Determination of the Pseudoscalar Decay Constant $f_{D_s^{+}}$ via $D_s^{+}\to {\mu }^{+}{\nu }_{\mu }$

Using a $3.19{\mathrm{fb}}^{-1}$ data sample collected at an $e^{+}{e}^{-}$ center-of-mass energy of $E_{\mathrm{cm}}=4.178\mathrm{GeV}$ with the BESIII detector, we measure the branching fraction of the leptonic decay $D_s^{+}\to {\mu }^{+}{\nu }_{\mu }$ to be ${\mathcal{B}}_{D_s^{+}\to {\mu }^{+}{\nu }_{\mu }}=(5.49\pm 0.16_{\text{stat}}\pm 0.15_{\text{syst}})\times {10}^{-3}$. Combining our branching fraction with the masses of the $D_s^{+}$ and ${\mu }^{+}$ and the lifetime of the $D_s^{+}$, we determine $f_{D_s^{+}}|V_{cs}|=246.2\pm 3.6_{\text{stat}}\pm 3.5_{\text{syst}}\mathrm{MeV}$. 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 $f_{D_s^{+}}=252.9\pm 3.7_{\text{stat}}\pm 3.6_{\text{syst}}\mathrm{MeV}$. Alternatively, using the value of $f_{D_s^{+}}$ calculated by lattice quantum chromodynamics, we find $|V_{cs}|=0.985\pm 0.014_{\text{stat}}\pm 0.014_{\text{syst}}$. These values of ${\mathcal{B}}_{D_s^{+}\to {\mu }^{+}{\nu }_{\mu }}$, $f_{D_s^{+}}|V_{cs}|$, $f_{D_s^{+}}$ and $|V_{cs}|$ are each the most precise results to date.

Figure 1

Fits to the $M_{\text{tag}}$ distributions of the accepted ST candidates. Dots with error bars are data. Blue solid curves are the fit results. Red dashed curves are the fitted backgrounds. The black dotted curve in the $K_S^0{K}^{-}$ mode is the $D^{-}\to K_S^0{\pi }^{-}$ component. The pairs of arrows denote the signal regions.

Figure 2

Fit to the ${\mathrm{MM}}^2$ distribution of the $D_s^{+}\to {\mu }^{+}{\nu }_{\mu }$ candidates. Inset plot shows the same distribution in log scale. Dots with error bars are data. Blue solid curve is the fit result. Red dotted curve is the fitted background. Orange hatched and blue cross-hatched histograms are the BKGI component and the combined BKGII and BKGIII components, respectively (see text).