Measurement of the absolute branching fractions for purely leptonic $D_s^{+}$ decays

Abstract

We report new measurements of the branching fraction $\mathcal{B}({\mathcal{D}}_s^{+}\to {\ell }^{+}\hat{\mathcal{I}}½)$, where ${\ell }^{+}$ is either $\hat{I}{¼}^{+}$ or $\ddot{I}{„}^{+}(\to \ddot{I}{€}^{+}\bar{\hat{I}}{½}_{\ddot{I}}„)$, based on $6.32$ 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 $D_s^{+}\to \hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼$ and $D_s^{+}\to \ddot{I}{„}^{+}\hat{I}{½}_{\ddot{I}}„$ components yields $\mathcal{B}({\mathcal{D}}_s^{+}\to \ddot{\mathcal{I}}{„}^{+}\hat{\mathcal{I}}{½}_{\ddot{\mathcal{I}}}„)=(5.21\pm 0.25\pm 0.17)\times 10^{-2}$, $\mathcal{B}({\mathcal{D}}_s^{+}\to \hat{\mathcal{I}}{¼}^{+}\hat{\mathcal{I}}{½}_{\hat{\mathcal{I}}}¼)=(5.35\pm 0.13\pm 0.16)\times 10^{-3}$, and the ratio of decay widths $R=\frac{\hat{I}“(D_s^{+}\to \ddot{I}{„}^{+}\hat{I}{½}_{\ddot{I}}„)}{\hat{I}“(D_s^{+}\to \hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼)}=9.73_{-0.58}^{+0.61}\pm 0.36$, where the first uncertainties are statistical and the second systematic. No evidence of $CP$ asymmetry is observed in the decay rates $D_s^{\pm }\to \hat{I}{¼}^{\pm }\hat{I}{½}_{\hat{I}}¼$ and $D_s^{\pm }\to \ddot{I}{„}^{\pm }\hat{I}{½}_{\ddot{I}}„$: $A_{CP}(\hat{I}{¼}^{\pm }\hat{I}½)=(-1.2\pm 2.5\pm 1.0)\%$ and $A_{CP}(\ddot{I}{„}^{\pm }\hat{I}½)=(+2.9\pm 4.8\pm 1.0)\%$. Constraining our measurement to the Standard Model expectation of lepton universality ($R=9.75$), we find the more precise results $\mathcal{B}({\mathcal{D}}_s^{+}\to \ddot{\mathcal{I}}{„}^{+}\hat{\mathcal{I}}{½}_{\ddot{\mathcal{I}}}„)=(5.22\pm 0.10\pm 0.14)\times 10^{-2}$ and $A_{CP}(\ddot{I}{„}^{\pm }\hat{I}{½}_{\ddot{I}}„)=(-0.1\pm 1.9\pm 1.0)\%$. Combining our results with inputs external to our analysis, we determine the $c\to \bar{s}$ quark mixing matrix element, $D_s^{+}$ decay constant, and ratio of the decay constants to be $|V_{cs}|=0.973\pm 0.009\pm 0.014$, $f_{D_s^{+}}=249.9\pm 2.4\pm 3.5\text{MeV}$, and $f_{D_s^{+}}/f_{D^{+}}=1.232\pm 0.035$, respectively.

Minor revisions, version accepted by PRD