Soft gluon resummation in transversely polarized Drell-Yan process at small transverse momentum NPB777 (07) 203 and more double-spin asymmetries and novel asymptotic formula Kazuhiro Tanaka (Juntendo U) H. Kawamura (RIKEN) J. Kodaira (KEK)

Transversity Chiral-odd : unmeasurable in inclusive DIS First global fit (LO): SIDIS at HERMES, COMPASS + Collins function from BELLE Anselminos talk Lattice study by QCDSF/UKQCD tDY data can provide an direct access to QCD corrections Transversely Polarized Drell-Yan DY) process RHIC,J-PARC,GSI

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

tD Y transversity KLN cancellation

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

All-order resummation IR Landau pole Contour deformation Contour deformation Laenen, Sterman, Vogelsang (00) Kulesza, Sterman, Vogelsang (02) Landau pole cut-off at b max Collins,Soper,Sterman (82)

Elaboration of resummation formalism systematic reorganization of the resummed series in the b-space LL NLL NNLL all-order resummation is accomplished at the ``partonic level Bozzi, Catani, de Florian, Glazzini (06) NNLL corrections are down by α s uniform accuracy classified by α s !

NLL resummation formula for spin-independent cross section from Altarelli, Ellis, Greco, Martinelli (84); Collins, Soper, Sterman (85) is universal ! same contour deformation for the b-integration same elaborations in terms of Gluon distributionparticipates !

Transversity distribution μ-dep.: NLO DGLAP evolution Hayashigaki, Kanazawa, Koike (97) Kumano, Miyama (97) Vogelsang(98) Soffer (95) x-dep.: Vogelsang et al (98) Nonperturbative inputs Gaussian smearing factor:

Dilepton Q T spectrum in tDY Kawamura, Kodaira, Shimizu, Tanaka (06) pp RHIC s = 200 GeV, Q = 5GeV, y=2, φ=0 NLL+LO: total (NLL+Y) prediction

Kawamura, Kodaira, Tanaka (07) flat behavior: universality of soft gluon effects nonuniversal contribution at NLL enhances

@ RHIC (y=2, φ=0)

pp J-PARC s = 10 GeV, y=0, φ=0 flat behavir due to universal soft gluon effects enhancement mechanism from nonuniversal NLL effects larger asymmetries than the RHIC casemoderate-x region

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

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

Most of soft gluon resummation effets cancel out unconventional scale associated with saddle point, instead of NNLL corrections would grow at small-x region probed by RHIC. Useful for direct comparison with experiment Clearly demonstrates the enhancement mechanism observed in numerical study a part of NLL-level contribution survives

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

@ GSI s = 14.5 GeV, y=0, φ=0 larger asymmetries than RHIC and J-PARC case flat behavir due to universal soft gluon effects valence region enhancement mechanism is not significant

unconventional scale NNLL corrections are small Useful for direct comparison with experiment does not cause siginificant modification in the valence region probed by GSI

Summary: Transversely Polarized DY at small Q T in QCD