hiroyuki kawamura (riken) qcd prediction of a tt for small q t dimuon production in pp and ppbar...
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Hiroyuki Kawamura (RIKEN)
QCD Prediction of ATT for small QT dimuon production
in pp and ppbar collisions
Hiroyuki Kawamura (RIKEN)Jiro Kodaira (KEK)Kazuhiro Tanaka (Juntendo Univ.)
2006 Sep. 29RSC2006 in RIKEN
Hiroyuki Kawamura (RIKEN)
Jiro Kodaira (1951-2006.09.16)
• Bj. sum rule• anomaly in g1• twist-3 operators in g2• J/ψ production at RHIC etc.
Special session on Wednesday in Kyoto
Spin Physics
Hiroyuki Kawamura (RIKEN)
p p l l X
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, …
Hiroyuki Kawamura (RIKEN)
Double spin asymmetry : ATT in tDY
QT 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 QT spectrum of dimuon
→ We calculated spin dep. part of QT distribution at O(α s )
♣ fixed order result : incorrect at small QT
→ QT resummation― recoil logs
Shimizu, Sterman, Yokoya, Vogelsang (’05)
(calculation in D-dim. : cumbersome due to φ dependence)
Hiroyuki Kawamura (RIKEN)
QT resummation
Next-to-leading logarithmic (NLL) resummation in tDY :
Collins, Soper ’81Collins, Soper, Sterman ‘85
b : impact parameter
H.K, Kodaira, Shimizu, Tanaka ‘06
universal
Sudakov factor
Catani et al. ‘01
coeff. function
Kodaira, Trentadue ‘81
Hiroyuki Kawamura (RIKEN)
contour deformation
1. b-integration
— integration in complex b plane
b
bL
C1
C2
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 kT ”
More on resummation
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
Hiroyuki Kawamura (RIKEN)
Numerical study
δq(x) a model saturating Soffer bound at−
INPUT : transversity
— GRV98
— GRSV01
+ NLO DGLAP evolution Hayashigaki, Kanawzawa, Koike ’97Kumano,Miyama ’97 Vogelsang ’98
Martin,Shäfer,Stratmann,Vogelsang (’99)
Hiroyuki Kawamura (RIKEN)
gNP = 0.3, 0.5, 0.8GeV2
pp collision @ RHIC
s = 200 GeV, Q = 8 GeV, y=2, φ=0
QT spectrum
↔ < kT > = 0.7, 0.9, 1.1 GeV
pol.
unpol.
Hiroyuki Kawamura (RIKEN)
Double spin asymmetry
pp collision @ RHIC
s = 200 GeV, Q = 8 GeV, y=2, φ=0
• ATT : 6% in small QT region• gNP dependences cancel • flat in small QT region
• larger ATT for larger Q
• y dependence is small
Q=15GeV
Q= 8GeV
Q= 3GeV
Q= 5GeV
Q = 3 - 15GeV, y = 0,1,2
gNP = 0.3, 0.5, 0.8GeV2
gNP = 0.5GeV2
suppressed at small x (due to evolution)
Hiroyuki Kawamura (RIKEN)
Double spin asymmetry
pp collision @ J-PARC
• ATT 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
• ATT 15-20%
Hiroyuki Kawamura (RIKEN)
Double spin asymmetry
• ATT can be 30% ↔ valence polarization large x• very small gNP 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
Hiroyuki Kawamura (RIKEN)
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 )