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 ${\beta }_0$-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.

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

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• Hunting BFKL in semi-hard reactions at the LHC
• Stability of Azimuthal-angle Observables under Higher Order Corrections in Inclusive Three-jet Production
• Evaluating the double parton scattering contribution to Mueller-Navelet jets production at the LHC
• High-energy resummation in heavy-quark pair photoproduction
• Diffractive production of $\Lambda$ hyperons in the high-energy limit of strong interactions
• Inclusive three- and four-jet production in multi-Regge kinematics at the LHC
• Mueller-Navelet jets at LHC: BFKL versus high-energy DGLAP
• The ${\gamma }^{\ast }{\gamma }^{\ast }$ total cross section in next-to-leading order BFKL and LEP2 data
• High energy effects in multi-jet production at LHC
• Multi-jet production in the high energy limit at LHC
• High-energy effects in forward inclusive dijet and hadron-jet production
• From semi-hard processes to the unintegrated gluon distribution: a phenomenological path in the high-energy framework
• Semihard processes with BLM renormalization scale setting
• The ${\gamma }^{\ast }{\gamma }^{\ast }$ total cross section in NLA BFKL