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We consider charmless weak decays of beauty-baryons into decuplet baryons andpseudoscalar mesons in a general framework based on $SU(3)$-flavordecomposition 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 isalso provided and compared with the $SU(3)$ decomposition in the limit of exact$SU(3)$-flavor symmetry. Furthermore, the symmetries of the effectiveHamiltonian is used to relate or neglect reduced $SU(3)$ amplitudes to deriveseveral sum rule relations between amplitudes and relations between $CP$asymmetries in these decays and identify those that hold even if $SU(3)$ isbroken.

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