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 $\Xi^0_b\to pK^-$ and $\Xi^-_b\to \Lambda^0 K^-$ decays. Furthermore, the K\"orner-Pati-Woo theorem can be tested by measuring the branching fractions of the $\Lambda_b^0\to\Sigma^0K^0_S$ and $\Lambda_b^0\to\Sigma^-K^+$ modes.