Quasiclassical theory of the Dirac equation with a scalar-vector interaction and its applications in the physics of heavy-light mesons

Abstract

We construct a relativistic potential quark model of D, Ds, B, and Bs mesons in which the light quark motion is described by the Dirac equation with a scalar-vector interaction and the heavy quark is considered a local source of the gluon field. Within the quasiclassical approximation, we obtain simple asymptotic formulas for the energy and mass spectra and for the mean radii of D, Ds, B, and Bs mesons, which ensure a high accuracy of calculations even for states with the radial quantum number nr >> 1. We show that the fine structure of P-wave states in heavy-light mesons is primarily sensitive to the choice of two parameters: the strong-coupling constant $\alpha_s$ and the coefficient $\lambda$ of mixing of the long-range scalar and vector potentials Sl.r.(r) and Vl.r.(r).