Measurement of the branching fraction of leptonic decay $D_s^{+}\to \ddot{I}{„}^{+}\hat{I}{½}_{\ddot{I}}„$ via $\ddot{I}{„}^{+}\to \ddot{I}{€}^{+}\ddot{I}{€}^0\bar{\hat{I}}{½}_{\ddot{I}}„$

Abstract

By analyzing $6.32{\mathrm{fb}}^{-1}$ of $e^{+}{e}^{-}$ annihilation data collected at the center-of-mass energies between 4.178 and 4.226\,GeV with the BESIII detector, we determine the branching fraction of the leptonic decay $D_s^{+}\to \ddot{I}{„}^{+}\hat{I}{½}_{\ddot{I}}„$ with $\ddot{I}{„}^{+}\to \ddot{I}{€}^{+}\ddot{I}{€}^0\bar{\hat{I}}{½}_{\ddot{I}}„$, to be ${\mathcal{B}}_{D_s^{+}\to \ddot{I}{„}^{+}\hat{I}{½}_{\ddot{I}}„}=(5.29\pm 0.25_{\mathrm{stat}}\pm 0.20_{\mathrm{syst}})\%$. We estimate the product of the Cabibbo-Kobayashi-Maskawa matrix element $|V_{cs}|$ and the $D_s^{+}$ decay constant $f_{D_s^{+}}$ to be $f_{D_s^{+}}|V_{cs}|=(244.8\pm 5.8_{\mathrm{stat}}\pm 4.8_{\mathrm{syst}})\mathrm{MeV}$ using the known values of the $\ddot{I}{„}^{+}$ and $D_s^{+}$ masses as well as the $D_s^{+}$ lifetime, together with our branching fraction measurement. Combining with the value of $|V_{cs}|$ obtained from a global fit in the standard model and $f_{D_s^{+}}$ from lattice quantum chromodynamics, we obtain $f_{D_s^{+}}=(251.6\pm 5.9_{\mathrm{stat}}\pm 4.9_{\mathrm{syst}})$\,MeV and $|V_{cs}|=0.980\pm 0.023_{\mathrm{stat}}\pm 0.019_{\mathrm{syst}}$.