Search for $CP$ violation in ${\mathrm{\Xi }}_c^{+}\to {\mathrm{\Sigma }}^{+}{h}^{+}{h}^{-}$ and ${\mathrm{\Lambda }}_c^{+}\to p{h}^{+}{h}^{-}$ at Belle II

We report decay-rate $CP$ asymmetries of the singly-Cabibbo-suppressed decays ${\mathrm{\Xi }}_c^{+}\to {\mathrm{\Sigma }}^{+}{h}^{+}{h}^{-}$ and ${\mathrm{\Lambda }}_c^{+}\to p{h}^{+}{h}^{-}$, with $h=K,\pi$, measured using 428 fb${}^{-1}$ of $e^{+}{e}^{-}$ collisions collected by the Belle II experiment at the SuperKEKB collider. The results, \begin{equation} A_{CP}(Ξ_c^+\toΣ^+K^+K^-) = (3.7\pm6.6\pm0.6)%, \end{equation} \begin{equation} A_{CP}(Ξ_c^+\toΣ^+π^+π^-) = (9.5\pm6.8\pm0.5)%, \end{equation} \begin{equation} A_{CP}(Λ_c^+\to pK^+K^-) = (3.9\pm1.7\pm0.7)%, \end{equation} \begin{equation} A_{CP}(Λ_c^+\to pπ^+π^-) = (0.3\pm1.0\pm0.2)%, \end{equation} where the first uncertainties are statistical and the second systematic, agree with $CP$ symmetry. From these results we derive the sums \begin{equation} A_{CP}(Ξ_c^+\toΣ^+π^+π^-) , + , A_{CP}(Λ_c^+\to pK^+K^-) = (13.4 \pm 7.0\pm 0.9)%, \end{equation} \begin{equation} A_{CP}(Ξ_c^+\toΣ^+K^+K^-) , + , A_{CP}(Λ_c^+\to pπ^+π^-) = (\phantom{0}4.0 \pm 6.6\pm 0.7)%, \end{equation} which are consistent with the $U$-spin symmetry prediction of zero. These are the first measurements of $CP$ asymmetries for individual hadronic three-body charmed-baryon decays.