Measurement of the branching fraction of $D_s^+\to τ^+ ν_τ$ via $τ^+ \to μ^+ ν_μ\bar{ν_τ}$

Abstract

Utilizing $7.33~\mathrm{fb}^{-1}$ of $e^+e^-$ collision data taken at the center-of-mass energies of 4.128, 4.157, 4.178, 4.189, 4.199, 4.209, 4.219, and 4.226 GeV with the BESIII detector, the branching fraction of the leptonic decay $D_s^+\toτ^+ν_τ$ via $τ^+\toμ^+ν_μ\bar ν_τ$ is measured to be $\mathcal{B}_{D_s^+\toτ^+ν_τ}=(5.34\pm0.16_{\rm stat}\pm0.10_{\rm syst})\%$. Combining this branching fraction with the world averages of the measurements of the masses of $τ^+$ and $D_s^+$ as well as the lifetime of $D_s^+$, we extract the product of the decay constant of $D_s^+$ and the $c\to s$ Cabibbo-Kobayashi-Maskawa matrix element to be $f_{D_s^+}|V_{cs}|=(246.2\pm3.7_{\rm stat}\pm2.5_{\rm syst})~\mathrm{MeV}$. Taking $|V_{cs}|$ from a global fit in the standard model we obtain $f_{D_s^+}=(252.7\pm3.8_{\rm stat}\pm2.6_{\rm syst})$ MeV. Conversely, taking $f_{D_s^+}$ from lattice quantum chromodynamics calculations, we obtain $|V_{cs}| = 0.984\pm0.015_{\rm stat}\pm0.010_{\rm syst}$.

26 pages, 8 figures