Semidirect Product Groups, Vacuum Alignment and Tribimaximal Neutrino Mixing

TL;DR

This paper introduces a novel class of models using semidirect product groups to achieve vacuum alignment in neutrino mixing, successfully reproducing tribimaximal mixing without disrupting the family symmetry, and also accommodating quark mixing.

Contribution

It proposes a new approach with semidirect product groups to solve the vacuum alignment problem in neutrino models, maintaining desired symmetry properties.

Findings

Models reproduce tribimaximal mixing pattern.

Framework allows straightforward inclusion of quarks.

Supersymmetry can be incorporated without issues.

Abstract

The neutrino oscillation data are in very good agreement with the tribimaximal mixing pattern: \sin^2\theta_{23}=1/2, \sin^2\theta_{12}=1/3, and \sin^2\theta_{13}=0. Attempts to generate this pattern based on finite family symmetry groups typically assume that the family symmetry is broken to different subgroups in the charged lepton and the neutrino mass matrices. This leads to a technical problem, where the cross-couplings between the Higgs fields responsible for the two symmetry breaking chains force their vacuum expectation values to align, upsetting the desired breaking pattern. Here, we present a class of models based on the semidirect product group (S_3)^4 \rtimes A_4, where the lepton families belong to representations which are not faithful. In effect, the Higgs sector knows about the full symmetry while the lepton sector knows only about the A_4 factor group. This can solve the alignment problem without altering the desired properties of the family symmetry. Inclusion of quarks into the framework is straightforward, and leads to small and arbitrary CKM mixing angles. Supersymmetry is not essential for our proposal, but the model presented is easily supersymmetrized, in which case the same family symmetry solves the SUSY flavor problem.