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

TL;DR

This paper introduces a Mathematica package for calculating analytic QCD couplings in various models, improving the evaluation of physical quantities at low energies by respecting the analytic properties of spacelike observables.

Contribution

The package provides a unified tool for evaluating analytic QCD couplings across three models, enhancing calculations in low-energy QCD regimes.

Findings

Enables accurate evaluations of QCD couplings at low momenta.

Reflects the correct analytic properties of spacelike observables.

Supports three different analytic QCD models.

Abstract

We provide a Mathematica package that evaluates the QCD analytic couplings (in the Euclidean domain) $\mathcal{A}_{\nu}(Q^2)$, which are analytic analogs of the powers $a(Q^2)^{\nu}$ of the underlying perturbative QCD (pQCD) coupling $a(Q^2) \equiv \alpha_s(Q^2)/\pi$, in three analytic QCD models (anQCD): Fractional Analytic Perturbation Theory (FAPT), Two-delta analytic QCD (2$\delta$anQCD), and Massive Perturbation Theory (MPT). The analytic (holomorphic) running couplings $\mathcal{A}_{\nu}(Q^2)$, in contrast to the corresponding pQCD expressions $a(Q^2)^{\nu}$, reflect correctly the analytic properties of the spacelike observables ${\cal D}(Q^2)$ 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 $|Q^2| \sim 1 \ {\rm GeV}^2$.