Chirality and Symmetry Breaking in a discrete internal Space

TL;DR

This paper proposes that a discrete internal symmetry space modeled by the pyritohedral group A_4 x Z_2 explains the mass structure of fermion generations and links chirality in this symmetry to parity violation in weak interactions.

Contribution

It introduces the pyritohedral group A_4 x Z_2 as a better symmetry model than S_4 for elementary particles, connecting internal symmetry chirality to weak interaction parity violation.

Findings

A_4 x Z_2 symmetry matches fermion mass multiplets

Chirality of A_4 explains weak interaction parity violation

Symmetry breaking from S_4 to A_4 underpins particle structure

Abstract

In previous papers the permutation group S_4 has been suggested as an ordering scheme for elementary particles, and the appearance of this finite symmetry group was taken as indication for the existence of a discrete inner symmetry space underlying elementary particle interactions. Here it is pointed out that a more suitable choice than the tetrahedral group S_4 is the pyritohedral group A_4 x Z_2 because its vibrational spectrum exhibits exactly the mass multiplet structure of the 3 fermion generations. Furthermore it is noted that the same structure can also be obtained from a primordial symmetry breaking S_4 --> A_4. Since A_4 is a chiral group, while S_4 is achiral, an argument can be given why the chirality of the inner pyritohedral symmetry leads to parity violation of the weak interactions.