Semiclassical approximation in the relativistic potential model of B and D 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. The effective interquark interaction is described by a combination of the perturbative one-gluon exchange potential VCoul(r) and the long-range Lorentz-scalar and Lorentz-vector linear potentials Sl.r.(r) and Vl.r.(r). In the semiclassical 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 αs and the coefficient λ of mixing of the long-range scalar and vector potentials Sl.r.(r) and Vl.r.(r).