Soft gluon resummation in transversely polarized DrellYan process

Soft gluon resummation in transversely polarized Drell-Yan process at small transverse momentum ― double-spin asymmetries and novel asymptotic formula ― Kazuhiro Tanaka (Juntendo U) H. Kawamura (RIKEN) J. Kodaira (KEK) NPB 777 (’ 07) 203 and more

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

Ø NLO double-spin asymmetries Martin, Schafer, Stratmann, Vogelsang(’ 99) “sea-quark region” is probed at the scale Ø double-spin asymmetries at a measured • bulk of dileptons produced at small QT • large perturbative corrections from gluon radiations make QT the relevant scale

t. DY KLN cancellation transversity

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 Laenen, Sterman, Vogelsang (’ 00) Kulesza, Sterman, Vogelsang (’ 02) cut-off at bmax ： Collins, Soper, Sterman (’ 82)

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

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

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

Dilepton QT spectrum in t. DY Kawamura, Kodaira, Shimizu, Tanaka (’ 06) pp collision @ RHIC s = 200 Ge. V, Q = 5 Ge. V, 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 collision @ J-PARC s = 10 Ge. V, y=0, φ=0 flat behavir due to universal soft gluon effects enhancement mechanism from nonuniversal NLL effects larger asymmetries than the RHIC case moderate-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 a part of NLL-level contribution survives unconventional scale associated with saddle point, instead of Clearly demonstrates the enhancement mechanism observed in numerical study NNLL corrections would grow at small-x region probed by RHIC. Useful for direct comparison with experiment

directly probe the valence-quark transversity at GSI For QT unobserved: Barone, Cafarella, Coriano, Guzzi, Ratcliffe (‘ 05) “threshold resummation’’ at the NNL level Shimizu, Sterman, Yokoya, Vogelsang (’ 05) Large asymmetries ～ 20 -40% QCD corrections are rather small We consider the QCD corrections for QT observed case

@ GSI s = 14. 5 Ge. V, y=0, φ=0 flat behavir due to universal soft gluon effects larger asymmetries than RHIC and J-PARC case enhancement mechanism is not significant “valence region”

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

Summary: Transversely Polarized DY at small QT in QCD