Updated measurement of the branching fraction of $D_s^+ \to \tau^+ \nu_{\tau}$

Abstract

Using a dataset of 7.33 fb$^{-1}$ of $e^+ e^-$ annihilation data collected with the BESIII detector at center-of-mass energies from 4.128 to 4.226 GeV, we report an updated measurement of the branching fraction of $D_s^+ \to \tau^+ \nu_{\tau}$ via four $\tau^+$ decay modes: $\tau^+ \to e^+ \nu_e \bar{\nu}_{\tau}$, $\mu^+ \nu_{\mu} \bar{\nu}_{\tau}$, $\pi^+\bar{\nu}_{\tau}$, and $\pi^+ \pi^{0} \bar{\nu}_{\tau}$. The branching fraction is determined to be $\mathcal{B}({D_s^+ \to \tau^+ \nu_{\tau}}) = (5.37 \pm 0.08_{\rm stat} \pm 0.06_{\rm syst})$ %. The product of the modulus of the Cabibbo-Kobayashi-Maskawa matrix element $|V_{cs}|$ and the $D_s^+$ decay constant $f_{D_s^+}$ is measured to be $f_{D_s^+} |V_{cs}| = (248.2 \pm 1.9_{\rm stat} \pm 1.4_{\rm syst} \pm 0.6_{\rm input} \pm 0.8_{\rm EM})$ MeV. Both the branching fraction and the product $f_{D_s^+} |V_{cs}|$ are the most precise results yet obtained. Then, taking $f_{D_s^+}$ from lattice quantum chromodynamics calculations results in $|V_{cs}| = 0.993 \pm 0.008_{\rm stat} \pm 0.006_{\rm syst} \pm 0.003_{\rm input} \pm 0.003_{\rm EM}$. Conversely, one finds $f_{D_s^+} = (255.0 \pm 1.9_{\rm stat} \pm 1.4_{\rm syst} \pm 0.6_{\rm input} \pm 0.8_{\rm EM})$ MeV when taking $|V_{cs}|$ from the CKMfitter group as an input. Combining with the world average value of $D_s^+ \to \mu^+ \nu_{\mu}$, the ratio of the branching fractions between $D_s^+ \to \tau^+ \nu_{\tau}$ and $D_s^+ \to \mu^+ \nu_{\mu}$ is estimated to be $10.04 \pm 0.29$, which is consistent with the Standard Model prediction of lepton flavor universality.