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) $\mathcal{A}_{\nu}(Q^2)$, which are analytic analogs of the powers $a(Q^2)^{\nu}$ of the underlying perturbative QCD (pQCD) coupling $a(Q^2) \equiv \alpha_s(Q^2)/\pi$, in three analytic QCD models (anQCD): Fractional Analytic Perturbation Theory (FAPT), Two-delta analytic QCD (2$\delta$anQCD), and Massive Perturbation Theory (MPT). The analytic (holomorphic) running couplings $\mathcal{A}_{\nu}(Q^2)$, in contrast to the corresponding pQCD expressions $a(Q^2)^{\nu}$, 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 $|Q^2| \sim 1 \ {\rm GeV}^2$.