Quantum number conservation in intergenerational interactions

TL;DR

This paper explores how quantum number conservation applies to intergenerational interactions of quarks and mesons, considering SU(3) representations, the CKM matrix, and the structure of J=0 mesons.

Contribution

It clarifies the application of quantum number conservation laws to quark interactions, incorporating SU(3) representations and the CKM matrix, and relates meson structures to SU(6) generators.

Findings

Quantum numbers are conserved in fermion and meson interactions.

SU(6) generators correspond to quark/anti-quark structures of J=0 mesons.

Applications include accounting for the CKM matrix in interaction processes.

Abstract

The seven binary quantum numbers that distinguish fundamental fermions have been shown to be conserved in decays and interactions. Here applications of this law are clarified to take account of odd (uct) and even (dsb) parity quarks defining separate representations of SU(3), each with its own definition of the F and G quantum numbers that distinguish generations. These representations are related by the CKM unitary matrix. The SU(3) groups define an SU(6) $\equiv$ SU(3)$\otimes$U(1)$\otimes$SU(3) group of transformations of all six quarks. Quark/anti-quark structures of J=0 mesons are shown to correspond to all the SU(6) generators. Applications of quantum number conservation to fermion and meson interactions, which take account of the CKM matrix, are described.