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Hiroyuki Kawamura (RIKEN) Jiro Kodaira (KEK) Kazuhiro Tanaka (Juntendo Univ.)

Transverse double-spin asymmetries for small Q T Drell-Yan pair production in pp and ppbar collisions. 2006 Apr. 21 DIS2006 in Tsukuba. Hiroyuki Kawamura (RIKEN) Jiro Kodaira (KEK) Kazuhiro Tanaka (Juntendo Univ.). Transeversly polarized DY process. at RHIC, JPARC, GSI ….

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Hiroyuki Kawamura (RIKEN) Jiro Kodaira (KEK) Kazuhiro Tanaka (Juntendo Univ.)

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  1. Transverse double-spin asymmetriesfor small QT Drell-Yanpair production in pp and ppbar collisions 2006 Apr. 21 DIS2006 in Tsukuba Hiroyuki Kawamura (RIKEN) Jiro Kodaira (KEK) Kazuhiro Tanaka(Juntendo Univ.)

  2. Transeversly polarized DY process at RHIC, JPARC, GSI … ♠ spin dependent part Ralston & Soper ‘79 • transversity : δq(x) — twist-2 pdf ↔ Soffer’s inequality Soffer ‘95 — chiral-odd : not measured in inclusive DIS → tDY, SIDIS, …

  3. QT spectrum of dimuon • Double spin asymmetry : ATT in tDY — small ( a few %) at RHIC : PP collider Martin,Shäfer,Stratmann,Vogelsang (’99) — can be very large at GSI : PP-bar collider Barone, Cafarella, Coriano, Guzzi, Ratcliffe (‘05) Shimizu, Sterman, Yokoya, Vogelsang (’05) • More information from QT spectrum of dimuon → We calculated spin dep. part of QT distribution at O(αｓ) (calculation in D-dim. : cumbersome due to φ dependence) ♣ fixed order result : incorrect at small QT ― recoil logs →QT resummation

  4. QT resummation Collins, Soper ’81 Collins, Soper, Sterman ‘85 Next-to-leading logarithmic (NLL) resummation in tDY : H.K, Kodaira, Shimizu, Tanaka : hep-ph/0512137 b : impact parameter Sudakov factor  universal Catani et al. ‘01 coeff. function

  5. finite at QT= 0

  6. More on resummation b C1 • Prescription for extremely large b-region bL C2 1. b-integration Landau pole : Kulesza, et al. ’02 contour deformation —integration in complex b plane • reproduce the fixed order results by expansion 2. Non-perturbative effects “intrinsic kT ” simplest form :

  7. Small b-region • remove unphysical singularity at b = 0 expS(b,Q) = 1 at b=0 “unitarity condition” Bozzi, Catani, De Florian, Grazzini, ’05 • Matching NLL resummation + LO without double counting : “NLL+LO” — uniform accuracy in the entire Q_T region

  8. Numerical results • INPUT : transversity Martin,Shäfer,Stratmann,Vogelsang (’99) δq(x) − a model saturating Soffer’s inequality at — GRV98 — GRSV01 + NLO DGLAP evolution Hayashigaki, Kanawzawa, Koike ’97 Kumano,Miyama ’97 Vogelsang ’98

  9. QT spectrum pol. pp collision @ RHIC s = 200 GeV, Q = 8 GeV, y=2, φ=0 gNP = 0.3, 0.5, 0.8GeV2 unpol. ↔ < kT >= 0.7, 0.9, 1.1 GeV

  10. Double spin asymmetry pp collision @ RHIC s = 200 GeV, Q = 8 GeV, y=2, φ=0 gNP = 0.3, 0.5, 0.8GeV2 • ATT : 5-6% in small QT region • small gNP dependence • flat in small QT region Q = 3 - 15GeV, gNP = 0.5GeV2 Q=15GeV • larger ATT for largerQ Q= 8GeV suppressed at small x (due to evolution) Q= 5GeV Q= 3GeV

  11. Double spin asymmetry pp collision @ JPARC s = 10 GeV, Q= 3 GeV, y=0, φ=0 gNP = 0.3, 0.5, 0.8GeV2 • ATT  15% ↔ pdf at large x ppbar collision @GSI s = 14.5 GeV, Q= 2-6 GeV, y=0, φ=0 gNP = 0.3, 0.5, 0.8GeV2 Q=6GeV Q=4GeV • ATT can be even30% • ↔ valence polarization • large x • very small gNP dependence Q=3GeV Q=2GeV

  12. Summary • We calculated QT spectrum of dimuon in tDY at O(αs) in MS-bar scheme. • Soft gluon effects are included by all order resummation — NLL QT resummation + LO → complete “NLL + LO” formula → uniform accuracy over entire range of QT (corrections are down by αs) • Double-spin asymmetry with transversity δq(x) satisfying Soffer inequality. — not sensitive to NP function (“intrinsic kT”) — flat in small QT region — large in low energy ppbar collision @GSI 15 ~ 30% (large-x, valence pdf )

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