Topological amplitudes of bottom baryon decays in the $SU(3{)}_F$ limit

Abstract

Motivated by the first observation of CP violation in baryon decays, we study the topological amplitudes of bottom baryon decays in the $SU(3{)}_F$ limit. The topological diagrams of the charmless two-body decays of bottom baryons are presented in detail. The linear relations between topologies and $SU(3)$ irreducible amplitudes are derived through tensor contraction and $SU(3)$ decomposition. Four amplitudes among the 13 independent amplitudes are critical to the CP asymmetries. The small CP asymmetries might indicate small relative strong phases between amplitudes $A_2$ and $A_{12,14}^{\prime }$. To avoid them, we suggest measuring CP asymmetries in the ${\Xi }_b^0\to p{K}^{-}$ and ${\Xi }_b^{-}\to {\Lambda }^0{K}^{-}$ decays. Furthermore, the Körner-Pati-Woo theorem can be tested by measuring the branching fractions of the ${\Lambda }_b^0\to {\Sigma }^0{K}_S^0$ and ${\Lambda }_b^0\to {\Sigma }^{-}{K}^{+}$ modes.

Comments: 23 pages, 1 figure, version published in CPC