Saturation and forward jets

Saturation and forward jets

Cyrille MarquetSPhT, Saclay

Low-x meeting, Prague, 2004

Contents

• Introductionfixed-scale evolution and saturation

• Forward-gluon production in terms of dipolesin the eikonal approximation and at leading log(1/x) accuracy

• Fit to the HERA forward-jet datausing a GBW parametrization

• Mueller-Navelet jetspredictions for the Tevatron and LHC

• Conclusion and outlook

Introduction

*-* total cross-section: ** Xsuitable to test fixed-scale evolution BFKL prediction:

• How does saturation set in?What is the saturation scale?

*-* scattering

)exp(),Q,Q( 21 BFKL

• High-energy behavior:determined by dipole-dipole scattering

• Tîmneanu, Kwiecinski and Motyka (2002) Kozlov and Levin (2003)

),,( 21 rrdd

Forward-jet production

)exp(),Q,k( T BFKL

• p+* jet+XQ, kT » QCD exp()» 1

• Same kind of process than *-* but more statisticsdata from H1 and ZEUS

• Are saturation effects sizable at HERA?

• What is the relation with the dipole-dipole scattering?

Forward-gluon production

C. M. hep-ph/0409023

Inclusive gluon production

• The cross-section is derived for an arbitrary target and for an incident dipole of sizer0= x0-x1

• Approximations: leading log(1/x) for the

emitted gluon (y = log(1/x)) the propagation through the

target is eikonal and described by the Wilson lines

)( 02 rkdyd

d

),(exp)( xATdxigPW aaS xx

An intermediate step

22

12

)2()1(

)2).(1(1

0,

)1().(

22

122

4402 )(

zxzx

zxzxzzk

ji

ji

ji

jiiCs ezdzdbdrkdyd

d F

• b=(x0+x1)/2 is the impact parameter

• Tgg(x, x’) is the forward scattering amplitude of a gluon dipole on the target:

),(),(),(),( 2112 zzxxzxzx ggjiggjggigg TTTT

tAA

cgg WWTr

NT ))()'((

111)',( 2 xxxx

• Doing the calculation in coordinate space, one obtains:

see also Kovchegov and Tuchin PRD 65 (2002) 074026 for a target nucleus

Final result

)(),,(2)( )(02

202 rkrrdrkCr

kdydd

tggFs

(gg)t(z) is the dipole(gg)-target total cross-section a dipole factorized form for the gluon-production cross-section

• An alternative to write the cross-section:

)()()/log()(2

)()(),,,( 220000

2

100 rrkrJrrkrJkkrJrkrrkzr

)()/log()(2)( )(000202

0

rr

rr

rrkrJdrkCr

kdydd

tgg

rFs

Gluon-production from an incident hadron

• gh is the gluon density inside the incident hadron

is the factorization scale and xJ = exp(-y)

)()(),(21

)(02

22r

rr

rkrJdrxg

kkdxdd

tggJhJ

XJth

evolutionbefore theemission

collinearlimit r0»1

Fitting the HERA data

In collaboration with R. Peschanski and C. Royonhep-ph/0407011, to appear in PLB

The forward-jet cross-section

• x, y, Q2 : usual kinematic variables of DIS

• xJ , k : longitudinal and transverse momentum of the jet

= log(xJ /x) : rapidity interval

22)1(

dkd

dkdy LT

),,(2

)()Q,( 21)(2

222

202

21,2

21

22, rr

rr

rrkrJrrdrd

dkd

dggLTLT

2

2

22

2

22 2Q2),(

Q dkdy

xkkxg

dkdxdxdd TJp

J

with the hard cross-section given by

The saturation model

)(4exp1),,( 20

2021)( Rrrr effdgg

• An extension of the GBW model Tîmneanu, Kwiecinski and Motyka (2002)

with

• The saturation radius is

we fit the parameters , 0 and a normalization

)(2

expQ1)( 0

00 R

)ln(122 rrrreff

),max(),min( 2121 rrrrrr

Q0 1 GeV

fit (/dof )

sat. 0.402 -0.82 6.8 (/11)

weak sat. 0.370 8.23 8.3 (/11)

Results of the fits

• The first solution corresponds to significant saturation effects

• The second solution corresponds to weak saturation effects

• The intercept is in both cases higher than what was found for F2 (GBW = 0.288)

The saturation fit

The saturation scales

• The saturation scale is QS 1/R0()

• The plot represents

• The weak saturation solution is compatible with the F2

parametrization

• The other solution shows a harder saturation scale

)()/QQlog( 020

2S

Mueller-Navelet jets

C. M., R. Peschanski, PLB587 (2004) 201

C. M., R. Peschanski and C. Royon, hep-ph/0407011, to appear in PLB

Mueller-Navelet jets

• p+p jet+X+jet :Q1, Q2 » QCD exp()» 1

• Can one reach saturation in these processes? at the Tevatron or LHC ?

• The cross-section is

),,()Q()Q(QQ 21))((2211112121 rrrJrJdrdr gggg

)Q,()Q,( 222

211

21xgxg

dxdxd

pp

Predictions for the LHC

)(

)()Q,Q(

21

2121/

j

i

ji

dxdxd

dxdxd

R

• The plot shows R 8/2 for Q1=Q2kT and the GBW parametrization

• The two saturation solutions give different predictions this measurement at the LHC would distinguish between the two solutions

a ratio studied to test the BFKL evolution at the Tevatron (DØ collaboration, 1999)

a suitable observable:

• Derivation of the cross-section dipole + target forward gluon + X introduction of a dipole formalism for the description of forward-jet emissions

• Studies of saturation effects in forward jets at HERA using a GBW parametrization two solutions for the saturation scale: weak or significant saturation

• Mueller-Navelet jets at Tevatron or LHC could distinguish between both solutions

• Is the saturation scale universal?

Conclusion and outlook