics Institute Millennium Prize Problem Long distance:? Soft, non-perturbative Short distance hard, perturbative Nonperturbative scale  QCD ~1GeV ~1/Length

5. Understanding the nucleon 5 Solving QCD  Numeric simulation: Lattice QCD BMW, Science, 2008 LHPC, 2011

6. Understanding the nucleon 6 Experimental probes  Study the quark and gluon structure through low and high-energy scattering  Matrix elements of local operators (e.g., form factors) or operators on the light-cone (parton distributions)  High energy experiments  perturbative QCD, factorization, universality  Sum rules:  Momentum  Bjorken  Nucleon spin  …

7. Deep Inelastic Scattering 9/19/20157 FriedmanKendallTaylor Bjorken Scaling: Q 2  Infinity Feynman Parton Model: Point-like structure in Nucleon

8. In particular DIS (Virtual Photon Q>> ∧ QCD ) 9/19/20158 Leading Born Diagram Higher Order Corrections:  Gluon Momentum (divergence)  Collinear: xP, x-finite  Soft: xP+kt, x-small P

9. 9 Factorization is essential to study nucleon structure Universality of the parton distributions  Predictive power of QCD Collins-Soper-Sterman 85, Bodwin 85, … Ji-Ma-Yuan 04, Dominguez-Xiao-Yuan 10,…

10. EIC Proposals in US 9/19/201510

11. Basics Inclusive DIS  Parton distributions Semi-inclusive DIS, measure additional hadron in final state  Kt-dependence Exclusive Processes, measure recoiled nucleon  Nucleon tomography Parity violating process 9/19/201511 Luminosity requirement

12. Big questions 9/19/201512

13. kt-dependence crucial to the saturation 13 QCD Phase structure of cold nuclei

14. Comprehensive study of small-x saturation at the EIC Inclusive observable Two-particle correlations 9/19/201514 xiao@EIC-Whitepaper

15. Diffractions 9/19/201515

16. Hadronization in cold nuclei vs hot matter 9/19/201516

17. Intensity Frontier (EW Physics) 9/19/201517 √S = 140GeV, 200fb -1

18. 189/19/2015 Ultimate goal of spin physics? Spin sum rule Quark spin, Best known Gluon spin, Start to know Orbital Angular Momentum of quarks and gluons, Little known Jaffe-Manohar, 90 Ji, 96

19. 19 EMC experiment at CERN Polarized muon + p deep inelastic scattering,  Virtual photon can only couple to quarks with opposite spin, because of angular momentum conservation  Select q + (x) or q - (x) by changing the spin direction of the nucleon or the incident lepton  The polarized structure function measures the quark spin density

20. 20 Summary of the polarized DIS data

22. EIC kinematics

23. 23 Back to DIS With EIC

24. In particular

25. Quark spin x2 gluon spin

26. Where is the rest of spin Back to the angular momentum density Energy-momentum tensors in quark and gluon 9/19/201526

27. Spin sum rule Taking forward limit, 9/19/201527 Ji, 1996

28. 28 Q2Q2 t A new type of parton “ distributions ” contains much more information Comprehensive program at JLab,HERMES,COMPASS and future EIC Quark OAM: L q Generalized Parton Distributions in hard exclusive processes: J q ( H + E) x dx = J q = 1/2  L z Mueller et al.,94;Ji,96; Radyushkin,96 (Ji 96)

29. Extract the GPDs The theoretical framework has been well established  Perturbative QCD corrections at NLO, some at NNLO 9/19/201529 Mueller, et al., 1310.5394 J u, J d, J g

30. EIC kinematics coverage 9/19/201530

31. Further decomposition of J q Quark spin explicitly OAM, twist-three nature 9/19/2015 Ji, Xiong, Yuan, PRL109, 152005 (2012); PRD 13; Hatta, Yoshita, JHEP 2012; Liuti, et al., 1310.5157

32. Related to the parton’s phase space Wigner Distributions 32 Phase space distribution: Projection onto p (x) to get the momentum (probability) density Quark orbital angular momentum Well defined in QCD: Ji, Xiong, Yuan, PRL, 2012; PRD, 2013 Lorce, Pasquini, Xiong, Yuan, PRD, 2012

33. Quark imaging from EIC 9/19/201533 Mueller, et al., 1304.0077

34. Gluon Tomography toward small-x 9/19/201534

35. Nucleon tomography 9/19/201535

36. Transverse momentum dependent parton distribution Straightforward extension  Spin average, helicity, and transversity distributions P T -spin correlations  Nontrivial distributions, S T XP T  In quark model, depends on S- and P-wave interference 9/19/201536

37. 9/19/201537 Quark Sivers function leads to an azimuthal asymmetric distribution of quark in the transverse plane Alex Prokudin @EIC-Whitepaper

38. Where can we learn TMDs Semi-inclusive hadron production in deep inelastic scattering (SIDIS) Drell-Yan lepton pair, photon pair productions in pp scattering Dijet correlation in DIS Relevant e+e- annihilation processes … 9/19/201538

39. 39 9/19/2015 Novel Single Spin Asymmetries U: unpolarized beam T: transversely polarized target Semi-inclusive DIS Sivers: Collins:

40. EIC kinematics 9/19/201540

41. Precision of 3-D PDFs at EIC 9/19/201541

42. all order factorization 9/19/201542 Similar calculations for pp collisions: Zhu HX, et al., PRL110 (2013) 082001

43. Conclusions: EIC Great opportunities in nuclear science Ultimate machine for nucleon spin physics Unique place to investigate gluon saturation Potential discovery in BSM physics 9/19/201543

44. TMDs in valence region Quark Sivers function leads to an azimuthal asymmetric distribution of quark in the transverse plane 9/19/201544 Alex Prokudin @EIC-Whitepaper

45. Current Research Focused on 45 Long. Momentum distributions Nucleon Spin 3D imaging Transverse-momentum-dependent and Generalized PDFs QCD: Factorization, Universality, Evolution, Lattice, …

46. Access the GPDs Deeply virtual Compton Scattering (DVCS) and deeply virtual exclusive meson production (DVEM) 9/19/201546 GPD In the Bjorken limit: Q 2 >>(-t), ∧ 2 QCD,M 2 Mueller, et al., hep-ph/0112108, 1310.5394

47. Nucleon tomography and Orbital angular momentum Momentum P T Factorization: Ji-Ma-Yuan 2004 Coordinate B T

48. 9/19/201548 1310.0461

49. 9/19/201549