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QCD Prediction of A TT for small Q T dimuon production in pp and ppbar collisions

QCD Prediction of A TT for small Q T dimuon production in pp and ppbar collisions. 2006 Sep. 29 RSC2006 in RIKEN. Hiroyuki Kawamura (RIKEN) Jiro Kodaira (KEK) Kazuhiro Tanaka (Juntendo Univ.). Spin Physics. Bj. sum rule anomaly in g1 twist-3 operators in g2 J/ ψ production at RHIC

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QCD Prediction of A TT for small Q T dimuon production in pp and ppbar collisions

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  1. QCD Prediction of ATTfor small QT dimuon production in pp and ppbar collisions 2006 Sep. 29 RSC2006 in RIKEN Hiroyuki Kawamura (RIKEN) Jiro Kodaira (KEK) Kazuhiro Tanaka (Juntendo Univ.)

  2. Spin Physics • Bj. sum rule • anomaly in g1 • twist-3 operators in g2 • J/ψ production at RHIC • etc. Jiro Kodaira (1951-2006.09.16) Special session on Wednesday in Kyoto

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

  4. QT spectrum of dimuon • Double spin asymmetry : ATT in tDY — 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) 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

  5. QT resummation Collins, Soper ’81 Collins, Soper, Sterman ‘85 Next-to-leading logarithmic (NLL) resummation in tDY : H.K, Kodaira, Shimizu, Tanaka ‘06 b : impact parameter Sudakov factor Kodaira, Trentadue ‘81  universal Catani et al. ‘01 coeff. function

  6. finite at QT= 0

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

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

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

  10. 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

  11. Double spin asymmetry pp collision @ RHIC s = 200 GeV, Q = 8 GeV, y=2, φ=0 gNP = 0.3, 0.5, 0.8GeV2 • ATT : 6% in small QT region • gNP dependences cancel • flat in small QT region Q = 3 - 15GeV, y = 0,1,2 gNP = 0.5GeV2 Q=15GeV • larger ATT for largerQ • y dependence is small Q= 8GeV suppressed at small x (due to evolution) Q= 5GeV Q= 3GeV

  12. Double spin asymmetry pp collision @ J-PARC s = 10 GeV, Q= 2,3,4 GeV, y=0, φ=0 • ATT  15% ↔ pdf at large x s = 10 GeV, Q= 2,3,4 GeV, y=0.5, φ=0 • ATT  15-20%

  13. Double spin asymmetry ppbar collision @GSI s = 14.5 GeV, Q= 2-6 GeV, y = 0, 0.5, 1,φ=0 • ATT can be 30% • ↔ valence polarization • large x • very small gNP dependence Q=6GeV Q=4GeV Q=3GeV Q=2GeV

  14. 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 — small y dependence — large in low energy ppbar collision @GSI 15 ~ 30% (large-x, valence pdf )

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