QCD coupling below 1 GeV from quarkonium spectrum

Understand

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).