Mass operator of a $b$-quark in an external non-Abelian chromomagnetic field

Based on the effective Lagrangian for the $b$-quark radiative decay process, the mass operator for a $b$-quark in a background non-Abelian chromomagnetic field has been considered. The imaginary part of the mass operator, which is proportional to the $b$-quark radiative decay rate, has been calculated in the one-loop approximation with due regard for the background field.