Testing saturation with diffractive jet production in DIS Cyrille Marquet SPhT, Saclay Elastic and Diffractive Scattering 2005, Blois, France based on hep-ph/ to be published in Phys. Rev. D In collaboration with Krzysztof Golec-Biernat

Contents Introduction the QCD dipole picture in high-energy scattering Diffractive gluon production in DIS at high energies and at leading logarithmic accuracy Diffractive photon dissociation strongly 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 Fundamental quantity : T qq (r, b, Y) the imaginary part of the forward scattering amplitude of the dipole does not depend on z in the high-energy limit 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 The same dipoles amplitudes T qq, T gg,T qqg … 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 size r 0 = x 0 -x 1 Approximations:  leading log(1/x) for the emitted gluon (y = log(1/x))  the propagation through the target is eikonal x 0 : transverse position of the quark x 1 : transverse position of the antiquark y: rapidity of the gluon k: transverse momentum of the gluon

Outline of the derivation The incoming state is The outgoing state is target z: transverse position of the gluon emission before interaction emission after interaction elastic contribution one has also to project the outgoing state on the color singlet states:

Final result one obtains S qq (x, y;  ) the forward scattering amplitude of a qq dipole on the target S qq (x, z; z, y;  ) the forward scattering amplitude of two qq dipoles on the target (2) expressed in terms of: with the amplitude rapidity gap r 0 = x 0 -x 1 b = (x 0 +x 1 )/2

Diffractive photon dissociation

y = log(1/  ) = log(M X 2 /Q 2 )  <<1 This is the dominant contribution to the diffractive cross-section  diff at large M X 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  = log(1/x pom ) x pom <<1  target proton

Analytical insight Independently of the precise form of the S-matrices as k goes to zero as k goes to infinity Example with a saturation model for the S-matrices

Behaviour of the cross-section as a function of k 1/k 0 : typical size at which the S-matrices are cut off  observable strongly sensitive to unitarity effects 0 k model dependent k²k² 1/k² model independent model independent k0k0 we studied this cross-section in the framework of saturation theory

GBW parametrization of the S-matrices R p : proton radius 1/Q S : size at which the S-matrices start decreasing to zero Q S : saturation scale Scales of the problem: Q S, Q², k This model was successful in fitting the ZEUS data for with one free parameter:  s=0.15 Munier and Shoshi (2004)

Plots of marked bump for k = k max Can we experimentally test this? extract Q S ? k max /Q S = independent of Q², Q S  1.5

with M X 2 >> Q 2 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 Q S 3 Gev  one does not have access to the whole bump Experimental considerations final state configuration: anything + jet + gap + proton

Predictions of the model with and the parameters, x 0 and  0 taken from the F 2 fits: In the HERA energy range = 0.288, x 0 = and  0  23 mb for full lines (no charm) = 0.277, x 0 = and  0  29 mb for 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 Q S and testing models