Relativistic pseudoscalarqq¯bound states: Results on Bethe-Salpeter wave functions and decay constants

Abstract

We discuss the properties of pseudoscalar $q\overline{q}$ bound states in the framework of their Bethe-Salpeter equations coupled to the Schwinger-Dyson equations for the quark propagators. The equations were solved numerically in the Landau gauge and in the ladder approximation, but without resorting to non-relativistic approximations, to obtain bound-state masses, leptonic decay constants, and wave functions. Light-light, light-heavy, and heavy-heavy $q\overline{q}$ bound states were treated with identical numerical procedures and with results which agree qualitatively and quantitatively with expectations both from current algebra for light quarks and from composite models for heavy quarks. Our results for asymptotic quark mass functions and bound-state wave functions agree with those derived from operator-product expansions and renormalization-group considerations.