QCD coupling below 1 GeV from the quarkonium spectrum

In this paper we extend the work synthetically presented by M. Baldicchi, A. V. Nesterenko, G. M. Prosperi, D. V. Shirkov, and C. Simolo [Phys. Rev. Lett. 99, 242001 (2007)] and give theoretical details and a complete set of numerical results. We exploit calculations within a Bethe-Salpeter (BS) formalism adjusted for QCD, in order to extract an experimental strong coupling alpha(exp)(s)(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 term and a confinement term. Besides, the common perturbative strong running 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(exp)(s)(Q(2)) with the APT coupling alpha(E)(Q(2)) turns out to be reasonably good from 1 GeV down to 200 MeV, thus confirming quantitatively the validity of the APT prescription in this range. Below this scale, the experimental points could give a hint on the vanishing of alpha(s)(Q(2)) as Q(2) approaches zero. This infrared behavior would be consistent with some lattice results as well as with the massive modification of the APT approach. As a main result, we claim that the combined BS-APT theoretical scheme provides quite satisfactory correlated understanding of very high and rather low energy phenomena from a few hundred MeV to a few hundred GeV.