Factorization and Resummation of Small x Scaling Violations with Running Coupling

We discuss the inclusion of running coupling effects in perturbative small x evolution equations. We show that a running coupling BFKL-like x-evolution equation is fully compatible, up to higher twist corrections, with the standard factorized perturbative evolution of parton distributions. We then use this result, combined with the well-known Airy asymptotics, to prove that the oscillations which are present in the running-coupling BFKL solution do not affect the associated splitting functions, which instead remain smooth in the small x limit. This allows us to give a prescription to include running-coupling corrections in the small-x resummation of scaling violations. We show that these corrections are small in the HERA region.