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

Within the limits of the large- N approximation (with N 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, well above the proton average saturation momentum <Qs2>, 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 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≫<Qs2>.