Measurements of the branching fractions of the semileptonic decays ${\mathrm{\Xi }}_c^0\to {\mathrm{\Xi }}^{-}{\mathrm{\ell }}^{+}{\nu }_{\mathrm{\ell }}$ and the asymmetry parameter of ${\mathrm{\Xi }}_c^0\to {\mathrm{\Xi }}^{-}{\pi }^{+}$

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 ${\mathrm{\Xi }}_c^0\to {\mathrm{\Xi }}^{-}{\mathrm{\ell }}^{+}{\nu }_{\mathrm{\ell }}$ ($\mathrm{\ell }=e$ or $\mu$) and the $CP$-asymmetry parameter of ${\mathrm{\Xi }}_c^0\to {\mathrm{\Xi }}^{-}{\pi }^{+}$ 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${\cal B}(\Xi_{c}^{0} \to \Xi^{-} \mu^{+} \nu_{\mu})=(1.27 \pm 0.06 \pm 0.10 \pm 0.37)%$,andthedecayparameter$\alpha_{\Xi\pi}$ismeasuredtobe$0.63 \pm 0.03 \pm 0.01$ 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 ${\mathrm{\Xi }}_c^0\to {\mathrm{\Xi }}^{-}{\pi }^{+}$ branching fraction.