6533b7d4fe1ef96bd1262eb6

RESEARCH PRODUCT

Updated measurement of the branching fraction of $D_s^+\to \tau^+\nu_\tau$ via $\tau^+\to\pi^+\bar{\nu}_\tau$

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We report the updated study of $D_s^+\to \tau^+\nu$ via $\tau^+\to\pi^+\bar{\nu}_\tau$ with a boosted decision trees analysis, with $7.33$ fb$^{-1}$ of $e^{+}e^{-}$ collision data collected by the BESIII detector at center-of-mass energies between $4.128$ and $4.226$~GeV. The branching fraction of $D_s^+\to \tau^+\nu_\tau$ is determined to be $(5.41\pm0.17_{\rm stat}\pm0.13_{\rm syst})\%$. The product of the $D_s^+$ decay constant $f_{D_s^+}$ and the Cabibbo-Kobayashi-Maskawa matrix element $|V_{cs}|$ is $f_{D_s^+}|V_{cs}| = (247.6\pm3.9_{\rm stat}\pm3.2_{\rm syst}\pm1.0_{\rm input})~\mathrm{MeV}$. Combining with the $|V_{cs}|$ obtained from the global fit in the Standard Model and the $f_{D_s^+}$ from the lattice quantum chromodynamics, we determine $|V_{cs}| = 0.991\pm0.015_{\rm stat}\pm0.013_{\rm syst}\pm0.004_{\rm input}$ and $f_{D_s^+} = (254.3\pm4.0_{\rm stat}\pm3.3_{\rm syst}\pm1.0_{\rm input})~\text{MeV}$, respectively. All results of $D_s^+\to\tau^+\nu_\tau$ via $\tau^+\to\pi^+\bar{\nu}_\tau$ obtained in this work supersede the BESIII previous results based on 6.32 fb$^{-1}$ of $e^+e^-$ collision data taken at center-of-mass energies between $4.178$ and $4.226$~GeV.