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Manuscript Title: anQCD: Fortran programs for couplings at complex momenta in various analytic QCD models
Authors: César Ayala, Gorazd Cvetic
Program title: AanQCDext
Catalogue identifier: AEYK_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 199(2016)114
Programming 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).
Keywords: Analytic (holomorphic) QCD coupling, Fractional Analytic Perturbation Theory, Two-delta analytic QCD model, Massive Perturbation Theory, Perturbative QCD, Renormalization group evolution.
PACS: 12.38.Bx, 11.15.Bt, 11.10.Hi, 11.55.Fv.
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 s(Q2;Nf)/π)ν. Here, Aν(Q2;Nf) is a holomorphic function in the Q2 complex plane, with the exception of the negative semiaxis (-∞,-M2thr), reflecting the analiticity 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.

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.

[1] C. Ayala and G. Cvetic, anQCD: a Mathematica package for calculations in general analytic QCD models, Comput. Phys. Commun. 190 (2015) 182. arXiv:1408.6868 [hep-ph].