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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.

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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