Radiative transitions and magnetic moments of the charmed and bottom vector mesons in chiral perturbation theory

In this work, we systematically study the radiative decays and magnetic moments of the charmed and bottom vector mesons with chiral perturbation theory up to one-loop level. We present the results in SU(2) and SU(3) cases with the mass splitting in loop diagrams kept and unkept, respectively. The obtained decay rates for $D^\ast$ and $B^\ast$ mesons in SU(3) case with the mass splitting kept are: $\Gamma_{\bar{D}^{\ast 0}\to \bar{D}^0\gamma}=16.2^{+6.5}_{-6.0}$ keV, $\Gamma_{D^{\ast-}\to D^-\gamma}=0.73^{+0.7}_{-0.3}$ keV, $\Gamma_{D_s^{\ast-}\to D_s^-\gamma}= 0.32^{+0.3}_{-0.3}$ keV, and $\Gamma_{B^{\ast+}\to B^+\gamma}=0.58^{+0.2}_{-0.2}$ keV, $\Gamma_{B^{\ast0}\to B^0\gamma}=0.23^{+0.06}_{-0.06}$ keV, $\Gamma_{B_s^{\ast0}\to B_s^0\gamma}=0.04^{+0.03}_{-0.03}$ keV. The decay width for $D^{\ast-}\to D^-\gamma$ is consistent with the experimental measurement. As a byproduct, the full widths of $\bar{D}^{\ast0}$ and $D_s^{\ast-}$ are $\Gamma_{\mathrm{tot}}(\bar{D}^{\ast0})\simeq77.7^{+26.7}_{-20.5}~\mathrm{keV}$ and $ \Gamma_{\mathrm{tot}}(D_s^{\ast-})\simeq0.62^{+0.45}_{-0.50}~\mathrm{keV}$, respectively. We also calculate the magnetic moments of the heavy vector mesons. The analytical chiral expressions derived in our work shall be helpful for the extrapolations of lattice QCD simulations in the coming future.