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 β-function and running coupling to the MS¯ scheme up to 4-loop order in general covariant gauges. We also demonstrate, by considering a selection of Nf=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¯ coupling version of this series in terms of the MiniMOM coupling, making the MiniMOM coupling also of potential interest in certain phenomenological applications.