Analysis of angular distribution asymmetries and the associated $C\text{\hspace{0.17em}⁣}P$ asymmetries in three-body decays of bottom baryons

We introduce a set of observables representing angular distribution asymmetries, which can be viewed as a generalization of the forward-backward asymmetry of angular distributions, and can be used as an effective tool to search for $C\text{\hspace{0.17em}⁣}P$ violation in three-body decays of bottom and charmed baryons. We propose to search for such $C\text{\hspace{0.17em}⁣}P$ asymmetries (1) in decays with ${\mathrm{\Lambda }}^0$, ${\mathrm{\Sigma }}^{\pm }$, or ${\mathrm{\Lambda }}_c^{+}$ involved, such as ${\mathrm{\Lambda }}_b\to {\mathrm{\Lambda }}^{0}D$ and ${\mathrm{\Lambda }}_b\to {\mathrm{\Lambda }}^0\rho (770{)}^0$; and (2) in three-body decays of bottom baryons with opposite parity intermediate resonances involved. Typical examples include ${\mathrm{\Xi }}_b^{-}\to p{K}^{-}{K}^{-}$, ${\mathrm{\Lambda }}_b^0\to p{K}_S{\pi }^{-}$ and ${\mathrm{\Lambda }}_b^0\to p{\pi }^0{\pi }^{-}$, in which the last decay channel is used as a toy model to illustrate of the basic idea.