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

Abstract

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 (Āν(s;nf) and Aνglob(s)) and Euclidean (Āν(Q2;nf) and Aνglob(Q2)) domains at arbitrary energy scales (s and Q2, correspondingly) for both schemes — with fixed number of active flavours nf=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 [10,69,70], and its generalization — Fractional APT, suggested in [42,46,43], needed to apply the APT imperative for renormalization-group improved hadronic observables. Program summaryProgram title: FAPTCatalogue identifier: AENJ_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENJ_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 1985No. of bytes in distributed program, including test data, etc.: 1895776Distribution format: tar.gzProgramming language: Mathematica.Computer: Any work-station or PC where Mathematica is running.Operating system: Windows XP, Mathematica (versions 5 and 7).Classification: 11.5.Nature of problem:The values of analytic images Āν(Q2) and Āν(s) of the QCD running coupling powers αsν(Q2) in Euclidean and Minkowski regions, correspondingly, are determined through the spectral representation in the QCD Analytic Perturbation Theory (APT). In the program FAPT we collect all relevant formulas and various procedures which allow for a convenient evaluation of Āν(Q2) and Āν(s) using numerical integrations of the relevant spectral densities.Solution method:FAPT uses Mathematica functions to calculate different spectral densities and then performs numerical integration of these spectral integrals to obtain analytic images of different objects.Restrictions:It could be that for an unphysical choice of the input parameters the results are without any meaning.Running time:For all operations the run time does not exceed a few seconds. Usually numerical integration is not fast, so that we advise the use of arrays of precalculated data and then to apply the routine Interpolate(as shown in supplied example of the program usage, namely in the notebook FAPT_Interp.nb).