1. Hiroyuki Kawamura (RIKEN) Transverse double-spin asymmetries for small Q T Drell-Yan pair production in pp and ppbar collisions Hiroyuki Kawamura (RIKEN) Jiro Kodaira (KEK) Kazuhiro Tanaka (Juntendo Univ.) 2006 Apr. 21 DIS2006 in Tsukuba

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

3. Hiroyuki Kawamura (RIKEN)  Double spin asymmetry : A TT in tDY Q T spectrum of dimuon — 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)  More information from Q T spectrum of dimuon → We calculated spin dep. part of Q T distribution at O(α ｓ ) ♣ fixed order result : incorrect at small Q T → Q T resummation― recoil logs Shimizu, Sterman, Yokoya, Vogelsang (’05) (calculation in D-dim. : cumbersome due to φ dependence)

4. Hiroyuki Kawamura (RIKEN) Q T resummation Next-to-leading logarithmic (NLL) resummation in tDY : Collins, Soper ’81 Collins, Soper, Sterman ‘85 b : impact parameter H.K, Kodaira, Shimizu, Tanaka : hep-ph/0512137  universal Sudakov factor Catani et al. ‘01 coeff. function

5. Hiroyuki Kawamura (RIKEN) finite at Q T = 0

6. Hiroyuki Kawamura (RIKEN) contour deformation 1. b-integration — integration in complex b plane b bLbL C1C1 C2C2 Kulesza, et al. ’02 reproduce the fixed order results by expansion  Prescription for extremely large b-region Landau pole : 2. Non-perturbative effects simplest form : “intrinsic k T ” More on resummation

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

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

9. Hiroyuki Kawamura (RIKEN) g NP = 0.3, 0.5, 0.8GeV 2 pp collision @ RHIC  s = 200 GeV, Q = 8 GeV, y=2, φ=0 Q T spectrum ↔ = 0.7, 0.9, 1.1 GeV pol. unpol.

10. Hiroyuki Kawamura (RIKEN) Double spin asymmetry pp collision @ RHIC  s = 200 GeV, Q = 8 GeV, y=2, φ=0 A TT : 5-6% in small Q T region small g NP dependence flat in small Q T region larger A TT for larger Q Q=15GeV Q= 8GeV Q= 3GeV Q= 5GeV Q = 3 - 15GeV, g NP = 0.3, 0.5, 0.8GeV 2 g NP = 0.5GeV 2 suppressed at small x (due to evolution)

11. Hiroyuki Kawamura (RIKEN) Double spin asymmetry pp collision @ JPARC A TT  15% ↔ pdf at large x A TT can be even 30% ↔ valence polarization large x very small g NP dependence  s = 10 GeV, Q = 3 GeV, y=0, φ=0 g NP = 0.3, 0.5, 0.8GeV 2 ppbar collision @GSI  s = 14.5 GeV, Q = 2-6 GeV, y=0, φ=0 g NP = 0.3, 0.5, 0.8GeV 2 Q=2GeV Q=3GeV Q=4GeV Q=6GeV

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