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Using a $3.19~\mathrm{fb}^{-1}$ data sample collected at an $e^+e^-$center-of-mass energy of $E_{\rm cm}=4.178$ GeV with the BESIII detector, wemeasure the branching fraction of the leptonic decay $D_s^+\to\mu^+\nu_\mu$ tobe $\mathcal{B}_{D_s^+\to\mu^+\nu_\mu}=(5.49\pm0.16_{\rm stat.}\pm0.15_{\rmsyst.})\times10^{-3}$. Combining our branching fraction with the masses of the$D_s^+$ and $\mu^+$ and the lifetime of the $D_s^+$, we determine$f_{D_s^+}|V_{cs}|=246.2\pm3.6_{\rm stat.}\pm3.5_{\rm syst.}~\mathrm{MeV}$.Using the $c\to s$ quark mixing matrix element $|V_{cs}|$ determined from aglobal standard model fit, we evaluate the $D_s^+$ decay constant$f_{D_s^+}=252.9\pm3.7_{\rm stat.}\pm3.6_{\rm syst.}$\,MeV. Alternatively,using the value of $f_{D_s^+}$ calculated by lattice quantum chromodynamics, wefind $|V_{cs}| = 0.985\pm0.014_{\rm stat.}\pm0.014_{\rm syst.}$. These valuesof $\mathcal{B}_{D_s^+\to\mu^+\nu_\mu}$, $f_{D_s^+}|V_{cs}|$, $f_{D_s^+}$ and$|V_{cs}|$ are each the most precise results to date.

Determination of the pseudoscalar decay constant $f_{D_s^+}$ via $D_s^+\to\mu^+\nu_\mu$