AnQCD: Fortran programs for couplings at complex momenta in various analytic QCD models

Abstract

We provide three Fortran programs which evaluate the QCD analytic (holomorphic) couplings Aν(Q2) for complex or real squared momenta Q2. These couplings are holomorphic 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 index ν can be noninteger. The provided programs do basically the same job as the Mathematica package anQCD.m published by us previously (Ayala and Cvetič, 2015), but are now written in Fortran. Program summaryProgram title: AanQCDextCatalogue identifier: AEYK_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEYK_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.: 12105No. of bytes in distributed program, including test data, etc.: 98822Distribution format: tar.gzProgramming language: Fortran.Computer: Any work-station or PC where Fortran 95/2003/2008 (gfortran) is running.Operating system: Operating system Linux (Ubuntu and Scientific Linux), Windows (in all cases using gfortran).Classification: 11.1, 11.5.Nature of problem: Calculation of values of the running analytic couplings Aν(Q2;Nf) for general complex squared momenta Q2≡−q2, in three analytic QCD models, where Aν(Q2;Nf) is the analytic (holomorphic) analog of the power (αs(Q2;Nf)/π)ν. Here, Aν(Q2;Nf) is a holomorphic function in the Q2 complex plane, with the exception of the negative semiaxis (−∞,−Mthr2], reflecting the analyticity properties of the spacelike renormalization invariant quantities D(Q2) in QCD. In contrast, the perturbative QCD power (αs(Q2;Nf)/π)ν has singularities even outside the negative semiaxis (Landau ghosts). The three considered models are: Analytic Perturbation theory (APT); Two-delta analytic QCD (2δanQCD); Massive Perturbation Theory (MPT). We refer to Ref. [1] for more details and literature.Solution method: The Fortran programs for FAPT and 2δanQCD models contain routines and functions needed to perform two-dimensional numerical integrations involving the spectral function, in order to evaluate Aν(Q2) couplings. In MPT model, one-dimensional numerical integration involving A1(Q2) is sufficient to evaluate any Aν(Q2) coupling.Restrictions: For unphysical choices of the input parameters the results are meaningless. When Q2 is close to the cut region of the couplings (Q2 real negative), the calculations can take more time and can have less precision.Running time: For evaluation of a set of about 10 related couplings, the times vary in the range t∼101–102 s. MPT requires less time, t∼1–101 s.