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FAPT: A Mathematica package for calculations in QCD fractional analytic perturbation theory. (English) Zbl 1296.81123
Summary: We provide here all the procedures in Mathematica which are needed for the computation of the analytic images of the strong coupling constant powers in Minkowski \((\overline{\mathfrak{A}}_\nu(s;n_f))\) and \(\mathfrak{A}^{\mathrm{glob}}_\nu(s))\) and Euclidean \((\overline{\mathcal{A}}_\nu(Q^2;n_f)\) and \(\mathcal A^{\mathrm{glob}}(Q^2))\) 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, proposed in [D. V. Shirkov and I. L. Solovtsov, JINR Rapid Commun. 2 (76), 5–10 (1996); Phys. Rev. Lett. 79, 1209–1212 (1997)], [K. A. Milton and I. L. Solovtsov, Phys. Rev. D 55, 5295–5298 (1997)] and [I. L. Solovtsov and D. V. Shirkov, Phys. Lett. B 442, 344–348 (1998)], and its generalization – Fractional APT, suggested in [A. P. Bakulev et al., Phys. Rev. D 72, 074014 (2005), erratum ibid. 119908(E)], [A. P. Bakulev et al., Phys. Rev. D 72, 074015 (2005)] and [A. P. Bakulev et al., Phys. Rev. D 75, 056005 (2007), erratum ibid. 77, 079901(E) (2008)], needed to apply the APT imperative for renormalization-group improved hadronic observables.

MSC:
81V05 Strong interaction, including quantum chromodynamics
81T15 Perturbative methods of renormalization applied to problems in quantum field theory
81T17 Renormalization group methods applied to problems in quantum field theory
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