anQCD: A Mathematica package for calculations in general analytic QCD models

作者：Ayala Cesar; Cvetic Gorazd^*

来源：Computer Physics Communications, 2015, 190: 182-199.

DOI：10.1016/j.cpc.2014.12.024

• Analytic (holomorphic) QCD coupling
• Fractional Analytic Perturbation Theory
• Two-delta analytic QCD model
• Massive Perturbation Theory

We provide a Mathematica package that evaluates the QCD analytic couplings (in the complex domain) A(nu) (Q(2)), which are analytic analogs of the powers a(Q(2))(nu) of the underlying perturbative QCD (pQCD) coupling a(Q(2)) equivalent to alpha(s)(Q(2))/pi, in three analytic QCD models. (anQCD): Fractional Analytic Perturbation Theory (FAPT), Two-delta analytic QCD (2 delta anQCD), and Massive Perturbation Theory (MPT). The analytic (holomorphic) running couplings A(nu)(Q(2)), in contrast to the corresponding pQCD expressions a(Q(2))(nu), reflect correctly the analytic properties of the spacelike observables D(Q(2)) in the complex Q(2) 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 vertical bar Q(2)vertical bar similar to 1 GeV2.
Program summary
Program title: anQCD
Catalogue identifier: AEVK_v1_0
Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEVK_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/licenceilicence.html
No. of lines in distributed program, including test data, etc.: 1678
No. of bytes in distributed program, including test data, etc.: 46323
Distribution format: tar.gz
Programming language: Mathemitica 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 A(nu)(Q(2); N-f) in analytic QCD [the analytic analog of the power (alpha(s)(Q(2); N-f)/pi)(nu)] based on the dispersion relation; A(nu) represents a physical (holomorphic) function in the plane of complex squared momenta -q(2) equivalent to Q(2). In anQCD.m we collect the formulas for three different analytic models depending on the energy scale, Q(2), number of flavors N-f, the QCD scale (Lambda) over bar (Nf), and the (nonpower) index v. The considered models are: Analytic Perturbation theory (APT), Two-delta analytic QCD (2 delta anQCD) 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 A(nu)(Q(2)) 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.

• 出版日期2015-5