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

TL;DR

This paper presents precise measurements of the leptonic decay branching fractions of the $D_s^+$ meson, testing lepton universality and extracting fundamental parameters like decay constants and CKM matrix elements.

Contribution

It provides the most accurate measurements to date of $D_s^+$ leptonic decays and derives key parameters, including the decay constant and CKM matrix element, with implications for the Standard Model.

Findings

Measured $ ext{Br}(D_s^+ o au^+ u_ au)$ and $ ext{Br}(D_s^+ o \mu^+ u_\mu)$ with high precision.

Found no evidence of CP asymmetry in these decay modes.

Determined the decay constant $f_{D_s^+}$ and the CKM matrix element $|V_{cs}|$.

Abstract

We report new measurements of the branching fraction $\cal B(D_s^+\to \ell^+\nu)$, where $\ell^+$ is either $\mu^+$ or $\tau^+(\to\pi^+\bar{\nu}_\tau)$, 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 $D_s^+\to\mu^+\nu_\mu$ and $D_s^+\to\tau^+\nu_\tau$ components yields $\cal B(D_s^+\to \tau^+\nu_\tau) = (5.21\pm0.25\pm0.17)\times10^{-2}$, $\cal B(D_s^+\to \mu^+\nu_\mu) = (5.35\pm0.13\pm0.16)\times10^{-3}$, and the ratio of decay widths $R=\frac{\Gamma(D_s^+\to \tau^+\nu_\tau)}{\Gamma(D_s^+\to \mu^+\nu_\mu)} = 9.73^{+0.61}_{-0.58}\pm 0.36$, where the first uncertainties are statistical and the second systematic. No evidence of ${\it CP}$ asymmetry is observed in the decay rates $D_s^\pm\to\mu^\pm\nu_\mu$ and $D_s^\pm\to\tau^\pm\nu_\tau$: $A_{\it CP}(\mu^\pm\nu) = (-1.2\pm2.5\pm1.0)\%$ and $A_{\it CP}(\tau^\pm\nu) = (+2.9\pm4.8\pm1.0)\%$. Constraining our measurement to the Standard Model expectation of lepton universality ($R=9.75$), we find the more precise results $\cal B(D_s^+\to \tau^+\nu_\tau) = (5.22\pm0.10\pm 0.14)\times10^{-2}$ and $A_{\it CP}(\tau^\pm\nu_\tau) = (-0.1\pm1.9\pm1.0)\%$. 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 $|V_{cs}| = 0.973\pm0.009\pm0.014$, $f_{D^+_s} = 249.9\pm2.4\pm3.5~\text{MeV}$, and $f_{D^+_s}/f_{D^+} = 1.232\pm0.035$, respectively.