How to Evade a No-Go Theorem in Flavor Symmetries

TL;DR

This paper reviews a no-go theorem in flavor symmetries that limits the incorporation of flavor symmetries into certain mass matrix models due to SU(2)_L constraints, and discusses three potential ways to bypass this limitation.

Contribution

It analyzes the no-go theorem in flavor symmetries and explores three methods to evade its constraints within mass matrix models.

Findings

The no-go theorem is based on SU(2)_L symmetry constraints.

Three possible strategies to evade the theorem are proposed.

The paper clarifies limitations and potential solutions in flavor symmetry models.

Abstract

A no-go theorem in flavor symmetries is reviewed. The theorem asserts that we cannot bring any flavor symmetry into mass matrix model in which number of Higgs scalars is, at most, one for each sector (e.g. H_u and H_d for up- and down-quark sectors, respectively). Such the strong constraint comes from the SU(2)_L symmetry. Possible three options to evade the theorem are discussed.