Relativistic effects in $\mbox{M1}$ radiative decays of heavy-light mesons

Abstract

We discuss the $\mbox{M1}$ radiative transitions $D^{\ast }\to D\gamma$, $D_s^{\ast }\to D_s\gamma$, $B^{\ast }\to B\gamma$, and $B_s^{\ast }\to B_s\gamma$. A relativistic potential model is proposed. The corresponding Hamiltonian, when expanded to terms of the order of $v^2/c^2$, where $v$ are the quark velocities, coincides with the Breit Hamiltonian. This model allows making predictions for the widths of radiative transitions of mesons with one light quark. Taking into account relativistic effects is especially important for the transitions $D_s^{\ast +}\to D_s^{+}\gamma$ and $D^{\ast +}\to D^{+}\gamma$, where there is a large compensation in the magnitude of the magnetic moment of these mesons. Our results are consistent with known experimental data.

18 pages, 5 tables