Study of $\it{\Lambda}_{\it{b}}^\rm{0}$ and $\it{\Xi}_{\it{b}}^\rm{0}$ decays to $\it{\Lambda} h^+h^{'-}$ and evidence for $CP$ violation in $\it{\Lambda}_{\it{b}}^\rm{0}\to\it{\Lambda} K^+K^-$ decays

A study of $\it{\Lambda}_{\it{b}}^\rm{0}$ and $\it{\Xi}_{\it{b}}^\rm{0}$ decays to $\it{\Lambda} h^{+} h^{\prime -}$ $(h^{(\prime)}=\pi, K)$ is performed using $pp$ collision data collected by the LHCb experiment during LHC Runs 1$-$2, corresponding to an integrated luminosity of $9~\rm{fb}^{-1}$. The branching fractions for these decays are measured using the $\it{\Lambda}_{\it{b}}^\rm{0}\to\it{\Lambda}_{\it{c}}^+(\to\it{\Lambda}\pi^+)\pi^-$ decay as control channel. The decays $\it{\Lambda}_{\it{b}}^\rm{0}\to\it{\Lambda}\pi^+\pi^-$ and $\it{\Xi}_{\it{b}}^\rm{0}\to\it{\Lambda}K^-\pi^+$ are observed for the first time. For decay modes with sufficient signal yields, $CP$ asymmetries are measured in the full and localized regions of the final-state phase space. Evidence is found for $CP$ violation in the $\it{\Lambda}_{\it{b}}^\rm{0}\to\it{\Lambda}K^+K^-$ decay, interpreted as originating primarily from an asymmetric $\it{\Lambda}_{\it{b}}^\rm{0} \to \it{N}^{*+} \it{K}^-$ decay amplitude. The measured $CP$ asymmetries for the other decays are compatible with zero.