Predictive $CP$ Violating Relations for Charmless Two-body Decays of Beauty Baryons $\Xi^{-,\;0}_b$ and $\Lambda_b^0$ With Flavor $SU(3)$ Symmetry

Several baryons containing a heavy b-quark have been discovered. The decays of these states provide new platform for testing the standard model (SM). We study $CP$ violation in SM for charmless two-body decays of the flavor $SU(3)$ anti-triplet beauty baryon (b-baryon) ${\cal B} = (\Xi^-_b,\;\Xi^0_b,\;\Lambda_b^0)$ in a model independent way. We found, in the flavor $SU(3)$ symmetry limit, a set of new predictive relations among the branching ratio $Br$ and $CP$ asymmetry $A_{CP}$ for $\cal B$ decays, such as $A_{CP}(\Xi_b^-\to K^0 \Xi^-)/A_{CP}(\Xi_b^-\to \bar K^0 \Sigma^-) = - Br(\Xi_b^- \to \bar K^0 \Sigma^-)/Br(\Xi_b^- \to K^0 \Sigma^-)$, $A_{CP}(\Lambda_b^0 \to \pi^- p)/A_{CP} (\Xi^0_b \to K^- \Sigma^+) = -Br(\Xi^0_b \to K^- \Sigma^+)\tau_{\Lambda_b^0}/Br(\Lambda_b^0 \to \pi^- p)\tau_{\Xi^0_b}$,and $A_{CP}(\Lambda_b^0 \to K^- p)/ A_{CP} (\Xi^0_b \to \pi^- \Sigma^+) = -Br(\Xi^0_b \to \pi^- \Sigma^+)\tau_{\Lambda_b^0}/ Br(\Lambda_b^0 \to K^- p)\tau_{\Xi^0_b}$. Future data from LHCb can test these relations and also other relations found.