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

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 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 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 coupling version of this series in terms of the MiniMOM coupling, making the MiniMOM coupling also of potential interest in certain phenomenological applications.

Determination of LambdaMS from the gluon and ghost propagators in Landau gauge

“…For this we use a renormalization scheme (Minimal MOM scheme in Landau gauge) that only requires lattice data for the gluon and ghost propagators in Landau gauge [4]. In this contribution we focused on a quantitative understanding of the hypercubic lattice artifacts at large momenta.…”

“…. , β 3 , can be found for general covariant gauges in [4]. Meanwhile this coupling has also been used by a French-Spanish collaboration [5] to estimate Λ (N f ) MS and a dimension-2 gluon condensate for different N f .…”

“…In Eq. (1.1), g 2 0 is the lattice coupling at lattice spacing a and the suffix MM refers to the Minimal MOM scheme, the underlying renormalization scheme of this coupling [4]. Note that α MM s (p) is defined also beyond Landau gauge.…”

Refining the detection of the zero crossing for the three-gluon vertex in symmetric and asymmetric momentum subtraction schemes

“…Other MOM schemes based on different QCD vertices and kinematical configurations, as that for the ghost-gluon vertex [62][63][64][65], lead to alternative nonperturbative definitions although they can be related at any order in perturbation theory [66,67] …”

QCD propagators and vertices from lattice QCD (in memory of Michael Müller-Preußker)

“…Besides this "lattice service work" for other scientific communities, calculating these n-point functions also provides access to the strong coupling and quark masses, i.e., the fundamental parameters of QCD. These can be obtained, for example, from the high-momentum dependence of quark, gluon and ghost propagators (see, e.g., [29][30][31][32][33]) or higher n-point functions. Also the chiral condensate ψ ψ can be determined in the massless limit (e.g., [31,34]).…”