Measurements of the branching fractions of the semileptonic decays $\Xi_{c}^{0} \to \Xi^{-} \ell^{+} \nu_{\ell}$ and the asymmetry parameter of $\Xi_{c}^{0} \to \Xi^{-} \pi^{+}$

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 $\Xi_{c}^{0} \to \Xi^{-} \ell^{+} \nu_{\ell}$ ($\ell=e$ or $\mu$) and the $CP$-asymmetry parameter of $\Xi_{c}^{0} \to \Xi^{-} \pi^{+}$ decay. The branching fractions are measured to be ${\cal B}(\Xi_{c}^{0} \to \Xi^{-} e^{+} \nu_{e})=(1.31 \pm 0.04 \pm 0.07 \pm 0.38)\%$ and ${\cal B}(\Xi_{c}^{0} \to \Xi^{-} \mu^{+} \nu_{\mu})=(1.27 \pm 0.06 \pm 0.10 \pm 0.37)\%$, and the decay parameter $\alpha_{\Xi\pi}$ 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 ${\cal B}(\Xi_{c}^{0} \to \Xi^{-} e^{+} \nu_{e})/{\cal B}(\Xi_{c}^{0} \to \Xi^{-} \mu^{+} \nu_{\mu})$ is $1.03 \pm 0.05\pm 0.07$, which is consistent with the expectation of lepton flavor universality. The first measured asymmetry parameter ${\cal A}_{CP} = (\alpha_{\Xi^{-}\pi^{+}} + \alpha_{\bar{\Xi}^{+}\pi^{-}})/(\alpha_{\Xi^{-}\pi^{+}} - \alpha_{\bar{\Xi}^{+}\pi^{-}}) = 0.024 \pm 0.052 \pm 0.014$ 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 $\Xi_{c}^{0} \to \Xi^{-} \pi^+$ branching fraction.