Meson masses within the model of induced nonlocal quark currents

Abstract

The model of induced quark currents formulated in our recent paper (Phys. Rev. D51, 176) is developed. The model being a kind of nonlocal extension of the bosonization procedure is based on the hypothesis that the QCD vacuum is realized by the (anti-)self-dual homogeneous gluon field. This vacuum field provides the analytical quark confinement. It is shown that a particular form of nonlocality of the quark and gluon propagators determined by the vacuum field, an interaction of quark spin with the vacuum gluon field and a localization of meson field at the center of masses of two quarks can explain the distinctive features of meson spectrum: Regge trajectories of radial and orbital excitations, mass splitting between pseudoscalar and vector mesons, the asymptotic mass formulas in the heavy quark limit: $M_{Q\bar Q}\to 2m_Q$ for quarkonia and $M_{Q\bar q}\to m_Q$ for heavy-light mesons. With a minimal set of parameters (quark masses, vacuum field strength and the quark-gluon coupling constant) the model describes to within ten percent inaccuracy the masses and weak decay constants of mesons from all qualitatively different regions of the spectrum.