The Unique Horizontal Symmetry of Leptons

TL;DR

This paper demonstrates that the minimal horizontal symmetry group for leptons, consistent with the tri-bimaximal neutrino mixing matrix, is uniquely identified as the permutation group S_4, based on a group-theoretical analysis.

Contribution

The paper establishes the unique identification of S_4 as the minimal horizontal symmetry group for leptons using a group-theoretical approach.

Findings

S_4 is the minimal horizontal symmetry group for leptons

Connection between fermion mixing matrices and symmetry groups

Application to tri-bimaximal neutrino mixing

Abstract

There is a group-theoretical connection between fermion mixing matrices and minimal horizontal symmetry groups. Applying this connection to the tri-bimaximal neutrino mixing matrix, we show that the minimal horizontal symmetry group for leptons is uniquely $S_4$, the permutation group of four objects.