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)