1. Hiroyuki Kawamura (RIKEN) QCD Prediction of A TT for Small Q T Dimuon Production in pp and ppbar Collisions Hiroyuki Kawamura (RIKEN) Jiro Kodaira (KEK) ** Kazuhiro Tanaka (Juntendo Univ.) 2006 Oct. 5 SPIN2006 in Kyoto ** passed away on Sep.16.

2. Hiroyuki Kawamura (RIKEN) Transeversly polarized DY process  Transversity : δq(x) — twist-2 pdf ♠ Spin dependent part tDY : no fragmentation function Ralston & Soper ‘79 at RHIC, J-PARC, GSI, …

3. Hiroyuki Kawamura (RIKEN)  Double spin asymmetry : A TT in tDY Q T spectrum of dimuon — small 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) in each order of perturbation

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 ‘06  universal Sudakov factor Catani et al. ‘01 coeff. function Kodaira, Trentadue ‘81 large logs

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, Sterman,Vogelsang ’02 reproduce the fixed order results order by order  Prescription for extremely large b-region Landau pole : 2. Non-perturbative effects Gaussian : ~ 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 normalization  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 study δq(x) − a model saturating Soffer bound at  INPUT : transversity — GRV98 — GRSV2000 + 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 : 6% in small Q T region g NP dependences cancel flat in small Q T region larger A TT for larger Q y dependence is small Q=15GeV Q= 8GeV Q= 3GeV Q= 5GeV Q = 3 - 15GeV, y = 0,1,2 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 @ J-PARC A TT  15% ↔ pdf at large x  s = 10 GeV, Q = 2,3,4 GeV, y=0, φ=0  s = 10 GeV, Q = 2,3,4 GeV, y=0.5, φ=0 A TT  15-20% g NP = 0.5GeV 2

12. Hiroyuki Kawamura (RIKEN) Double spin asymmetry A TT can be 30% ↔ valence polarization large x very small g NP dependence ppbar collision @GSI  s = 14.5 GeV, Q = 2-6 GeV, y = 0, 0.5, 1,φ=0 Q=2GeV Q=3GeV Q=4GeV Q=6GeV

13. 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 resummed at NLL level. — complete QCD predictions at “NLL + LO” → uniform accuracy over entire range of Q T  A TT was estimated with a model transversity δq(x) — flat in small Q T region — larger A TT for larger Q — y dependence is small — can be large for ppbar collision at moderate energy @GSI 15 ~ 30% (large-x, valence pdf )