Analysis of angular distribution asymmetries and the associated $CP$ asymmetries in three-body decays of bottom baryons

Abstract

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 $CP$ violation in three-body decays of bottom and charmed baryons. We propose to search for such $CP$ asymmetries (1) in decays with ${\Lambda }^0$, ${\Sigma }^{\pm }$, or ${\Lambda }_c^{+}$ involved, such as ${\Lambda }_b\to {\Lambda }^{0}D$ and ${\Lambda }_b\to {\Lambda }^0\rho (770{)}^0$; and (2) in three-body decays of bottom baryons with opposite parity intermediate resonances involved. Typical examples include ${\Xi }_b^{-}\to p{K}^{-}{K}^{-}$, ${\Lambda }_b^0\to p{K}_S{\pi }^{-}$ and ${\Lambda }_b^0\to p{\pi }^0{\pi }^{-}$, in which the last decay channel is used as a toy model to illustrate of the basic idea.

Comments: 13 pages, 1 figure, discussion on a toy model added with contribution from J.-J. Qi