Testing saturation with diffractive jet production in DIS

Cyrille MarquetSPhT, Saclay

Elastic and Diffractive Scattering 2005, Blois, France

based on hep-ph/0504214to be published in Phys. Rev. D

In collaboration with Krzysztof Golec-Biernat

Contents

• Introductionthe QCD dipole picture in high-energy scattering

• Diffractive gluon production in DISat high energies and at leading logarithmic accuracy

• Diffractive photon dissociationstrongly sensitive to unitarity effects and saturation

• Conclusion and outlook

Introduction

High-energy scattering

r: transverse size of the dipole

b: impact parameter

z: longitudinal momentum fraction of the quark

qqzrrdzbdd )Q,,( 222*

2* pSfd f

Fundamental quantity : Tqq(r, b, Y) the imaginary part of the forward scattering amplitude of the dipole

does not depend on z in the high-energy limit

2

22 )Q,,()Q,( zrdzr

Y: total rapidity

• In DIS:

• In DDIS:

DVCS, vector mesons, …

• Other observables have been expressed in terms of dipole scattering amplitude: jet cross-sections, heavy-quark production, di-lepton production…

Observables at high energies

2222 );,()Q,( YbrTrrdbd qqelas

);,()Q,( 222 YbrTbdrrd qqDIS

The same dipoles amplitudes Tqq, Tgg,Tqqg… enter in the formulation of any cross-section

Y: total rapidity

Diffractive gluon production in DIS

C. M., Nucl. Phys. B 705 (2005) 319

Diffractive 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

)( 02 rkdyd

d

x0: transverse position of the quark

x1: transverse position of the antiquark

y: rapidity of the gluon

k: transverse momentum of the gluon

Outline of the derivation

...00 gqqqqqq

physin

tS inout

The incoming state is

The outgoing state is 21

12

0

0

)()( zxzx

zxzx

target z: transverse position of the gluon

tgqqStqqStgqqS qqphysqqgqqout 00

emission before interaction

emission after interaction

elastic contribution

outdiff Ptt sing

one has also to project the outgoing state on the color singlet states:

Final result

),,().,,()( 0*

02

402 2

2

kbrAkbrA bdrkdyd

dF

c

C

Nsdiff

diffdiffdiff ykaykar

kdydd ),(),()( 02

one obtains

• Sqq(x, y; ) the forward scattering amplitude of a qq dipole on the target

• Sqq(x, z; z, y; ) the forward scattering amplitude of two qq dipoles on the target

(2)

expressed in terms of:

);,();,;,()()(2

),,( 1010)2(

21

12

0

0.2

0

xxxzzx

zxzx

zxzxkbrA zk

qqqqi SSe

zdwith the amplitude

rapidity gap

r0= x0-x1 b = (x0+x1)/2

Diffractive photon dissociation

Diffractive photon dissociation

y = log(1/) = log(MX2/Q2) <<1

)()Q,(202

200

22 r

kdydd

rrdMkddM

d diff

XX

dissoc

• This is the dominant contribution to the diffractive cross-section diff at large MX in DIS:

elas: involves the qq dipole fluctuation, dominant for small-mass final states dissoc: involves higher Fock state fluctuations: qqg, …dominant for large-mass final states

dissocelasdiff

= log(1/xpom) xpom<<1

target

proton

Analytical insight

• Independently of the precise form of the S-matrices

421kkddM

dX

dissoc

);,();,;,()()(2

),,( 1010)2(

21

12

0

0.2

0

xxxzzx

zxzx

zxzxkbrA zk

qqqqi SSe

zd

cste),,( 0 kbrA

201),,(k

kbrA

as k goes to zero

as k goes to infinity

• Example with a saturation model for the S-matrices

cstekddM

dX

dissoc 2

Behaviour of the cross-section as a function of k

• 1/k0: typical size at which the S-matrices are cut off

observable strongly sensitive to unitarity effects

0 k

modeldependent

kddMdk

X

dissoc2

2

k²

1/k²

modelindependent

modelindependent

k0

we studied this

cross-section in the

framework of

saturation theory

GBW parametrization of the S-matrices

pSpqq RbbRS 4/x)(Qexp);x,x( 201

210

pSSpqq RbbRS 4/x)(Qexp4/x)(Qexp);x,x;x,x( 221

2202

21220

)2(

Rp: proton radius

1/QS: size at which the S-matrices start decreasing to zero

QS: saturation scale

Scales of the problem: QS, Q², k

• This model was successful in fitting the ZEUS data forwith one free parameter: s=0.15

XdMd

Munier and Shoshi (2004)

Plots of kddMdk

X

dissoc2

2

marked bump for k = kmax

Can we experimentally test this? extract QS?

kmax/QS = independent of Q², QS 1.5

• with MX2 >> Q2 has been measured (ZEUS)

• What about ?

• The jet should also be close to the rapidity gap to be identifed with the gluon jet of our calculation (the softest particule in the final state)

• Important limitation: at HERA QS < 1 Gev and k > 3 Gev one does not have access to the whole bump

Experimental considerations

XdMd

kddMd

X 2

final state configuration: anything + jet + gap + proton

• Predictions of the model with

and the parameters , x0 and 0 taken from the F2 fits:

In the HERA energy range

2/0Gev.1)(Q

pompomS xxx

02 pR

= 0.288, x0 = 3.10-4 and 0 23 mbfor full lines (no charm)

= 0.277, x0 = 4.10-5 and 0 29 mbfor dashed lines (charm included)

Conclusion and outlook• In diffractive DIS at large mass, the dominant contribution to the cross-

section comes from the qqg part of the photon wavefunction dissociation of the photon

• We derived the diffractive photon dissociation cross-section photon + target X + gluon + gap + target expressed in terms of a one-dipole amplitude and a two-dipole amplitude

• As a function of the gluon transverse momentum, the cross-section is resonant with the scale at which unitarity effects become important observable with a great potential to study high-energy QCD

• Study using a saturation model for the dipole amplitudes, prediction for the HERA energy range strong potential for extracting QS and testing models