Non-leptonic beauty baryon decays and $CP$-asymmetries based on $SU(3)$-Flavor analysis

TL;DR

This paper uses $SU(3)$ flavor symmetry to analyze non-leptonic beauty baryon decays, deriving relations between decay amplitudes and $CP$ asymmetries that hold even with symmetry breaking.

Contribution

It introduces an $SU(3)$-based framework for analyzing beauty baryon decays without specific dynamical assumptions, accounting for arbitrary symmetry breaking.

Findings

Derived sum rule relations between decay amplitudes.

Established relations between $CP$ asymmetries.

Identified symmetry-breaking independent relations.

Abstract

We consider hadronic weak decays of beauty-baryons into charmless baryons and pseudoscalar mesons in a general framework based on $SU(3)$ decomposition of the decay amplitudes. The advantage of the approach lies in the ability to perform an $SU(3)$ analysis of these decays without any particular set of dynamical assumptions while accounting for the effects of an arbitrarily broken $SU(3)$ flavor symmetry. Dictated by the symmetries of the effective Hamiltonian that allow us to relate or neglect reduced $SU(3)$ amplitudes, we 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.