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

TL;DR

This paper introduces three Fortran programs that compute complex-momentum analytic QCD couplings across various models, extending previous Mathematica tools to a more versatile programming language.

Contribution

The paper provides Fortran implementations of analytic QCD couplings for complex momenta, enabling broader computational applications beyond existing Mathematica packages.

Findings

Programs accurately evaluate couplings in three analytic QCD models.

Supports complex and real squared momenta Q^2.

Extends previous Mathematica tools to Fortran for wider use.

Abstract

We provide three Fortran programs which evaluate the QCD analytic (holomorphic) couplings $\mathcal{A}_{\nu}(Q^2)$ for complex or real squared momenta $Q^2$. These couplings are holomorphic analogs of the powers $a(Q^2)^{\nu}$ of the underlying perturbative QCD (pQCD) coupling $a(Q^2) \equiv \alpha_s(Q^2)/\pi$, in three analytic QCD models (anQCD): Fractional Analytic Perturbation Theory (FAPT), Two-delta analytic QCD (2$\delta$anQCD), and Massive Perturbation Theory (MPT). The index $\nu$ can be noninteger. The provided programs do basically the same job as the Mathematica package anQCD.m in Mathematica published by us previously, Ref.[1], but are now written in Fortran.