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

Abstract

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 <Q_s^2>, 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, 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 >> <Q_s^2>.

69 pages, 20 figures