Prediction of the $D_s^*$ width from a calculation of its radiative decay in full lattice QCD

Abstract: We determine the rate for $D_s^* \rightarrow D_s \gamma$ for the first time from lattice QCD and include the full effect of $u$, $d$ and $s$ sea quarks. The valence quarks are implemented using the Highly Improved Staggered Quark (HISQ) formalism and we normalise the vector current nonperturbatively. We obtain $M(D_s^*)-M(D_s)$ of 148(4) MeV, in good agreement with experiment. The value of the decay constant of the $D_s^*$ we find to be 274(6) MeV, so that $f_{D_s^*}/f_{D_s} = 1.10(2)$. For the radiative decay we find $\Gamma(D_s^* \rightarrow D_s \gamma)$ = 0.066(26) keV. Given the experimental branching fraction for this decay we predict a total width for the $D_s^*$ of 0.070(28) keV, making this the longest lived charged vector meson.