Z(3) Flavor Symmetry and Possible Implications

TL;DR

This paper explores how Z(3) flavor symmetry, linked to gauge symmetry and topological charges, can explain neutrino mixing patterns and potentially extend to quark flavor physics.

Contribution

It proposes a novel gauge-theoretic framework for Z(3) flavor symmetry using Wilson loops, offering a topological interpretation of flavor charges.

Findings

Z(3) flavor symmetry can produce tri-bimaximal neutrino mixing

Flavor charge may be interpreted as a topological charge

Implications for quark sector are discussed

Abstract

We show in this paper that the Z(3) flavor symmetry, which can successfully produce the tri-bimaximal mixing and flavor pattern of neutrino sector, has a possible explanation in the framework of gauge symmetry by constructing a wavefunction of flavor state particles with the help of the Wilson loop. In this implementation of Z(3) flavor symmetry, we suggest that the flavor charge in weak interaction can be interpreted as a topological charge. Its possible implications and generalizations to the quark sector are also discussed.