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

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 (MS) over bar 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 (MS) over bar coupling version of this series in terms of the MiniMOM coupling, making the MiniMOM coupling also of potential interest in certain phenomenological applications. (C) 2009 Elsevier B.V. All rights reserved.