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Status Report (theory): Unveil the Mysterious of Single Spin Asymmetry

Status Report (theory): Unveil the Mysterious of Single Spin Asymmetry. Feng Yuan Lawrence Berkeley National Laboratory RBRC, Brookhaven National Laboratory. Outline. Introduction Two approaches: Transverse Momentum Dependent and Twist-three Collinear

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Status Report (theory): Unveil the Mysterious of Single Spin Asymmetry

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  1. Status Report (theory): Unveil the Mysterious of Single Spin Asymmetry Feng Yuan Lawrence Berkeley National Laboratory RBRC, Brookhaven National Laboratory

  2. Outline • Introduction • Two approaches: Transverse Momentum Dependent and Twist-three Collinear • Highlights (bias) of recent developments • Unifying the two approach • QCD dynamics: Universality and Factorization • Phenomenology • First attempt to extract transversity, … • Challenges and Puzzles

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

  4. Single Spin Asymmetry • Motivations: • It is hard to understand it in QCD • Its strong tied with the quark orbital angular momentum • We have beautiful data • Nontrivial QCD dynamics, and fundamental test of the factorization, and the universality of Parton Distribution Functions, Fragmentation Functions,…

  5. 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 • See also, Ma-Sang, arXive: 0809.1791 • We have to go beyond this naïve picture

  6. ST kT Two mechanisms in QCD • Spin-dependent transverse momentum dependent (TMD) function • Sivers 90 • Colllins 93 • Brodsky-Hwang-Schmidt, 02 • Twist-3 quark-gluon correlations (coll.) • Efremov-Teryaev, 82, 84 • Qiu-Sterman, 91,98 . Sivers function ~ ST (PXkT) P

  7. Two contributions, e.g., in DIS pTXsT • Fragmentation: • Collins Function sT STXkT • Distribution: • Sivers Function ST

  8. QCD Dynamics Transverse momentum dependence

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

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

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

  12. Universality of the Collins Fragmentation HERMES, COMPASS, JLab BELLE (KEK), BESIII(?) Yuan PRL08 ep--> e Pi X pp--> jet(->Pi) X e+e--> Pi Pi X Metz 02, Collins-Metz 02, Yuan 07, Gamberg-Mukherjee-Mulders 08 Under investigate by STAR experiments at RHIC

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

  14. By using the Ward Identity: same Collins fun. Similar arguments for pp collisions Yuan, PRL08,PRD08 Conjecture: the Collins function will be the same as e^+e^- and SIDIS

  15. 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

  16. Sivers effect is different • It is the final state interaction providing the phase to a nonzero SSA • Ward identity is not easy to apply • Non-universality in general • Only in special case, we have “Special Universality”

  17. Testable prediction at RHIC • Initial state vs. final state interactions • “Universality”: QCD prediction * * DIS Drell-Yan HERMES Brodsky-Hwang-Schmidt 02 Collins 02

  18. 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/

  19. 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 Braun et al., 0909.3410

  20. Collinear factorization verified at one-loop order • Soft-collinear divergence cancelled out between virtual and real diagrams • Collinear divergence identified as the splitting functions for the antiquark and twist-three correlation functions

  21. Finite terms +...

  22. Threshold limits • Large-z, • The asymmetry should not change dramatically with energy in the forward region

  23. RHIC Twist-3 Fit (LO) to data: STAR E704 BRAMHS Kouvaris,Qiu,Vogelsang,Yuan, 06

  24. New challenge from STAR data (2006) • Anselmino et al., • Kouvaris et al., SPIN Workshop, JLab

  25. Summary and Outlook • Based on recent developments, we have shown that the TMD and collinear factorization approaches are consistent in the intermediate transverse momentum region • Next-to-leading order QCD corrections to the Drell-Yan SSA have been calculated for the first time • There are still puzzles!!

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