Lepton Mixing Predictions from Delta(6n^2) Family Symmetry

TL;DR

This paper explores lepton mixing predictions from Delta(6n^2) family symmetry models, identifying new candidates for large n that align with recent experimental data and predicting specific mixing angles and phases.

Contribution

It develops the group theory of Delta(6n^2), finds new large n models predicting lepton mixing parameters, and connects these predictions with current and future experimental tests.

Findings

Predicts reactor angle within 3 sigma of global fits

Identifies trimaximal mixing with fixed reactor angle and phase

Derives atmospheric angle sum rules consistent with data

Abstract

We obtain predictions of lepton mixing parameters for direct models based on Delta(6n^2) family symmetry groups for arbitrarily large n in which the full Klein symmetry is identified as a subgroup of the family symmetry. After reviewing and developing the group theory associated with Delta(6n^2), we find many new candidates for large n able to yield reactor angle predictions within 3 sigma of recent global fits. We show that such Delta(6n^2) models with Majorana neutrinos predict trimaximal mixing with reactor angle theta_{13} fixed up to a discrete choice, an oscillation phase of either zero or pi and the atmospheric angle sum rules theta_{23}=45 degrees -/+ theta_{13}/sqrt{2}, respectively, which are consistent with recent global fits and will be tested in the near future.