QCD coupling below 1 GeV from quarkonium spectrum

TL;DR

This paper uses a Bethe-Salpeter formalism combined with Analytic Perturbation Theory to extract the strong coupling constant below 1 GeV from quarkonium spectra, supporting the idea that ppa_s(Q^2) vanishes as Q approaches zero.

Contribution

It introduces a combined Bethe-Salpeter and APT framework to analyze the QCD coupling at low energies, extending previous work with detailed numerical results.

Findings

ppa_s^{exp}(Q^2) agrees with APT coupling from 1 GeV to 200 MeV.

Evidence suggests ppa_s(Q^2) may vanish as Q at low energies.

The scheme provides a unified understanding of QCD phenomena across a wide energy range.

Abstract

In this paper we extend the work synthetically presented in Ref.[1] and give theoretical details and complete tables of numerical results. We exploit calculations within a Bethe-Salpeter (BS) formalism adjusted for QCD, in order to extract an ``experimental'' strong coupling \alpha_s^{exp}(Q^2) below 1 GeV by comparison with the meson spectrum. The BS potential follows from a proper ansatz on the Wilson loop to encode confinement and is the sum of a one-gluon-exchange and a confinement terms. Besides, the common perturbative strong coupling is replaced by the ghost-free expression \alpha_E(Q^2) according to the prescription of Analytic Perturbation Theory (APT). The agreement of \alpha_s^{exp}(Q^2) with the APT coupling \alpha_E(Q^2) turns out to be reasonable from 1 GeV down to the 200 MeV scale, thus confirming quantitatively the validity of the APT prescription. Below this scale, the experimental points could give a hint on the vanishing of \alpha_s(Q^2) as Q approaches zero. This infrared behaviour would be consistent with some lattice results and a ``massive'' generalization of the APT approach. As a main result, we claim that the combined BS-APT theoretical scheme provides us with a rather satisfactory correlated understanding of very high and rather low energy phenomena from few hundreds MeV to few hundreds GeV.