"Hidden" O(2) and SO(2) Symmetry in Lepton Mixing

TL;DR

This paper explores how implementing O(2) or related symmetries in lepton mixing models can naturally produce the observed neutrino mixing patterns, including large theta_13, through a minimal three-Higgs-doublet model.

Contribution

It introduces a minimal model with O(2) symmetry that explains neutrino mixing angles and mass differences, including the spontaneous symmetry breaking mechanism.

Findings

O(2) symmetry generates minimal neutrino mass matrix with free solar mixing angle.

Flavor-democratic perturbations lead to tri-bimaximal mixing.

Model achieves large theta_13 and small Delta m_sol^2 = 0 through symmetry decomposition.

Abstract

To generate the minimal neutrino Majorana mass matrix that has a free solar mixing angle and Delta m_sol^2 = 0 it suffices to implement an O(2) symmetry, or one of its subgroups SO(2), Z_N (N>2), or D_N (N>2). This O(2) generalizes the hidden Z_2^s of lepton mixing and leads in addition automatically to mu-tau symmetry. Flavor-democratic perturbations, as expected e.g. from the Planck scale, then result in tri-bimaximal mixing. We present a minimal model with three Higgs doublets implementing a type-I seesaw mechanism with a spontaneous breakdown of the symmetry, leading to large theta_13 and small Delta m_sol^2 = 0 due to the particular decomposition of the perturbations under mu-tau symmetry.