Diffusion corrections to the hard pomeron

The high energy behaviour of two-scale hard processes is investigated in th e framework of small-x models with running coupling, having the Airy diffus ion model as prototype. We show that, in some intermediate high energy regi me, the perturbative hard Pomeron exponent determines the energy dependence , and we prove that diffusion corrections have the form hinted at before in particular cases. We also discuss the breakdown of such regime at very lar ge energies, and the onset of the non-perturbative Pomeron behaviour. (C) 2 001 Published by Elsevier Science B.V.