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We perform a lattice calculation on the radiative decay of $D_s^*$ using the2+1 Wilson Clover gauge ensembles generated by CLQCD collaboration. Theradiative transition $D_s^*\rightarrow D_s\gamma$ and Dalitz decay$D_s^*\rightarrow D_s e^+e^-$ are studied respectively. After a continuumextrapolation using three lattice spacings, we obtain $\Gamma(D_s^*\rightarrowD_s \gamma)=0.0549(54)$ keV, which is consistent with previous latticecalculations but with much improved precision. The Dalitz decay rate is alsocalculated for the first time and the ratio with the radiative transition isfound to be $R_{ee}=0.624(3)\%$. A total decay width of $D_s^*$ can then bedetermined as 0.0587(54) keV taking into account the experimental branchingfraction. Combining with the most recent experimental measurement on thebranching fraction of the purely leptonic decay $D_s^{+,*}\rightarrowe^+\nu_e$, we obtain$f_{D_s^*}|V_{cs}|=(190.5^{+55.1}_{-41.7_{\textrm{stat.}}}\pm12.6_{\textrm{syst.}})$ MeV, with a significantly improved systematicuncertainty compared to $42.7_{\textrm{syst.}}$ obtained using previous latticeprediction of total decay width $0.070(28)$ keV as input.

Lattice QCD calculation of $D_s^{*}$ radiative decay using the 2+1 Wilson Clover fermion