Download - QCD corrections to the dilepton production near partonic threshold in pp and ppbar collisions
QCD corrections to the dilepton production near partonic threshold in pp and ppbar collisions
• H. Shimizu (Hiroshima U, KEK)
• G. Sterman (SUNY)
• W. Vogelsang (BNL, RBRC)
• H. Yokoya (Niigata U)
J-PARC Workshop @ KEK, JAPAN Nov.30- Dec.2, 2005
ref. Phys.Rev.D71,114007,2005 (hep-ph/0503270)
Introduction
Drell-Yan process :
: parton distribution functions
: partonic cross section ← perturbatively calculable
• Asymmetry (Ratio)
Target (beam) polarization :single spin asymmetry → twist-3, intrinsic-kT
double spin asymmetry → twist-2 pol. PDFs
Nuclear dependence : → nuclear effects
• Cross section
: qT-distribution → (hard) gluon radiations
: mass distribution
: rapidity distribution
see next talk by H.Kawamura
→ x1,x2 distributions
→ simplest and basic
Observables
Measurements of DY at J-PARC (GSI) gives :
• new information of the PDFs :flavor structure, nuclear effects,
polarized PDFs,,,
• precise confirmation of the pQCD predictions :
scaling violation (i.e. evolution),
qT-distribution, absolute cross section,,,
• indication of the NP corrections (power-suppressed, ISI,,) :
ambiguity of PT, renormalon,,,
OPE cannot be applied to DY process
In this talk, I would examine a phenomenology of
the pQCD corrections to the DY X-sec.
order (how large?),
convergency and ambiguity
(fixed order calculation, threshold resummation,,)
• Keypoints :
• Factorization Theorem
Drell-Yan cross section formula
Status of DY higher order calculations
LO
LO : Drell,Yan (’70)
virtual : real:
LO NLO
Altarelli,Ellis,Martinelli(’78,’79);Kubar-Andre’,Paige(’79);Harada,Kaneko,Sakai(’79)
LO :
NLO :
Drell,Yan (’70)
qg :
Status of DY higher order calculations
LO NLO
Altarelli,Ellis,Martinelli(’78,’79);Kubar-Andre’,Paige(’79);Harada,Kaneko,Sakai(’79)
LO :
NLO :
Drell,Yan (’70)
Status of DY higher order calculations
Hamberg,van Neerven,Matsuura(’91,’02);Harlander, Kilgore(’02)Anastasiou,Dixon,Melnikov,Petriello(Rapidity,’04);
LO :
NLO :
NNLO :
LO NNLONLO
Status of DY higher order calculations
Altarelli,Ellis,Martinelli(’78,’79);Kubar-Andre’,Paige(’79);Harada,Kaneko,Sakai(’79)
Drell,Yan (’70)
LO :
NLO :
NNLO :
Status of DY higher order calculations
Status of DY higher order calculations
K-factor
NLO/LO
NNLO/LO
Large corrections come from the partonic threshold region (z~1)
real emission suppressed by the phase space restriction
imbalance occurs between real and virtual gluon corrections
→ only soft gluon can be emitted
→ soft gluon (eikonal) approximation
to treat these logs up to all orders
(after the cancellation of IR pole)
Threshold logs
Threshold resummation
Sterman(’87);Catani,Trentadue(’89)
• General Formula : Sudakov Exponent
• First, goto Mellin-moment space :
threshold log →
LL : NLL :
NNLL :
• NNLL : Moch,Vermaseren,Vogt(’04)
Threshold resummation
3-loop split. func. gives
Catani,Mangano,Nason,Trentadue(’96)• employ “Minimal Prescription” :
define the inverse Mellin contour as the left of the Landau pole
may not complete : NNLO PDFs (we use GRV(NLO)), precise determination of at NNLO
• collinear improvement : Kramer,Laenen,Spira(‘98),,,
universal collinear (non-soft) gluon →
Threshold resummation
LL : NLL :
NNLL :
Threshold resummation
LL : NLL :
NNLL :
not only the convergency of resummation accuracy (NnLL), but also the convergency of the power expansion of Sudakov exponent to
Convergency
note : “Minimal Prescription” defined so that PT has no factorial growth
power corr. should be added later if required phenomenologicaly
LL :
NLL+NLO :
NNLL+NNLO :
Matching to fixed order calc.
relevant for all phase space regions
qg sub-process contributions
Renormalization scale ambiguity
f.o.
resum.
Factorization scale ambiguity
f.o.
resum.
Summary
① pQCD corrections to DY process are given for the J-PARC energy
K= 3~10, good convergency, scale ambiguities are reduced
② Resummation is a powerful tool to know the insight of pQCD
corrections at very higher order, and also the structure of
factorizable hadronic interaction
③ Resummation also as a tool to find the hint of non-pert. effects
(analytically and/or phenomenologically),
and the connection between pert. and non-pert. regime
Collinear improvement
Taking into account the universal collinear (non-soft) gluon radiation
Kramer,Laenen,Spira(‘98);Catani,de Florian,Grazzini(‘02); Kulesza,Sterman,Vogelsang(’02,’04)
• numerically sizable effects
• correctly re-produce the terms to all orders
• re-cover the full evolution kernel by
• re-arrange the exponent
Collinear improvement
Kramer,Laenen,Spira(‘98);Catani,de Florian,Grazzini(‘02); Kulesza,Sterman,Vogelsang(’02,’04)
1st order expansion ⇔ NLO
2nd order expansion ⇔ NNLO
soft-gluon resummation formula includes far infra-red region, where the perturbative treatment of QCD may not be justified.
may be replaced by non-perturbative approach, power suppressed correction, etc
Apply a explicit cut-off to avoid the double counting between pert. and non-pert.
we don’t know the NP pert yet, however, tentatively
it tells “ how much the far-IR region is
involved? ”
Far infra-red cut-off
Far infra-red cut-off
Far infra-red cut-off
Data in the past
McGaughey,Moss,Peng(’99)
Data consistent with NLO !
CERN-NA3,FNAL-E605,E772
FNAL-E772 (’90)
DATA / NLO ~ 0.641
W.J.Stirling,M.R.Whalley (’93)
FNAL-E772 (’90)
DATA consistent with LO (!?)
KNNLL = 3 ~ 5
CERN-WA39 experiment (‘80)
Drell-Yan dimuon production by π-Tungsten scattering
GRV π-PDF, isospin symmetry and no nuclear effects
NLL reproduce data best
Spin asymmetry
Model of Transverse PDFs → upper limit of Soffer’s inequality with GRV&GRSV
e.g.
GRV98(NLO)
Parton intensity :
Matching to fixed order calc.
note : differences only come from the parton intensity
PDF rescaling : effective resummation scheme
Resummed Cross Section with NLO PDFs
→ possible double counting of higher-order enhancement between
partonic CS and PDF
PDF rescaling : effective resummation scheme
Sterman,Vogelsang(’99)