1. Testing saturation with diffractive jet production in DIS Cyrille Marquet SPhT, Saclay Elastic and Diffractive Scattering 2005, Blois, France based on hep-ph/0504214 to be published in Phys. Rev. D In collaboration with Krzysztof Golec-Biernat

2. 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

3. Introduction

4. 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

5. 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

6. Diffractive gluon production in DIS C. M., Nucl. Phys. B 705 (2005) 319

7. 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

8. 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:

9. 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

10. Diffractive photon dissociation

11. 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

12. 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

13. 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

14. 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)

15. 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

16. 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

17. 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 = 3.10 -4 and  0  23 mb for full lines (no charm) = 0.277, x 0 = 4.10 -5 and  0  29 mb for dashed lines (charm included)

18. 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