Diffusive scaling and the high-energy limit of deep inelastic scattering in QCD at large $N_c$

Y. Hatta , E. Iancu (1) , C. Marquet (1) , Gregory Soyez (1) , D.N. Triantafyllopoulos

1 SPhT - Service de Physique Théorique

Within the limits of the large--$N_c$ approximation (with $N_c$ the number of colors), we establish the high--energy behaviour of the diffractive and inclusive cross--sections for deep inelastic scattering at fixed impact parameter. We demonstrate that for sufficiently high energies and up to very large values of $Q^2$, well above the proton average saturation momentum $\langle Q_s^2\rangle$, the cross--sections are dominated by dense fluctuations in the target wavefunction, that is, by the relatively rare gluon configurations which are at saturation on the resolution scale $Q^2$ of the virtual photon. This has important physical consequences, like the emergence of a new, {\em diffusive}, scaling, which replaces the `geometric scaling' property characteristic of the mean field approximation. To establish this, we shall rely on a dipole version of the Good--Walker formula for diffraction (that we shall derive here in the context of DIS), together with the high--energy estimates for the dipole scattering amplitudes which follow from the recently established evolution equations with Pomeron loops and include the relevant fluctuations. We also find that, as a consequence of fluctuations, the diffractive cross--section at high energy is dominated by the elastic scattering of the quark--antiquark component of the virtual photon, up to relatively large virtualities $Q^2\gg \langle Q_s^2\rangle$.

Domaines: Physique Générale [physics.gen-ph]; Physique des Hautes Energies - Phénoménologie [hep-ph]

Y. Hatta, E. Iancu, C. Marquet, Gregory Soyez, D.N. Triantafyllopoulos. Diffusive scaling and the high-energy limit of deep inelastic scattering in QCD at large $N_c$. Nuclear Physics A, 2006, 773, pp.95-155. ⟨10.1016/j.nuclphysa.2006.04.003⟩. ⟨hal-00163663⟩