We report the discovery of $Xi_{c}(3055)^{0}$, observed by its decay into the final state $Lambda D^{0}$, and present the first observation and evidence of the decays of $Xi_c(3055)^{+}$ and $Xi_c(3080)^{+}$ into $Lambda D^{+}$. We also perform a combined analysis of the $Lambda D^{+}$ with the $Sigma_{c}^{++}K^{-}$ and $Sigma_{c}^{ast ++}K^{-}$ decay modes to measure the ratios of branching fractions, masses and widths with improved accuracy. We measure the ratios of branching fractions ${cal B}(Xi_{c}(3055)^{+} to Lambda D^{+})/{cal B}(Xi_{c}(3055)^{+} to Sigma_{c}^{++}K^{-})=5.09pm1.01pm0.76$, ${cal B}(Xi_{c}(3080)^{+} to Lambda D^{+})/{cal B}(Xi_{c}(3080)^{+} to Sigma_{c}^{++}K^{-})=1.29pm0.30pm0.15$, and ${cal B}(Xi_{c}(3080)^{+} to Sigma_{c}^{ast ++}K^{-})/{cal B}(Xi_{c}(3080)^{+} to Sigma_{c}^{++}K^{-})=1.07pm0.27pm0.01$, where the uncertainties are statistical and systematic. The analysis is performed using a 980 fb$^{-1}$ data sample collected with the Belle detector at the KEKB asymmetric-energy $e^{+}e^{-}$ collider.
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