Measurement of the Absolute Branching Fraction of ${D}_{s}^{+}\to {\tau }^{+}{\nu }_{\tau }$ via ${\tau }^{+}\to {e}^{+}{\nu }_{e}{\overline{\nu }}_{\tau }$

Using a dataset of $6.32\text{}\text{}{\mathrm{fb}}^{-1}$ 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 ${\tau }^{+}\to {e}^{+}{\nu }_{e}{\overline{\nu }}_{\tau }$, and find ${B}_{{D}_{s}^{+}\to {\tau }^{+}{\nu }_{\tau }}=\left(5.27±0.10±0.12\right)×{10}^{-2}$, 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 $|{V}_{cs}|=0.978±0.009±0.012$ and ${f}_{{D}_{s}^{+}}=\left(251.1±2.4±3.0\right)\text{}\text{}\mathrm{MeV}$, respectively. Combining our result with the world averages of ${B}_{{D}_{s}^{+}\to {\tau }^{+}{\nu }_{\tau }}$ and ${B}_{{D}_{s}^{+}\to {\mu }^{+}{\nu }_{\mu }}$, we obtain the ratio of the branching fractions ${B}_{{D}_{s}^{+}\to {\tau }^{+}{\nu }_{\tau }}/{B}_{{D}_{s}^{+}\to {\mu }^{+}{\nu }_{\mu }}=9.72±0.37$, which is consistent with the standard model prediction of lepton flavor universality.