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 (A(s;n_{f}) and Aνglob(s)) and Euclidean (A(Q^{2};n_{f}) and Aνglob(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 heavyquark thresholds. These singularityfree 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 renormalizationgroup improved hadronic observables. Program summaryProgram title: FAPT Catalogue identifier: AENJ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENJ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 1985 No. of bytes in distributed program, including test data, etc.: 1895776 Distribution format: tar.gz Programming language: Mathematica. Computer: Any workstation 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 A(Q^{2}) and A(s) of the QCD running coupling powers αsν(Q^{2}) 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 A(Q^{2}) and A(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).
 Publication:

Computer Physics Communications
 Pub Date:
 January 2013
 DOI:
 10.1016/j.cpc.2012.08.014
 arXiv:
 arXiv:1204.2679
 Bibcode:
 2013CoPhC.184..183B
 Keywords:

 High Energy Physics  Phenomenology;
 High Energy Physics  Theory;
 Mathematical Physics
 EPrint:
 23 pages, 6 figures. Citations added. Now it matches version approved for publication in Comp. Phys. Commun