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

Using a $3.19{\mathrm{f}\mathrm{b}}^{-1}$ data sample collected at an $e^{+}{e}^{-}$ center-of-mass energy of $E_{\mathrm{c}\mathrm{m}}=4.178$ GeV with the BESIII detector, we measure the branching fraction of the leptonic decay $D_s^{+}\to {\mu }^{+}{\nu }_{\mu }$ to be $$\mathcal{B}${D_s^+\to\mu^+\nu\mu}=(5.49\pm0.16_{\rm stat.}\pm0.15_{\rm syst.})\times10^{-3}$\mathrm{.}Combiningourbranchingfractionwiththemassesofthe$D_s^+$and$\mu^+$andthelifetimeofthe$D_s^+$,wedetermine$f_{D_s^+}|V_{cs}|=246.2\pm3.6_{\rm stat.}\pm3.5_{\rm syst.}~$\mathrm{M}\mathrm{e}\mathrm{V}$$. Using the $c\to s$ quark mixing matrix element $\mathrm{\mid }{V}_{cs}\mathrm{\mid }$ determined from a global standard model fit, we evaluate the $D_s^{+}$ decay constant $f_{D_s^{+}}=252.9\pm {3.7}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{.}}\pm {3.6}_{\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}\mathrm{.}}$,MeV. Alternatively, using the value of $f_{D_s^{+}}$ calculated by lattice quantum chromodynamics, we find $\mathrm{\mid }{V}_{cs}\mathrm{\mid }=0.985\pm {0.014}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{.}}\pm {0.014}_{\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}\mathrm{.}}$. These values of ${\mathcal{B}}_{D_s^{+}\to {\mu }^{+}{\nu }_{\mu }}$, $f_{D_s^{+}}\mathrm{\mid }{V}_{cs}\mathrm{\mid }$, $f_{D_s^{+}}$ and $\mathrm{\mid }{V}_{cs}\mathrm{\mid }$ are each the most precise results to date.