Neutrino Mixing from $\Delta(6n^2)$ Groups

TL;DR

This paper demonstrates that direct flavour models with $ ext{Δ}(6n^2)$ groups can predict lepton mixing parameters, including angles and CP phases, in a model-independent way, aligning with experimental data and future tests.

Contribution

It provides the first model-independent predictions for lepton mixing parameters from an infinite series of $ ext{Δ}(6n^2)$ groups in direct flavour models.

Findings

Predicted mixing angles are fixed up to discrete choices.

Dirac CP phase is predicted to be 0 or π.

Sum rule relates mixing angles: $ heta_{23}=45^\u00b0 \u2212 heta_{13}/\u221a{2}$.

Abstract

Experimentally viable lepton mixing parameters can be predicted in so-called direct flavour models with Majorana neutrinos using $\Delta(6n^2)$ groups as a flavour group. In direct models, in which the flavour group is broken to a $Z_2\times Z_2$ subgroup in the neutrino sector, mixing angles and Dirac CP phase are purely predicted from symmetry. General predictions of direct models with $\Delta(6n^2)$ flavour groups are that all mixing angles are fixed up to a discrete choice and that the Dirac CP phase is $0$ or $\pi$; Furthermore, the middle column of the mixing matrix is trimaximal which yields the sum rule $\theta_{23}=45^\circ \mp \theta_{13}/\sqrt{2}$ depending on the Dirac phase. These predictions of lepton mixing parameters are compatible with recent global fit results or will be tested experimentally in the near future. It is the first time that such predictions have been obtained model-independently for an infinite series of groups.