Measurement of the Absolute Branching Fraction of $D_s^+ \to \tau^+ \nu_{\tau}$ via $\tau^+ \to e^+ \nu_e \bar{\nu}_{\tau}$

Abstract

Using a dataset of 6.32 fb$^{-1}$ of $e^+ e^-$ annihilation data collected with the BESIII detector at center-of-mass energies between 4178 and 4226 MeV, we have measured the absolute branching fraction of the leptonic decay $D_s^+ \to \tau^+ \nu_{\tau}$ via $\tau^+ \to e^+ \nu_e \bar{\nu}_{\tau}$, and find $\mathcal{B}_{D_s^+ \to \tau^+ \nu_{\tau}}=(5.27\pm0.10\pm0.12)\times10^{-2}$, where the first uncertainty is statistical and the second is systematic. The precision is improved by a factor of 2 compared to the previous best measurement. Combining with $f_{D_s^+}$ from Lattice quantum chromodynamics calculations or the $|V_{cs}|$ from the CKMfitter group, we extract $|V_{cs}|=0.978\pm0.009\pm0.012$ and $f_{D_s^+}= (251.1\pm2.4\pm3.0)$ MeV, respectively. Combining our result with the world averages of $\mathcal{B}_{D_s^+ \to \tau^+ \nu_{\tau}}$ and $\mathcal{B}_{D_s^+ \to \mu^+ \nu_{\mu}}$, we obtain the ratio of the branching fractions $\mathcal{B}_{D_s^+ \to \tau^+ \nu_{\tau}} / \mathcal{B}_{D_s^+ \to \mu^+ \nu_{\mu}} = 9.72\pm0.37$, which is consistent with the standard model prediction of lepton flavor universality.