Improved measurement of the branching fraction of $D_s^{+}\to {\mu }^{+}{\nu }_{\mu }$

Using $e^{+}{e}^{-}$ collision data with an integrated luminosity of $7.33{\mathrm{f}\mathrm{b}}^{-1}$ collected at center-of-mass energies between 4.128 and 4.226 GeV with the BESIII detector operating at the BEPCII collider, the branching fraction of the leptonic decay $D_s^{+}\to {\mu }^{+}{\nu }_{\mu }$ is measured to be $(0.5294\pm {0.0108}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}}\pm {0.0085}_{\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}})$%. Based on this, the product of the $D_s^{+}$ decay constant $f_{D_s^{+}}$ and the magnitude of the $c\to s$ quark mixing matrix element $\mathrm{\mid }{V}_{cs}\mathrm{\mid }$ is determined to be $f_{D_s^{+}}\mathrm{\mid }{V}_{cs}\mathrm{\mid }=241.8\pm {2.5}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}}\pm {2.2}_{\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}}\mathrm{M}\mathrm{e}\mathrm{V}$. Using the value of $\mathrm{\mid }{V}_{cs}\mathrm{\mid }$ given by the global standard model fit, $f_{D_s^{+}}$ is found to be $248.4\pm {2.5}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}}\pm {2.2}_{\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}}$,MeV. Alternatively, using the value of $f_{D_s^{+}}$ from a recent lattice quantum chromodynamics calculation, $\mathrm{\mid }{V}_{cs}\mathrm{\mid }$ is determined to be $0.968\pm {0.010}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}}\pm {0.009}_{\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}}$.