Brodsky-Lepage-Mackenzie optimal renormalization scale setting for semihard processes

The Balitsky-Fadin-Kuraev-Lipatov (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 an optimization procedure of the perturbative series. In this respect, one of the most common methods is the Brodsky-Lepage-Mackenzie (BLM) one, which eliminates the renormalization scale ambiguity by absorbing the nonconformal β0 terms into the running coupling. In this paper, we apply the BLM scale setting procedure directly to the amplitudes (cross sections) of several semihard processes. We show that, due to the presence of β0 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 questionD. I. thanks the Dipartimento di Fisica dell’Università della Calabria and the Istituto Nazionale di Fisica Nucleare (INFN), Gruppo collegato di Cosenza for the warm hospitality and financial support. The work of D. I. was also supported in part by the Russian Foundation for Basic Research via Grant No. RFBR-13-02-00695-a. The work of B. M. was supported by the European Commission, European Social Fund and Calabria Region, who disclaim any liability for any use made of the information provided in this paper. B. M. thanks the Sobolev Institute of Mathematics of Novosibirsk for warm hospitality during the preparation of this wor