Measurements of the branching fractions of the semileptonic decays $Xi_{c}^{0} to Xi^{-} ell^{+} u_{ell}$ 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 $Xi_{c}^{0} to Xi^{-} ell^{+} u_{ell}$ ($ell=e$ or $mu$) and the $CP$-asymmetry parameter of $Xi_{c}^{0} to Xi^{-} pi^{+}$ decay. The branching fractions are measured to be ${cal B}(Xi_{c}^{0} to Xi^{-} e^{+} u_{e})=(1.31 pm 0.04 pm 0.07 pm 0.38)%$ and ${cal B}(Xi_{c}^{0} to Xi^{-} mu^{+} u_{mu})=(1.27 pm 0.06 pm 0.10 pm 0.37)%$, and the decay parameter $alpha_{Xipi}$ 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 ${cal B}(Xi_{c}^{0} to Xi^{-} e^{+} u_{e})/{cal B}(Xi_{c}^{0} to Xi^{-} mu^{+} u_{mu})$ is $1.03 pm 0.05pm 0.07$, 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.