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Transverse spin and 3-D Parton Structure of Nucleon

Transverse spin and 3-D Parton Structure of Nucleon. Feng Yuan Lawrence Berkeley National Laboratory RBRC, Brookhaven National Laboratory. Exploring nucleon is of fundamental in Science. Search for New Physics. Fundamental question of our universe. Jlab, RHIC, Tevatron, LHC,….

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Transverse spin and 3-D Parton Structure of Nucleon

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  1. Transverse spin and 3-D Parton Structure of Nucleon Feng Yuan Lawrence Berkeley National Laboratory RBRC, Brookhaven National Laboratory

  2. Exploring nucleon is of fundamental in Science Search for New Physics Fundamental question of our universe Jlab, RHIC, Tevatron, LHC,… Mass, energy-momentum, Spin structure, … Nucleon Structure How nuclei formed from nucleons, etc.. Study the strong interaction physics FRIB (RIA), Jlab, … Partonic Structure QCD dynamics: confinement Factorization, universality,…

  3. Hadronic reactions Feynman Parton Model • Inclusive cross sections probe the momentum (longitudinal) distributions of partons inside nucleon Electron- Ion Collider 12 GeV JLab

  4. Extension to transverse direction… • Semi-inclusive measurements • Transverse momentum dependent (TMD) parton distributions • Deeply Virtual Compton Scattering and Exclusive processes • Generalized parton distributions (GPD)

  5. Quantum phase space distribution • Wigner distributions After integrating over r, one gets TMD After integrating over k, one gets Fourier transform of GPDs Ji: PRL91,062001(2003)

  6. 3D image of quarks at fixed-x • GPDs can be used to picture quarks in the proton (Belitsky-Ji-Yuan, PRD 04) Beam direction fm z fm x y fm low x high x moderate x

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

  8. Motivations… • Nucleon Structure, spin correlation, orbital motion of quarks and gluon • Nontrivial QCD dynamics, and fundamental test of the factorization, and the universality of PDFs, FFs,… • Single spin asymmetry (SSA) phenomena

  9. Where can we learn TMDs • Semi-inclusive hadron production in deep inelastic scattering (SIDIS) • Drell-Yan lepton pair production in pp scattering • Di-jet (photon+jet) correlation in pp scattering • Relevant e+e- annihilation processes • Many others…

  10. Inclusive and Semi-inclusive DIS JLab & EIC Inclusive DIS: Partonic Distribution depending on the longitudinal momentum fraction Q Semi-inclusive DIS: Probe additional information for partons’ transverse distribution in nucleon Q

  11. JLab & EIC • Transverse Momentum Dependent (TMD) Parton Distributions and Fragmentations • Novel Single Spin Asymmetries U: unpolarized beam T: transversely polarized target

  12. ST kT Two major contributions • Sivers effect in the distribution • Collins effect in the fragmentation • Other contributions… ST (PXkT) P (zk+pT) (k,sT) ~pTXsT

  13. Universality of the Collins Fragmentation ep--> e Pi X pp--> jet(->Pi) X e+e--> Pi Pi X Metz 02, Collins-Metz 02, Yuan 07, Gamberg-Mukherjee-Mulders08 Meissner-Metz 0812.3783 Yuan-Zhou, 0903.4680

  14. Model calculations of the Collins Effects Metz 02, Collins-Metz 02: Gamberg-Mukherjee-Mulders, 08 Universality of the Collins function!!

  15. By using the Ward Identity: same Collins fun. Similar arguments for pp collisions Yuan, 0709.3272 The Collins function is the same as e^+e^- and SIDIS

  16. Extend to two-gluon exchange Universality preserved

  17. Key observations • Final state interactions DO NOT provide a phase for a nonzero SSA • Eikonal propagators DO NOT contribute to a pole • Ward identity is applicable to warrant the universality arguments

  18. Sivers effect is different • It is the final state interaction providing a phase to the nonzero SSA • Ward identity is not easy to apply • Non-universality in general • Only in special case, we have “Special Universality” Brodsky,Hwang,Schmidt02 Collins, 02; Ji,Yuan,02; Belitsky,Ji,Yuan,02

  19. DIS and Drell-Yan • Initial state vs. final state interactions • “Universality”: QCD prediction * * DIS Drell-Yan HERMES

  20. Experiment SIDIS vs Drell Yan HERMES Sivers Results RHIC II Drell Yan Projections 0 Markus Diefenthaler DIS Workshop Munich, April 2007 0 0.1 0.2 0.3 x http://spin.riken.bnl.gov/rsc/

  21. QCD Dynamics Transverse momentum dependence

  22. Transition from Perturbative region to Nonperturbative region • Compare different region of PT Nonperturbative TMD Perturbative region

  23. Perturbative tail is calculable • Transverse momentum dependence Power counting, Brodsky-Farrar, 1973 Integrated Parton Distributions Twist-three functions

  24. A unified picture Transverse momentum dependent Collinear/ longitudinal PT QCD PT Q << << Ji-Qiu-Vogelsang-Yuan,2006 Yuan-Zhou, 2009

  25. NLO corrections to SSA Vogelsang-Yuan, arXiv:0904.0410 • SSA in Drell-Yan as an example, • Collinear factorization Collinear functions, evolution: Kang-Qiu, 08; Zhou-Yuan-Liang 08

  26. Future perspective • Current and planed experiments will have more and more data on various transverse spin observables • Recent developments have laid solid theoretical ground to apply QCD theory to study the relevant nucleon structure • Quark transversity • Orbital motion of quarks and gluon

  27. Semi-Inclusive DIS • Transverse Momentum Dependent (TMD) Parton Distributions and Fragmentations • Novel Single Spin Asymmetries U: unpolarized beam T: transversely polarized target

  28. What’s Single spin asymmetry? Transverse plane Final state particle is Azimuthal symmetric Single Transverse Spin Asymmetry (SSA)

  29. SSAs in Modern era : RHIC, JLab, HERMES, … STAR Central rapidity!! BRAHMS Large SSA continues at DIS ep and collider pp experiments!!

  30. Naïve parton model fails • If the underlying scattering mechanism is hard, the naïve parton model generates a very small SSA: (G. Kane et al, 1978), • It is in general suppressed byαSmq/Q • We have to go beyond this naïve picture

  31. ST kT Two mechanisms in QCD • Spin-dependent transverse momentum dependent (TMD) function • Sivers 90 • Brodsky,Hwang,Schmidt, 02 (FSI) • Gauge Property: Collins 02;Belitsky-Ji-Yuan,NPB03 Boer-Mulders-Pijlman,03 • Factorization: Ji-Ma-Yuan,PRD04;Collins,Metz,04 • Twist-3 quark-gluon correlations (coll.) • Efremov-Teryaev, 82, 84 • Qiu-Sterman, 91,98 Sivers function ~ ST (PXkT) . P

  32. Quantum Phase Space Distribution • Wigner operator • Wigner distribution: “density” for quarks having position r and 4-momentum k(off-shell) a la Saches 7-dimensional distribtuion No known experiment can measure this!

  33. Polarized TMD Quark Distributions Nucleon Unpol. Long. Trans. Quark Unpol. Long. Trans. Boer, Mulders, Tangerman (96&98)

  34. Three classes in the view of a quark model • S-wave • Unpolarized, helicity, transversity • S-P interference • g1T, h1L • f1T┴, h1┴ • P-P or S-D interference • h1T┴ • Miller 07, Burkardt 07, Avakian et al 08.

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