Prediction of the $D_s^{\ast }$ width from a calculation of its radiative decay in full lattice QCD

Abstract

We determine the rate for $D_s^{\ast }\to D_s{\hat{I}}^3$ 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 $M(D_s^{\ast })-M(D_s)$ of 148(4) MeV, in good agreement with experiment. The value of the decay constant of the $D_s^{\ast }$ we find to be 274(6) MeV, so that $f_{D_s^{\ast }}/f_{D_s}=1.10(2)$. For the radiative decay we find $\hat{I}“(D_s^{\ast }\to D_s{\hat{I}}^3)$ = 0.066(26) keV. Given the experimental branching fraction for this decay we predict a total width for the $D_s^{\ast }$ of 0.070(28) keV, making this the longest lived charged vector meson.

5 pages, 3 figures