Covariant description of hydrogenlike mesons

A formalism, covariant up to terms of O(1/${\mathit{M}}_{\mathit{Q}}$), is presented, which describes from the center-of-mass frame a (hydrogenlike) system consisting of a heavy quark (Q) and a light quark (q). The effective interaction between them is characterized by a color Coulomb-like potential V=-ξ/r, a linear scalar potential S=br (b>0), and a Breit potential. The formalism is applied to B- and D-meson spectroscopy and to the calculation of the M1 widths Γ${(}^3$ ${\mathit{S}}_1$ ${\to }^1$ ${\mathit{S}}_0$γ). Recoil effects on these widths are included through a boost (in the opposite direction to the photon momentum) on the final (Q,q) bound state wave function. By plotting the ratio ${\mathit{R}}_{\gamma \mathit{D}}^{\mathrm{*}}$=Γ(${\mathit{D}}^{\mathrm{*}+}$→${\mathit{D}}^{+}$γ)/Γ(${\mathit{D}}^{\mathrm{*}0}$→${\mathit{D}}^0$γ) as a function of the magnetic moment of the charm quark (${\mathrm{\mu }}_{\mathit{c}}$) it is found that according to the present experimental value ${\mathit{R}}_{\gamma \mathit{D}}^{\mathrm{*}\left(\mathit{e}\mathit{x}\mathit{p}\mathit{t}\right)}$=0.04±0.08 an anomalous value for ${\mathrm{\mu }}_{\mathit{c}}$ could be discarded.