Nucleon Spin: Final Solution at the EIC

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

2. Next Big Thing in QCD

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]

4. Clay Mathematics Institute Millennium Prize Problem QCD and Strong-Interactions • QCD: Non-Abelian gauge theory • Building blocks: quarks (spin ½, mq, 3 colors; gluons: spin 1, massless, 32-1 colors) • Asymptotic freedom and confinement Short distance hard, perturbative Long distance:? Soft, non-perturbative ~1/Length Nonperturbative scale QCD~1GeV

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

6. Understanding the nucleon • 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 Friedman Kendall Taylor Bjorken Scaling: Q2Infinity Feynman Parton Model: Point-like structure in Nucleon

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

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

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 Luminosity requirement

12. Big questions

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

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

15. Diffractions

16. Hadronization in cold nuclei vs hot matter

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

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

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. Summary of the polarized DIS data

22. EIC kinematics

23. Back to DIS With EIC

24. In particular

25. gluon spin Quark spin x2

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

27. Spin sum rule Ji, 1996 • Taking forward limit,

28. Q2 t ( H + E) x dx =Jq Quark OAM: Lq = 1/2 DS+ Lz (Ji 96) Generalized Parton Distributions in hard exclusive processes: • A new type of parton “distributions” contains much more information • Comprehensive program at JLab,HERMES,COMPASS and future EIC Mueller et al.,94;Ji,96; Radyushkin,96

29. Extract the GPDs • The theoretical framework has been well established • Perturbative QCD corrections at NLO, some at NNLO Mueller, et al., 1310.5394 Ju, Jd, Jg

30. EIC kinematics coverage

31. Further decomposition of Jq • Quark spin explicitly • OAM, twist-three nature 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 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 Mueller, et al., 1304.0077

34. Gluon Tomography toward small-x

35. Nucleon tomography

36. Transverse momentum dependent parton distribution • Straightforward extension • Spin average, helicity, and transversity distributions • PT-spin correlations • Nontrivial distributions, STXPT • In quark model, depends on S- and P-wave interference

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

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 • …

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

40. EIC kinematics

41. Precision of 3-D PDFs at EIC

42. all order factorization 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

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

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

46. Access the GPDs • Deeply virtual Compton Scattering (DVCS) and deeply virtual exclusive meson production (DVEM) GPD In the Bjorken limit: Q2>>(-t),∧2QCD,M2 Mueller, et al., hep-ph/0112108, 1310.5394

47. Nucleon tomography and Orbital angular momentum Coordinate BT Momentum PT Factorization: Ji-Ma-Yuan 2004

48. 1310.0461