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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_0Distribution 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 A for general complex squared momenta _{ν}(Q^{2};N_{f})Q, in three analytic QCD models, where ^{2} ≡ -q^{2}A is the analytic (holomorphic) analog of the power _{ν}(Q^{2};N_{f})(α. Here, _{s}(Q^{2};N_{f})/π)^{ν}A is a holomorphic function in the _{ν}(Q^{2};N_{f})Q complex plane, with the exception of the negative semiaxis (-∞,-^{2}M^{2}_{thr}), reflecting the analiticity properties of the spacelike renormalization invariant quantities D(Q in QCD. In contrast, the perturbative QCD power (α^{2})_{s}(Q^{2};N_{f})/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 A couplings. In MPT model, one-dimensional numerical integration involving _{ν}(Q^{2})A is sufficient to evaluate any _{1}(Q^{2})A coupling._{ν}(Q^{2}) | ||

Restrictions:For unphysical choices of the input parameters the results are meaningless. When Q is close to the cut region of the couplings (^{2}Q real negative), the calculations can take more time and can have less precision.^{2} | ||

Running time:For evaluation of a set of about 10 related couplings, the times vary in the range t ~ 10^{1}-10^{2} s. MPT requires less time, t ~ 1-10^{1} s. | ||

References: | ||

[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]. |

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