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 $\mathcal{D}(Q^2)$ 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 $|Q^2|\sim 1{\mathrm{GeV}}^2$.

v3: 35 pp., 7 figs.; improved programs which work in Mathematica 9 and 10; improved presentation of the text (Sec.2 shorter, Sec.4 enlarged); to appear in Computer Physics Communications

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