Meson masses within the model of induced nonlocal quark currents

Abstract

The model of induced quark currents being a kind of nonlocal extension of the bosonization procedure is developed. The model is based on the hypothesis that the QCD vacuum is realized by the (anti-)self-dual homogeneous gluon field. We study manifestations of confinement and chiral symmetry breaking due to the vacuum field in meson spectra and weak decay constants. It is shown that the confining properties of the vacuum field, chiral symmetry breaking, and localization of a composite field at the center of masses of quarks can explain the distinctive features of the meson spectrum: mass splitting between pseudoscalar and vector mesons, Regge trajectories, the asymptotic mass formulas in the heavy quark limit, ${M}_{Q\overline{Q}}\ensuremath{\rightarrow}2{m}_{Q}$ for quarkonia and ${M}_{Q\overline{q}}\ensuremath{\rightarrow}{m}_{Q}$ for heavy-light mesons. Within the model, the chiral symmetry breaking due to the vacuum field is a dominating factor in forming the masses and decay constants of light mesons, while confinement is responsible for Regge trajectories, heavy quarkonia, and 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.