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Abstract

We provide a Mathematica package that evaluates the QCD analytic couplings (in the complex domain) Aν(Q2), which are analytic analogs of the powers a(Q2)ν of the underlying perturbative QCD (pQCD) coupling a(Q2)≡αs(Q2)/π, in three analytic QCD models (anQCD): Fractional Analytic Perturbation Theory (FAPT), Two-delta analytic QCD (2δanQCD), and Massive Perturbation Theory (MPT). The analytic (holomorphic) running couplings Aν(Q2), in contrast to the corresponding pQCD expressions a(Q2)ν, reflect correctly the analytic properties of the spacelike observables D(Q2) in the complex Q2 plane as dictated by the general principles of quantum field theory. They are thus more suited for evaluations of such physical quantities, especially at low momenta |Q2|∼1GeV2.Program title:anQCDCatalogue identifier: AEVK_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEVK_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.: 1678No. of bytes in distributed program, including test data, etc.: 46323Distribution format: tar.gzProgramming language: Mathematica versions 9.0.1 and 10.0.1.Computer: Any work-station or PC where Mathematica is running.Operating system: Linux and Mac OS X, software Mathematica 9.0.1 and Mathematica 10.0.1.Classification: 11.1, 11.5.Nature of problem:Evaluation of the values for analytic couplings Aν(Q2;Nf) in analytic QCD [the analytic analog of the power (αs(Q2;Nf)/π)ν] based on the dispersion relation; Aν represents a physical (holomorphic) function in the plane of complex squared momenta −q2≡Q2. In anQCD.m we collect the formulas for three different analytic models depending on the energy scale, Q2, number of flavors Nf, the QCD scale Λ¯Nf, and the (nonpower) index ν. The considered models are: Analytic Perturbation theory (APT), Two-delta analytic QCD (2δanQCD) and Massive Perturbation Theory (MPT).Solution method:anQCD uses Mathematica functions to perform numerical integration of spectral function for each analytic model, in order to obtain the corresponding analytic images Aν(Q2) via dispersion relation.Restrictions:It could be that for an unphysical choice of the input parameters the results are meaningless.Running time:For all operations the running time does not exceed a few seconds.