Structure of radiative interferences and $g=2\mathrm{}$ for vector mesons

The result of Burnett and Kroll (BK) states that for radiative decays, the interference of $O\left({\omega }^{-1}\right)$ in the photon energy $\omega$ vanishes after the sum over polarizations of the involved particles. Using radiative decays of vector mesons, we show that if the vector meson is polarized, the $O\left({\omega }^{-1}\right)$ terms are null only for the canonical value of the magnetic dipole moment of the vector meson, namely, $\mathbf{g}=2\mathrm{}$ in Bohr magneton units. A subtle cancellation of all $O\left({\omega }^{-1}\right)$ terms happens when summing over all polarizations to recover the Burnett-Kroll result. We also show the source of these terms and the corresponding cancellation for the unpolarized case and exhibit a global structure that can make them individually vanish in a particular kinematical region.