Updated measurement of the branching fraction of ${D}_{s}^{+}\to {\tau }^{+}{\nu }_{\tau }$ via ${\tau }^{+}\to {\pi }^{+}{\overline{\nu }}_{\tau }$

This paper reports the study of ${D}_{s}^{+}\to {\tau }^{+}\nu $ via ${\tau }^{+}\to {\pi }^{+}{\overline{\nu }}_{\tau }$ using a boosted decision tree method, with $7.33\text{}\text{}{\mathrm{fb}}^{-1}$ 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 $\left(5.44±0.1{7}_{\mathrm{stat}}±0.1{3}_{\mathrm{syst}}\right)%$. The product of the ${D}_{s}^{+}$ decay constant ${f}_{{D}_{s}^{+}}$ and the Cabibbo-Kobayashi-Maskawa matrix element $|{V}_{cs}|$ is ${f}_{{D}_{s}^{+}}|{V}_{cs}|=\left(248.3±{3.9}_{\mathrm{stat}}±{3.1}_{\mathrm{syst}}±{1.0}_{\text{input}}\right)\text{}\text{}\mathrm{MeV}$. Combining with the $|{V}_{cs}|$ value obtained from the Standard Model global fit or the ${f}_{{D}_{s}^{+}}$ from the lattice quantum chromodynamics, we determine $|{V}_{cs}|=0.993±0.01{5}_{\mathrm{stat}}±0.01{2}_{\mathrm{syst}}±0.00{4}_{\text{input}}$ and ${f}_{{D}_{s}^{+}}=\left(255.0±{4.0}_{\mathrm{stat}}±{3.2}_{\mathrm{syst}}±{1.0}_{\text{input}}\right)\text{}\text{}\mathrm{MeV}$. The first uncertainty is statistical, the second one is systematic and the third one is due to the input parameters, mainly the lifetime of ${D}_{s}^{+}$. All results obtained in this work supersede the BESIII previous results based on $6.32\text{}\text{}{\mathrm{fb}}^{-1}$ of ${e}^{+}{e}^{-}$ collision data taken at center-of-mass energies between 4.178 and 4.226 GeV.