Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2012-04-12
Physics
High Energy Physics
High Energy Physics - Phenomenology
23 pages, 6 figures. Eqs. (10a) and (10b) corrected; clarifications about "Bar" notations at the beginning of Sect. 3 added
Scientific paper
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.
Bakulev Alexander P.
Khandramai Vyacheslav L.
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