Bound state approach to the QCD coupling at low energy scales

We exploit theoretical results on the meson spectrum within the framework of a Bethe-Salpeter (BS) formalism adjusted for QCD, in order to extract an “experimental” coupling α s (Q) below 1 GeV by comparison with the data. The relativistic BS potential follows from a proper ansatz on the Wilson loop to encode confinement. The experimental points α s (Q) exhibit a reasonable agreement with the infrared safe Analytic Perturbation Theory (APT) coupling from 1 GeV down to 200 MeV, while, below this scale, give a hint on the vanishing of αs(Q ) as Q → 0 , consistently with a “massive” modification of APT. 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 low energy phenomena.