Involution symmetries and the PMNS matrix

TL;DR

This paper explores how involution symmetries can be embedded into larger symmetry groups to predict elements of the PMNS matrix, advancing the understanding of leptonic mixing patterns.

Contribution

It investigates the implementation of Lam's idea by focusing on residual symmetries composed solely of involution generators.

Findings

Involution symmetries can be embedded to predict PMNS matrix elements.

A framework for implementing involution-based residual symmetries is proposed.

Potential constraints on leptonic mixing patterns are identified.

Abstract

Lam suggested that the PMNS matrix (or at least some of its elements) can be predicted by embedding the residual symmetry of the leptonic mass terms into a bigger symmetry. We analyze the possibility that the residual symmetries consist of involution generators only and explore how Lam's idea can be implemented.