Measurement of the $D_s^{+}\to {\ell }^{+}{\nu }_{\ell }$ branching fractions and the decay constant $f_{D_s^{+}}$

Using $482{\mathrm{pb}}^{-1}$ of $e^{+}{e}^{-}$ collision data collected at a center-of-mass energy of $\sqrt{s}=4.009\mathrm{GeV}$ with the BESIII detector, we measure the branching fractions of the decays $D_s^{+}\to {\mu }^{+}{\nu }_{\mu }$ and $D_s^{+}\to {\tau }^{+}{\nu }_{\tau }$. By constraining the ratio of decay rates of $D_s^{+}$ to ${\tau }^{+}{\nu }_{\tau }$ and to ${\mu }^{+}{\nu }_{\mu }$ to the Standard Model prediction, the branching fractions are determined to be $\mathcal{B}(D_s^{+}\to {\mu }^{+}{\nu }_{\mu })=(0.495\pm 0.067\pm 0.026)\%$ and $\mathcal{B}(D_s^{+}\to {\tau }^{+}{\nu }_{\tau })=(4.83\pm 0.65\pm 0.26)\%$. Using these branching fractions, we obtain a value for the decay constant $f_{D_s^{+}}$ of $(241.0\pm 16.3\pm 6.5)\mathrm{MeV}$, where the first error is statistical and the second systematic.

Figure 1

Annihilation process for $D_s^{+}$ leptonic decays in the Standard Model.

Figure 2

Fits to the $M_{\mathrm{BC}}$ distributions of $D_s^{-}$ candidates. The points with error bars are data. The red curves are the fit results. The blue dashed curves are the fitted combinatorial backgrounds.

Figure 3

Projections of the simultaneous fit to the ${\mathrm{MM}}^2$ distributions of the events in (a) the $D_s^{-}$ signal region and (b) $M_{\mathrm{BC}}$ sideband region. Data are shown as the points with error bars. The red dotted curve shows the ${\mu }^{+}{\nu }_{\mu }$ signal and the black dot-dashed curve shows the ${\tau }^{+}{\nu }_{\tau }$ signal. The purple long-dashed line shows the non-$D_s^{+}$ background while the green dashed line shows the real-$D_s^{+}$ background. The blue curve shows the sum of all these contributions.

Figure 4

Projections of the simultaneous fit to the ${\mathrm{MM}}^2$ distributions of (a) part I, (b) part II and (c) part III data subsamples as defined in Sec. 4d2. (b’) and (c’) are the corresponding ${\mathrm{MM}}^2$ distributions from the $M_{\mathrm{BC}}$ sideband. Data are shown as the points with error bars. The red dotted curve shows the ${\mu }^{+}{\nu }_{\mu }$ signal and the black dot-dashed curve shows the ${\tau }^{+}{\nu }_{\tau }$ signal. The purple long-dashed line shows the non-$D_s^{+}$ background while the green dashed line shows the real-$D_s^{+}$ background. The blue curve shows the sum of all these contributions.