$CP$-violating polarization asymmetry in charmless two-body decays of beauty baryons

Several baryons containing a heavy b-quark, the b-baryons, have been discovered. The charmless two-body decays of b-baryons can provide a new platform for $CP$ violating studies in a similar way provided by charmless two-body decays of B-meson. There are new $CP$ violating observables related to baryon polarization in b-baryon decays. We show that in the flavor $SU(3)$ limit, there exists relations involving different combinations of the decay amplitudes compared with those in $CP$ violating rate asymmetry. These new relations therefore provide interesting tests for the mechanism of $CP$ violations in the standard model (SM) and flavor $SU(3)$ symmetry. Such tests could complement the b-meson decay studies which hint at a better flavor $SU(3)$ conservation in b-hadron decays than in kaon and hyperon decays. Future data from LHCb can provide new information about $CP$ violation in the SM.