Determination of the Pseudoscalar Decay Constant ${f}_{{D}_{s}^{+}}$ via ${D}_{s}^{+}\to {\mu }^{+}{\nu }_{\mu }$

Using a $3.19\text{}\text{}{\mathrm{fb}}^{-1}$ data sample collected at an ${e}^{+}{e}^{-}$ center-of-mass energy of ${E}_{\mathrm{cm}}=4.178\text{}\text{}\mathrm{GeV}$ with the BESIII detector, we measure the branching fraction of the leptonic decay ${D}_{s}^{+}\to {\mu }^{+}{\nu }_{\mu }$ to be ${B}_{{D}_{s}^{+}\to {\mu }^{+}{\nu }_{\mu }}=\left(5.49±0.1{6}_{\text{stat}}±0.1{5}_{\text{syst}}\right)×{10}^{-3}$. Combining our branching fraction with the masses of the ${D}_{s}^{+}$ and ${\mu }^{+}$ and the lifetime of the ${D}_{s}^{+}$, we determine ${f}_{{D}_{s}^{+}}|{V}_{cs}|=246.2±3.{6}_{\text{stat}}±3.{5}_{\text{syst}}\text{}\text{}\mathrm{MeV}$. Using the $c\to s$ quark mixing matrix element $|{V}_{cs}|$ determined from a global standard model fit, we evaluate the ${D}_{s}^{+}$ decay constant ${f}_{{D}_{s}^{+}}=252.9±3.{7}_{\text{stat}}±3.{6}_{\text{syst}}\text{}\text{}\mathrm{MeV}$. Alternatively, using the value of ${f}_{{D}_{s}^{+}}$ calculated by lattice quantum chromodynamics, we find $|{V}_{cs}|=0.985±0.01{4}_{\text{stat}}±0.01{4}_{\text{syst}}$. These values of ${B}_{{D}_{s}^{+}\to {\mu }^{+}{\nu }_{\mu }}$, ${f}_{{D}_{s}^{+}}|{V}_{cs}|$, ${f}_{{D}_{s}^{+}}$ and $|{V}_{cs}|$ are each the most precise results to date.