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

Based on $10.64{\mathrm{f}\mathrm{b}}^{-1}$ 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 $e^{+}{e}^{-}\to D_s^{\ast +}{D}_s^{\ast -}$ process. The branching fractions of $D_s^{+}\to {\mathrm{\ell }}^{+}{\nu }_{\mathrm{\ell }}(\mathrm{\ell }=\mu ,\tau )$ are measured to be $\mathcal{B}(D_s^{+}\to {\mu }^{+}{\nu }_{\mu })=(0.547\pm {0.026}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}}\pm {0.016}_{\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}})\mathrm{\%}$ and $\mathcal{B}(D_s^{+}\to {\tau }^{+}{\nu }_{\tau })=(5.60\pm {0.16}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}}\pm {0.20}_{\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}})\mathrm{\%}$, respectively. The product of the decay constant and Cabibbo-Kobayashi-Maskawa matrix element $\mathrm{\mid }{V}_{cs}\mathrm{\mid }$ is determined to be $f_{D_s^{+}}\mathrm{\mid }{V}_{cs}\mathrm{\mid }=(246.5\pm {5.9}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}}\pm {3.6}_{\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}}\pm {0.5}_{\mathrm{i}\mathrm{n}\mathrm{p}\mathrm{u}\mathrm{t}}{)}_{\mu \nu }\mathrm{M}\mathrm{e}\mathrm{V}$ and $f_{D_s^{+}}\mathrm{\mid }{V}_{cs}\mathrm{\mid }=(252.7\pm {3.6}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}}\pm {4.5}_{\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}}\pm {0.6}_{\mathrm{i}\mathrm{n}\mathrm{p}\mathrm{u}\mathrm{t}}){)}_{\tau \nu }\mathrm{M}\mathrm{e}\mathrm{V}$, respectively. Taking the value of $\mathrm{\mid }{V}_{cs}\mathrm{\mid }$ from a global fit in the Standard Model, we obtain $f_{D_s^{+}}=(252.8\pm {6.0}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}}\pm {3.7}_{\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}}\pm {0.6}_{\mathrm{i}\mathrm{n}\mathrm{p}\mathrm{u}\mathrm{t}}{)}_{\mu \nu }$ MeV and $f_{D_s^{+}}=(259.2\pm {3.6}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}}\pm {4.5}_{\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}}\pm {0.6}_{\mathrm{i}\mathrm{n}\mathrm{p}\mathrm{u}\mathrm{t}}{)}_{\tau \nu }$ MeV, respectively. Conversely, taking the value for $f_{D_s^{+}}$ from the latest lattice quantum chromodynamics calculation, we obtain $\mathrm{\mid }{V}_{cs}\mathrm{\mid }=(0.986\pm {0.023}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}}\pm {0.014}_{\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}}\pm {0.003}_{\mathrm{i}\mathrm{n}\mathrm{p}\mathrm{u}\mathrm{t}}{)}_{\mu \nu }$ and $\mathrm{\mid }{V}_{cs}\mathrm{\mid }=(1.011\pm {0.014}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}}\pm {0.018}_{\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}}\pm {0.003}_{\mathrm{i}\mathrm{n}\mathrm{p}\mathrm{u}\mathrm{t}}{)}_{\tau \nu }$, respectively.