Semihard processes with BLM renormalization scale setting

TL;DR

This paper applies the BLM scale setting to semihard processes, revealing that the optimal renormalization scale varies with energy and process due to $eta_0$-terms, affecting predictions in high-energy QCD.

Contribution

It demonstrates the process-dependent nature of the BLM scale in semihard QCD processes when applied directly to amplitudes.

Findings

Optimal renormalization scale depends on energy and process.

BLM scale setting affects predictions for high-energy scattering.

Process-specific variations observed in impact factors.

Abstract

We apply the BLM scale setting procedure directly to amplitudes (cross sections) of several semihard processes. It is shown that, due to the presence of $\beta_0$-terms in the NLA results for the impact factors, the obtained optimal renormalization scale is not universal, but depends both on the energy and on the process in question. We illustrate this general conclusion considering the following semihard processes: (i) inclusive production of two forward high-$p_T$ jets separated by large interval in rapidity (Mueller-Navelet jets); (ii) high-energy behavior of the total cross section for highly virtual photons; (iii) forward amplitude of the production of two light vector mesons in the collision of two virtual photons.