FAPT: a Mathematica package for calculations in QCD Fractional Analytic Perturbation Theory

Abstract

We provide here all the procedures in \texttt{Mathematica} which are needed for the computation of the analytic images of the strong coupling constant powers in Minkowski (${\bar{\mathfrak{A}}}_{\nu }(s;n_f)$ and ${\mathfrak{A}}_{\nu }^{\text{glob}}(s)$) and Euclidean (${\bar{\mathcal{A}}}_{\nu }(Q^2;n_f)$ and ${\mathcal{A}}_{\nu }^{\text{glob}}(Q^2)$) domains at arbitrary energy scales ($s$ and $Q^2$, correspondingly) for both schemes --- with fixed number of active flavours $n_f=3,4,5,6$ and the global one with taking into account all heavy-quark thresholds. These singularity-free couplings are inevitable elements of Analytic Perturbation Theory (APT) in QCD and its generalization --- Fractional APT, needed to apply the APT imperative for renormalization-group improved hadronic observables.

Comments: 23 pages, 6 figures. Citations added. Now it matches version approved for publication in Comp. Phys. Commun