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

Abstract

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) $\mathcal{B}=({\Xi }_b^{-},{\Xi }_b^0,{\Lambda }_b^0)$ 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 $\mathcal{B}$ decays, such as $A_{CP}({\Xi }_b^{-}\to K^0{\Xi }^{-})/A_{CP}({\Xi }_b^{-}\to {\bar{K}}^0{\Sigma }^{-})=-Br({\Xi }_b^{-}\to {\bar{K}}^0{\Sigma }^{-})/Br({\Xi }_b^{-}\to K^0{\Sigma }^{-})$, $A_{CP}({\Lambda }_b^0\to {\pi }^{-}p)/A_{CP}({\Xi }_b^0\to K^{-}{\Sigma }^{+})=-Br({\Xi }_b^0\to K^{-}{\Sigma }^{+}){\tau }_{{\Lambda }_b^0}/Br({\Lambda }_b^0\to {\pi }^{-}p){\tau }_{{\Xi }_b^0}$,and $A_{CP}({\Lambda }_b^0\to K^{-}p)/A_{CP}({\Xi }_b^0\to {\pi }^{-}{\Sigma }^{+})=-Br({\Xi }_b^0\to {\pi }^{-}{\Sigma }^{+}){\tau }_{{\Lambda }_b^0}/Br({\Lambda }_b^0\to K^{-}p){\tau }_{{\Xi }_b^0}$. Future data from LHCb can test these relations and also other relations found.

Comments: 13 pages, no figure, 6 tables, several missing terms in eq.11 are added