1. 偏極核子・反核子衝突における 小横運動量ドレル・ヤン過程 arXiv:0801.0026 [hep-ph] ― ＱＣＤの摂動高次項の影響と核子の transversity 分布 ― 田中和廣 ( 順天堂大 ) 川村浩之 ( 理研 ) 小平治郎 (KEK)

2. — Transversity Chiral-odd : unmeasurable in inclusive DIS First global fit (LO): SIDIS at HERMES, COMPASS + Collins function from BELLE Anselmino et al. (’07) Lattice study by QCDSF/UKQCD tDY data can provide an direct access to QCD corrections Transversely Polarized Drell-Yan （ｔ DY) process RHIC,J-PARC

3. bulk of dileptons produced at small Q T large perturbative corrections from gluon radiations make Q T the relevant scale  NLO double-spin asymmetries Martin, Schafer, Stratmann, Vogelsang(’99) “sea-quark region” is probed at the scale  double-spin asymmetries at a measured Kawamura, Kodaira, Tanaka, NPB777 (’07) 203 PTP 118 (’07) 581

4. Barone, Cafarella, Coriano, Guzzi, Ratcliffe (‘05) Shimizu, Sterman, Yokoya, Vogelsang (’05) directly probe the valence-quark transversity at GSI For Q T unobserved: Large asymmetries ～ 20-40% QCD corrections are rather small We consider the QCD corrections for Q T observed case “threshold resummation’’ at the NNL level Kawamura, Kodaira, Tanaka, arXiv:0801.0026 [hep-ph]

5. Next-to-leading logarithmic (NLL) resummation formula Process-indep.: Kodaira, Trentadue (’82) Davies, Stirling,Webber (’85) Collins, Soper, Sterman ( ‘85) Kawamura,Kodaira,Shimizu,Tanaka, PTP 115 (’06) 667

7. NLL resummation formula for spin-independent cross section from Altarelli, Ellis, Greco, Martinelli (’84); Collins, Soper, Sterman (’85) is universal ! Gluon distribution participates !

8. Gaussian smearing factor:

9. Transversity distribution μ-dep.: NLO DGLAP evolution Hayashigaki, Kanazawa, Koike (’97) Kumano, Miyama (’97) Vogelsang(’98) x-dep.: Vogelsang et al (’98) Input PDFs nucleon models, empirical fit

10. Shaded area : LO empirical fit Anselmino et al., PRD75 (’07) 054032

11. S = 210 GeV 2, Q = 4GeV, y=φ=0 NLL+LO: total (“NLL+Y’’) prediction @ GSI “Soffer bound PDF” flat behavior: universality of soft gluon effects @ J-PARC

12. Novel asymptotoic formula Saddle-point formula at the NLL level “degree 0 approximation’’ suggested by CSS (’85)

13. “very large prefactor” is universal ! gluon distribution decouples ! extension of LL-level saddle point formula by Parisi, Petronzio (’79) to NLL level

14. Most of soft gluon resummation effets cancel out “unconventional scale” a part of NLL-level resummation contribution survives

15. “Soffer bound PDF” @ GSI S = 210 GeV 2, y=φ=0

16. S = 80 GeV 2, y=φ=0

17. y=φ=0 S = 30 GeV 2 S = 45 GeV 2

18. φ=0 S = 45 GeV 2, y=0.3S = 210 GeV 2, y=0.5

21. Summary: DY at small Q T in QCD