On the BLM optimal renormalization scale setting for semihard processes

TL;DR

This paper applies the BLM scale setting procedure to semihard process amplitudes within the BFKL framework, revealing that the optimal renormalization scale varies with energy and process type due to impact factor corrections.

Contribution

It demonstrates the direct application of BLM scale setting to process amplitudes and highlights the non-universality of the optimal scale in semihard processes.

Findings

Optimal renormalization scale depends on energy and process type.

BLM procedure applied directly to amplitudes clarifies scale setting.

Impact factors influence the non-universality of the scale.

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 $\beta_0$-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 $\beta_0$-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.