1. QCD のツイスト３機構による シングルスピン非対称 田中和廣 ( 順天堂大医 ) 江口桐士 （新潟大自） 小池裕司 ( 新潟大理 )

2. Eguchi, Koike, Tanaka, NPB752 (’06) 1; NPB763 (’07) 198 Contents: 0. introduction 1. QCD Factorization for twist-3 mechanism & gauge invariance 2. New master formula for twist-3 soft-gluon mechanism Koike, Tanaka, hep-ph/0612117

3. Single (Transverse) Spin Asymmetry SSA q SIDIS FNAL-E704(‘91), RHIC-STAR(‘04) HERMES(’99,’03,’04,’05), COMPASS(’05,’06) RHIC, JPARC, … Direct γ Drell-Yan

4. FNAL-E704:

6. Single (Transverse) Spin Asymmetry SSA q Conventional twist-2 mechanism: tiny!

7. q Three indispensable elements to produce SSA NP P P&NP TMD-factorizationcollinear-factorization Sivers & Collins function twist-3 function Eguchi,Koike,Tanaka (’06)Ji,Qiu,Vogelsang,Yuan (’06) SIDIS:

8. Sivers Collins Twist-3

9. Source of complication Work hard! Resolved! Eguchi, Koike, Tanaka, NPB752 (’06) 1 Gauge-invariance?Ward Identity

10. Eguchi, Koike, Tanaka, NPB752 (’06) 1

11. Necessary condition for gauge invariance: decoupling of scalar polarized gluon detailed calculation shows, this in fact guarantees

12. Gauge invariance for HP Ward identity:

13. Gauge invariance for SFP Ward identity: Gauge invariance for SGP trivial Ward identity!

14. Ward Identity Eguchi, Koike, Tanaka, NPB763 (’07) 198

23. Eguchi, Koike, Tanaka, NPB752 (’06) 1

24. Summary for part 1 SSA in Semi-Inclusive DIS

25. Eguchi, Koike, Tanaka, NPB752 (’06) 1; NPB763 (’07) 198 Contents: 0. introduction 1. QCD Factorization for twist-3 mechanism & gauge invariance 2. New master formula for twist-3 soft-gluon mechanism Koike, Tanaka, hep-ph/0612117

26. SGP SFP SGP HP

27. SGP SFP, HP single poles non-derivative gauge invariance ??

28. Remarkable simplicity in SSA from SGP the derivative term Direct γ: Qiu, Sterman (’91) Drell-Yan: Ji,Qiu,Vogelsang,Yuan (’06) SIDIS: Eguchi, Koike, Tanaka (’06) SGP deserves special attention! Kanazawa, Koike (’01) Qiu, Sterman (’99), Kanazawa, Koike (’00)

29. SGP ・ systematic diagrammatic manipulation approach in Feynman gauge ・ contributions from a number of Feynman diagrams are “master formula” Koike, Tanaka, hep-ph/0612117 united into a derivative of 2 → 2 Born diagram

30. Proof ＝ ＋ Ward ID ＋ eikonal prop.“contact” term propagator pole disentangled; collinear expansion simple; (cancel with mirror diagram) ＋ Background field gauge

31. + mirror diagrams + mirror diagrams Relevant diagrams for

32. ・ exact master formula for Drell- Yan exact master formula ・ Crossing the incoming unpolarized exact master formula for SIDIS ・ applicable to Drell-Yan, direct γ, SIDIS for direct γ proton into the outgoing hadron

33. Using master formula for Drell-Yan

34. Results for SGP contributions using master formula for Drell-Yan Universal structure for derivative & non-derivative terms

35. Results for SGP contributions using master formula for Drell-Yan ・ coincide with Ji,Qiu,Vogalsang,Yuan (’06) derivative & non-derivative terms ： direct γ

36. Results for SGP contributions using master formula for Diret γ one single coefficient for derivative & non-derivative terms Dramatically compact result due to scale invariance! Disagree with Qiu, Sterman (’91) Similar simplification by scale invariance can be shown for Koike, Tanaka (’07)

37. Using master formula for SIDIS ・ coincide with Eguchi, Koike, Tanaka, NPB763 (’07) 198 derivative & non-derivative terms; all azimuthal dependence

38. Summary for part 2 Soft gluonic pole for SSA twist-3 mechanism a new diagrammatic approach in Feynman gauge systematic reduction of SGP contributions Ward identity; eikonal propagator & contact term identification & cancellation of SGP at diagrammatic level unity of many Feynman diagrams into a derivative of 2 → 2 Born diagram master formula for twist-3 SSA from twist-2 unpolarized cross section exact, applicable to a range of processes Drell-Yan, direct γ, SIDIS, …