Semidirect Product Groups, Vacuum Alignment and Tribimaximal Neutrino Mixing

Understand

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.