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)

finite at QT= 0

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 )