Measurement of the branching fraction of $D_s^{+}\to {\ell }^{+}{\nu }_{\ell }$ via $e^{+}{e}^{-}\to D_s^{*+}{D}_s^{*-}$

Based on $10.64{\mathrm{fb}}^{-1}$ of $e^{+}{e}^{-}$ collision data taken at center-of-mass energies between 4.237 and 4.699 GeV with the BESIII detector, we study the leptonic $D_s^{+}$ decays using the $e^{+}{e}^{-}\to D_s^{*+}{D}_s^{*-}$ process. The branching fractions of $D_s^{+}\to {\ell }^{+}{\nu }_{\ell }(\ell =\mu ,\tau )$ are measured to be $B_{D_s^{+}\to {\mu }^{+}{\nu }_{\mu }}=(0.547\pm 0.026_{\mathrm{stat}}\pm 0.016_{\mathrm{syst}})\%$ and $B_{D_s^{+}\to {\tau }^{+}{\nu }_{\tau }}=(5.60\pm 0.16_{\mathrm{stat}}\pm 0.20_{\mathrm{syst}})\%$, respectively. The product of the decay constant and Cabibbo-Kobayashi-Maskawa matrix element $\left|V_{cs}\right|$ is determined to be $f_{D_s^{+}}\left|V_{cs}\right|=(246.5\pm {5.9}_{\mathrm{stat}}\pm {3.6}_{\mathrm{syst}}\pm {0.5}_{\text{input}}{)}_{\mu \nu }$ and $f_{D_s^{+}}\left|V_{cs}\right|=(252.7\pm {3.6}_{\mathrm{stat}}\pm {4.5}_{\mathrm{syst}}\pm {0.6}_{\text{input}}{)}_{\tau \nu }\mathrm{MeV}$, respectively. Taking the value of $\left|V_{cs}\right|$ from a global fit in the Standard Model, we obtain $f_{D_s^{+}}=(253.2\pm {6.0}_{\mathrm{stat}}\pm {3.7}_{\mathrm{syst}}\pm {0.6}_{\text{input}}{)}_{\mu \nu }$ and $f_{D_s^{+}}=(259.6\pm {3.7}_{\mathrm{stat}}\pm {4.6}_{\mathrm{syst}}\pm {0.6}_{\text{input}}{)}_{\tau \nu }\mathrm{MeV}$, respectively. Conversely, taking the value for $f_{D_s^{+}}$ from the latest lattice quantum chromodynamics calculation, we obtain $\left|V_{cs}\right|=(0.986\pm 0.023_{\mathrm{stat}}\pm 0.014_{\mathrm{syst}}\pm 0.003_{\text{input}}{)}_{\mu \nu }$ and $\left|V_{cs}\right|=(1.011\pm 0.014_{\mathrm{stat}}\pm 0.018_{\mathrm{syst}}\pm 0.003_{\text{input}}{)}_{\tau \nu }$, respectively.