arXiv2021
We report new measurements of the branching fraction $\cal B(D_s^+\to \ell^+ν)$, where $\ell^+$ is either $μ^+$ or $τ^+(\toπ^+\barν_τ)$, based on $6.32$ fb$^{-1}$ of electron-positron annihilation data collected by the BESIII experiment at six center-of-mass energy points between $4.178$ and $4.226$ GeV. Simultaneously floating the $D_s^+\toμ^+ν_μ$ and $D_s^+\toτ^+ν_τ$ components yields $\cal B(D_s^+\to τ^+ν_τ) = (5.21\pm0.25\pm0.17)\times10^{-2}$, $\cal B(D_s^+\to μ^+ν_μ) = (5.35\pm0.13\pm0.16)\times10^{-3}$, and the ratio of decay widths $R=\frac{Γ(D_s^+\to τ^+ν_τ)}{Γ(D_s^+\to μ^+ν_μ)} = 9.73^{+0.61}_{-0.58}\pm 0.36$, where the first uncertainties are statistical and the second systematic. No evidence of ${\it CP}$ asymmetry is observed in the decay rates $D_s^\pm\toμ^\pmν_μ$ and $D_s^\pm\toτ^\pmν_τ$: $A_{\it CP}(μ^\pmν) = (-1.2\pm2.5\pm1.0)\%$ and $A_{\it CP}(τ^\pmν) = (+2.9\pm4.8\pm1.0)\%$. Constraining our measurement to the Standard Model expectation of lepton universality ($R=9.75$), we find the more precise results $\cal B(D_s^+\to τ^+ν_τ) = (5.22\pm0.10\pm 0.14)\times10^{-2}$ and $A_{\it CP}(τ^\pmν_τ) = (-0.1\pm1.9\pm1.0)\%$. Combining our results with inputs external to our analysis, we determine the $c\to \bar{s}$ quark mixing matrix element, $D_s^+$ decay constant, and ratio of the decay constants to be $|V_{cs}| = 0.973\pm0.009\pm0.014$, $f_{D^+_s} = 249.9\pm2.4\pm3.5~\text{MeV}$, and $f_{D^+_s}/f_{D^+} = 1.232\pm0.035$, respectively.