The strong coupling and its running to four loops in a minimal MOM scheme

TL;DR

This paper introduces the minimal MOM scheme for QCD, defining a new way to fix the strong coupling using gluon and ghost propagators, and calculates its four-loop beta-function, showing potential for improved perturbative convergence.

Contribution

It provides the explicit perturbative definition of the minimal MOM scheme and relates its beta-function to the MSbar scheme up to four loops, including practical examples.

Findings

The minimal MOM scheme can improve perturbative series convergence in some cases.

Explicit four-loop relation between minimal MOM and MSbar schemes is established.

Potential applications in phenomenology due to better series convergence.

Abstract

We introduce the minimal momentum subtraction (MiniMOM) scheme for QCD. Its definition allows the strong coupling to be fixed solely through a determination of the gluon and ghost propagators. In Landau gauge this scheme has been implicit in the early studies of these propagators, especially in relation to their non-perturbative behaviour in the infrared and the associated infrared fixed-point. Here we concentrate on its perturbative use. We give the explicit perturbative definition of the scheme and the relation of its beta-function and running coupling to the MSbar scheme up to 4-loop order in general covariant gauges. We also demonstrate, by considering a selection of N_f=3 examples, that the apparent convergence of the relevant perturbative series can in some (though not all) cases be significantly improved by re-expanding the MSbar coupling version of this series in terms of the MiniMOM coupling, making the MiniMOM coupling also of potential interest in certain phenomenological applications.