Infrared behavior of the running coupling constant and bound states in QCD

The perturbative expression of the running strong coupling constant αₛ(Q²) has an unphysical singularity for Q²=ΛQCD². Various modification have been proposed for the infrared region. The effect of some of such proposals on the quark-antiquark spectrum is tested on a Bethe-Salpeter (second order) formalism which was successfully applied in previous papers to an overall evaluation of the spectrum in the light-light, light-heavy and heavy-heavy sectors (the only serious discrepancy with data being for the light pseudoscalar meson masses). In this paper only the cc̄, bb̄ and qq̄ $(q=u$ or $d)$ cases are considered and fine structure is neglected. It is found that in the bb̄ and cc̄ cases the results are little sensitive to the specific choice. In the light-light case the Dokshitzer et al. prescription is again essentially equivalent to the truncation prescription used in the previous calculation and it is consistent with the same a priori fixing of the light quark masses on the typical current values mᵤ=md=10MeV (only the pion mass resulting completely out of scale at about 500 MeV). With the Shirkov-Solovtsov prescription, on the contrary, a reasonable agreement with the data is obtained only at the price of using a phenomenological momentum dependent effective mass for the quark. The use of such an effective mass amounts to a correction of the free quark propagator. It is remarkable that this also has the effect of bringing the pion mass into the correct range.