On the BLM optimal renormalization scale setting for semihard processes

Abstract

The BFKL approach for the investigation of semihard processes is plagued by large next-to-leading corrections, both in the kernel of the universal BFKL Green's function and in the process-dependent impact factors, as well as by large uncertainties in the renormalization scale setting. All that calls for some optimization procedure of the perturbative series. In this respect, one of the most common methods is the Brodsky-Lepage-Mackenzie (BLM) one, that eliminates the renormalization scale ambiguity by absorbing the non-conformal $β_0$-terms into the running coupling. In this paper, we apply BLM scale setting procedure directly to the amplitudes (cross sections) of several semihard processes. We show that, due to the presence of $β_0$-terms in the next-to-leading expressions for the impact factors, the optimal renormalization scale is not universal, but depends both on the energy and on the type of process in question.

21 pages, 4 figures; added a few sentences and two references in the Summary section; version accepted for publication by Phys. Rev. D