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Semidirect Product Groups, Vacuum Alignment and Tribimaximal Neutrino Mixing
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.Comment: Typos fixed, 26 pages in LaTe
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