Factorization and Resummation of Small x Scaling Violations with Running Coupling

Abstract

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.

30 pages, 8 figures, plain TeX with harvmac

References in corpus (5)

• Resummation of Singlet Parton Evolution at Small x
• On factorisation at small x
• Small-x Resummation and HERA Structure Function Data
• Explicit Calculation Of the Running Coupling BFKL Anomalous Dimension
• The Small x Behaviour of Altarelli-Parisi Splitting Functions

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