Beauty baryon non-leptonic decays into decuplet baryons and $CP$-asymmetries based on $SU(3)$-Flavor analysis

We consider charmless weak decays of beauty baryons into decuplet baryons and pseudoscalar mesons in a general framework based on the SU(3)-flavor decomposition of the decay amplitudes. The dynamical assumption independent SU(3) analysis accounts for the effects of an arbitrarily broken SU(3) symmetry in these decays. An alternative approach in terms of quark diagrams is also provided and compared with the SU(3) decomposition in the limit of an exact SU(3)-flavor symmetry. Furthermore, the symmetries of the effective Hamiltonian is used to relate or neglect reduced SU(3) amplitudes to derive several sum rule relations between amplitudes and relations between CP asymmetries in these decays and identify those that hold even if SU(3) is broken.