Measurements of the branching fractions of the semileptonic decays $Ξ_{c}^{0} \to Ξ^{-} \ell^{+} ν_{\ell}$ and the asymmetry parameter of $Ξ_{c}^{0} \to Ξ^{-} π^{+}$
Using data samples of 89.5 and 711 fb$^{-1}$ recorded at energies of $\sqrt{s}=10.52$ and $10.58$ GeV, respectively, with the Belle detector at the KEKB $e^+e^-$ collider, we report measurements of branching fractions of semileptonic decays $Ξ_{c}^{0} \to Ξ^{-} \ell^{+} ν_{\ell}$ ($\ell=e$ or $μ$) and the $CP$-asymmetry parameter of $Ξ_{c}^{0} \to Ξ^{-} π^{+}$ decay. The branching fractions are measured to be ${\cal B}(Ξ_{c}^{0} \to Ξ^{-} e^{+} ν_{e})=(1.31 \pm 0.04 \pm 0.07 \pm 0.38)\%$ and ${\cal B}(Ξ_{c}^{0} \to Ξ^{-} μ^{+} ν_μ)=(1.27 \pm 0.06 \pm 0.10 \pm 0.37)\%$, and the decay parameter $α_{Ξπ}$ is measured to be $0.63 \pm 0.03 \pm 0.01$ with much improved precision compared to the current world average. The corresponding ratio ${\cal B}(Ξ_{c}^{0} \to Ξ^{-} e^{+} ν_{e})/{\cal B}(Ξ_{c}^{0} \to Ξ^{-} μ^{+} ν_μ)$ is $1.03 \pm 0.05\pm 0.07$, which is consistent with the expectation of lepton flavor universality. The first measured asymmetry parameter ${\cal A}_{CP} = (α_{Ξ^{-}π^{+}} + α_{\barΞ^{+}π^{-}})/(α_{Ξ^{-}π^{+}} - α_{\barΞ^{+}π^{-}}) = 0.024 \pm 0.052 \pm 0.014$ is found to be consistent with zero. The first and the second uncertainties above are statistical and systematic, respectively, while the third ones arise due to the uncertainty of the $Ξ_{c}^{0} \to Ξ^{-} π^+$ branching fraction.