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

Using ${e}^{+}{e}^{-}$ collision data with an integrated luminosity of $7.33\text{}\text{}{\mathrm{fb}}^{-1}$ 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 $\left(0.5294±0.010{8}_{\mathrm{stat}}±0.008{5}_{\mathrm{syst}}\right)%$. 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 $|{V}_{cs}|$ is determined to be ${f}_{{D}_{s}^{+}}|{V}_{cs}|=241.8±{2.5}_{\mathrm{stat}}±{2.2}_{\mathrm{syst}}\text{}\text{}\mathrm{MeV}$. Using the value of $|{V}_{cs}|$ given by the global standard model fit, ${f}_{{D}_{s}^{+}}$ is found to be $248.4±{2.5}_{\mathrm{stat}}±{2.2}_{\mathrm{syst}}\text{}\text{}\mathrm{MeV}$. Alternatively, using the value of ${f}_{{D}_{s}^{+}}$ from a recent lattice quantum chromodynamics calculation, $|{V}_{cs}|$ is determined to be $0.968±0.01{0}_{\mathrm{stat}}±0.00{9}_{\mathrm{syst}}$.