Dilepton production near partonic threshold in transversely polarized p\bar{p} scatterings
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Transcript of Dilepton production near partonic threshold in transversely polarized p\bar{p} scatterings
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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)
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• Introduction• Polarized Antiproton experiments @
GSI
• QCD correction to the Drell-Yan
process
• Fixed order calculation
• Threshold resummation
• Far IR cut-off
• Numerical results
• Summary
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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
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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
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• Cross Section Formula
We report on studies of pQCD correction to the
Drell-Yan cross section for GSI p\bar{p}
kinematics
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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
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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
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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)
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• 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 :
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• Unpolarized cross section :
with GRV98 (NLO) PDFs
K-factor become order 101 (103) at the large M !!
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• 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
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Far-infrared cut-off dependence
K-factor :
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Double Spin Asymmetry :
Model of Transverse PDFs
→ upper limit of Soffer’s inequality with
GRV&GRSV
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• 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
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• 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)
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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%
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• 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
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Renormalization/Factorization scale dependence :
• truncation of perturbative series at nth order induces scale dependence (ambiguity) at n+1th order
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Renormalization/Factorization scale dependence :
see also pion production@GSI Mukherjee,Stratmann,Vogelsang (’05)
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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
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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)
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transparency taken from the talk of F.Rathmann in Spin 2004 (Trieste, ITALY)
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transparency taken from the talk of F.Rathmann in Spin 2004 (Trieste, ITALY)