Dilepton production near partonic threshold in transversely polarized p\

bar{p} scatterings• H. Shimizu (Hiroshima U, KEK)

• G. Sterman (SUNY)

• W. Vogelsang (BNL, RBRC)

• H. Yokoya (Niigata U)

APS/JPS Joint Meeting @ Kapalua, Hawaii 2005.9.21

Phys.Rev.D71,114007,2005 (hep-ph/0503270)

• Introduction• Polarized Antiproton experiments @

GSI

• QCD correction to the Drell-Yan

process

• Fixed order calculation

• Threshold resummation

• Far IR cut-off

• Numerical results

• Summary

Polarized Antiproton Beam may be available at the proposed Proton – Anti-Proton experiments at GSI.

• Polarized Antiproton Beam @ GSI

• PAX experiment proposal

LoI, hep-ex/0412064,0505054

a) Asymmetric Collider Experiment :

b) Fixed Target Experiment :

polarized antiproton beam and polarized proton beam

polarized antiproton beam with polarized hydrogen gas target

Drell-Yan dilepton production :

measurement of double transverse spin asymmetry

→ measurement of the transversely polarized PDF :

twist-2 distribution functions, chiral-odd, no gluon function, no measurement so far (first indication by HERMES, first measurement by RHIC?)

advantage for the GSI experiments :

→ both valence quark contribution

→ large asymmetry is expected→ large x ～ 0.5 region will be probed

valence quark structure of trans. pol. nucleon

• Cross Section Formula

We report on studies of pQCD correction to the

Drell-Yan cross section for GSI p\bar{p}

kinematics

Altarelli,Ellis,Martinelli(’78,’79);Kubar-Andre’,Paige(’79);Harada,Kaneko,Sakai(’79)

Hamberg,van Neerven,Matsuura(’91,’02);van Neerven,Zijlstra(’92,’04)

Partonic Cross Section (unpolarized)

LO :

NLO :

NNLO :

Drell,Yan (’70)

LO NLO NNLO

Vogelsang,Weber(’93);Kamal(’96);Contogouris,Kamal,Merebashvili(‘94);Vogelsang(’98)

Partonic Cross Section (Trans. Polarized)

LO :

NLO :

NNLO :

Ralston,Soper (’79)

not calculated yet

LO NLO NNLO

Threshold Resummation

logarithmic correction, as remnant of IR singularity, become important

kth order

sum these terms up to all orders → Threshold Resummation giving Sudakov Exponent

Sterman(’87);Catani,Trentadue(’89)

• Mellin-moments space :

only soft gluon can be emitted (partonic threshold)

threshold logs

Sudakov Exponent :

(N → large)

• For the numerical evaluation, we employ “Minimal Prescription”Catani,Mangano,Nason,Trentadue(’96)

• no factorial growth• converge asymptotically• define the perturbative content from resummation formalism 　

LL NLL NNLL

• Integral in the exponent is evaluated as functions of

and re-arranged again as the series of alpha_s and lnN.

LL : NLL :

• Unpolarized cross section :

with GRV98 (NLO) PDFs

K-factor become order 101 (103) at the large M !!

• Far Infrared cut-off

soft-gluon resummation formula includes far-infrared region, where the perturbative treatment of QCD may not be justified.

simply cut-off the small kT region

our study

may be replaced by non-perturbative approach, power suppressed correction, etc

Far-infrared cut-off dependence

K-factor :

Double Spin Asymmetry :

Model of Transverse PDFs

→ upper limit of Soffer’s inequality with

GRV&GRSV

• dilepton production process :

double spin asymmetry → transversity distributions

fixed target experiment and/or asymmetric collider

valence quark distributions in valence region

• Polarized Anti-proton Beam may be available @ GSI

SUMMARY

PAX experiment proposal :

• QCD corrections to the Drell-Yan process at GSI

K-factor is very large, significant threshold logs enhancement,

far IR cut-off dependence is serious for fixed target case

• ATT ~ 30 % is stable under QCD corrections

• New report on the NNLL resummation

NNLL resummation is now available, since the historical calculation

of three-loop splitting functions by Moch,Vermaseren,Vogt (‘04)

Including

gives the resummation at NNLL accuracy

Vogt(‘01); Catani et al.(’03)

Good behavior ! : resummation is stable by including NNLL, even such a low energy collision cross section.

scale ambiguity is also reduced significantly.

NNLL resummation : unpolarized cross section :

effect is at most 15%

• 1st order exp.⇔NLO, 2nd order exp.⇔NNLO agree very well

• Convergency seems good, but need more higher order

term

• Re-expansion of resummed cross section by order by order of αs

Renormalization/Factorization scale dependence :

• truncation of perturbative series at nth order induces scale dependence (ambiguity) at n+1th order

Renormalization/Factorization scale dependence :

see also pion production@GSI Mukherjee,Stratmann,Vogelsang (’05)

CERN-WA39 Experiment (‘80)

Drell-Yan dimuon production by π-Tungsten scattering

GRV π-PDF, Isospin symmetry and no nuclear effects

Resummation results reproduce experimental data well

A hint of soft-gluon large enhancement

PDF rescaling : effective resummation scheme of PDF

we calculate Resummed Cross Section with “NLO” PDFs

→ possible double counting of higher-order enhancement

between partonic CS and PDF

PDF rescaling :

Sterman,Vogelsang(’99)

transparency taken from the talk of F.Rathmann in Spin 2004 (Trieste, ITALY)

transparency taken from the talk of F.Rathmann in Spin 2004 (Trieste, ITALY)