Mathematica and Fortran programs for various analytic QCD couplings

TL;DR

This paper introduces analytic QCD models with couplings free of Landau singularities, providing a construction method for their powers and offering computational tools in Mathematica and Fortran.

Contribution

It presents a general procedure to construct analytic analogs of QCD couplings and their powers, along with practical computational programs.

Findings

Developed three analytic QCD models without Landau singularities.

Provided Mathematica and Fortran programs for calculating these couplings.

Enabled practical applications of analytic QCD models through downloadable software.

Abstract

We outline here the motivation for the existence of analytic QCD models, i.e., QCD frameworks in which the running coupling $A(Q^2)$ has no Landau singularities. The analytic (holomorphic) coupling $A(Q^2)$ is the analog of the underlying pQCD coupling $a(Q^2) \equiv \alpha_s(Q^2)/\pi$, and any such $A(Q^2)$ defines an analytic QCD model. We present the general construction procedure for the couplings $A_{\nu}(Q^2)$ which are analytic analogs of the powers $a(Q^2)^{\nu}$. Three analytic QCD models are presented. Applications of our program (in Mathematica) for calculation of $A_{\nu}(Q^2)$ in such models are presented. Programs in both Mathematica and Fortran can be downloaded from the web page: gcvetic.usm.cl.