We report new measurements of the branching fraction $\mathcal{B}(D_s^{+}\to {\ell }^{+}\nu )$, where ${\ell }^{+}$ is either ${\mu }^{+}$ or ${\tau }^{+}(\to {\pi }^{+}{\overline{\nu }}_{\tau })$, based on $6.32{\mathrm{fb}}^{-1}$ of electron-positron annihilation data collected by the BESIII experiment at six center-of-mass energy points between 4.178 and 4.226 GeV. Simultaneously floating the $D_s^{+}\to {\mu }^{+}{\nu }_{\mu }$ and $D_s^{+}\to {\tau }^{+}{\nu }_{\tau }$ components yields $\mathcal{B}(D_s^{+}\to {\tau }^{+}{\nu }_{\tau })=(5.21\pm 0.25\pm 0.17)\times {10}^{-2}$, $\mathcal{B}(D_s^{+}\to {\mu }^{+}{\nu }_{\mu })=(5.35\pm 0.13\pm 0.16)\times {10}^{-3}$, and the ratio of decay widths $R=\frac{\mathrm{\Gamma }(D_s^{+}\to {\tau }^{+}{\nu }_{\tau })}{\mathrm{\Gamma }(D_s^{+}\to {\mu }^{+}{\nu }_{\mu })}=9.73_{-0.58}^{+0.61}\pm 0.36$, where the first uncertainties are statistical and the second systematic. No evidence of $CP$ asymmetry is observed in the decay rates $D_s^{\pm }\to {\mu }^{\pm }{\nu }_{\mu }$ and $D_s^{\pm }\to {\tau }^{\pm }{\nu }_{\tau }$: $A_{CP}({\mu }^{\pm }\nu )=(-1.2\pm 2.5\pm 1.0)\%$ and $A_{CP}({\tau }^{\pm }\nu )=(+2.9\pm 4.8\pm 1.0)\%$. Constraining our measurement to the Standard Model expectation of lepton universality ($R=9.75$), we find the more precise results $\mathcal{B}(D_s^{+}\to {\tau }^{+}{\nu }_{\tau })=(5.22\pm 0.10\pm 0.14)\times {10}^{-2}$ and $A_{CP}({\tau }^{\pm }{\nu }_{\tau })=(-0.1\pm 1.9\pm 1.0)\%$. Combining our results with inputs external to our analysis, we determine the $c\to \overline{s}$ quark mixing matrix element, $D_s^{+}$ decay constant, and ratio of the decay constants to be $|V_{cs}|=0.973\pm 0.009\pm 0.014$, $f_{D_s^{+}}=249.9\pm 2.4\pm 3.5\mathrm{MeV}$, and $f_{D_s^{+}}/f_{D^{+}}=1.232\pm 0.035$, respectively.

• Received 23 February 2021
• Accepted 27 July 2021

DOI:https://doi.org/10.1103/PhysRevD.104.052009

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Published by the American Physical Society