anQCD: a Mathematica package for calculations in general analytic QCD models

Abstract

We provide a Mathematica package that evaluates the QCD analytic couplings (in the Euclidean domain) $\mathcal{A}_ν(Q^2)$, which are analytic analogs of the powers $a(Q^2)^ν$ of the underlying perturbative QCD (pQCD) coupling $a(Q^2) \equiv α_s(Q^2)/π$, in three analytic QCD models (anQCD): Fractional Analytic Perturbation Theory (FAPT), Two-delta analytic QCD (2$δ$anQCD), and Massive Perturbation Theory (MPT). The analytic (holomorphic) running couplings $\mathcal{A}_ν(Q^2)$, in contrast to the corresponding pQCD expressions $a(Q^2)^ν$, reflect correctly the analytic properties of the spacelike observables ${\cal D}(Q^2)$ in the complex $Q^2$ plane as dictated by the general principles of quantum field theory. They are thus more suited for evaluations of such physical quantities, especially at low momenta $|Q^2| \sim 1 \ {\rm GeV}^2$.