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

TL;DR

This paper analyzes charmless weak decays of beauty baryons into decuplet baryons and mesons using $SU(3)$-flavor symmetry, deriving sum rules and $CP$ asymmetry relations that account for symmetry breaking.

Contribution

It provides a comprehensive $SU(3)$-flavor decomposition framework for these decays, including symmetry-breaking effects, and compares it with quark diagram approaches.

Findings

Derived sum rule relations between decay amplitudes.

Identified $CP$ asymmetry relations valid under $SU(3)$ breaking.

Compared $SU(3)$-based analysis with quark diagram approach.

Abstract

We consider charmless weak decays of beauty-baryons into decuplet baryons and pseudoscalar mesons in a general framework based on $SU(3)$-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 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.