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 (${\bar{\mathfrak A}_ν(s;n_f)}$ and ${\mathfrak A_ν^\text{glob}(s)}$) and Euclidean (${\bar{\mathcal A}_ν(Q^2;n_f)}$ and ${\mathcal A_ν^\text{glob}(Q^2)}$) 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.