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An approach to permutation symmetry for the electroweak theory
The form of the leptonic mixing matrix emerging from experiment has, in the
last few years, generated a lot of interest in the so-called tribimaximal type.
This form may be naturally associated with the possibility of a discrete
permutation symmetry () among the three generations. However, trying to
implement this attractive symmetry has resulted in some problems and it seems
to have fallen out of favor. We suggest an approach in which the holds to
first approximation, somewhat in the manner of the old SU(3) flavor symmetry of
the three flavor quark model. It is shown that in the case of the neutrino
sector, a presently large experimentally allowed region can be fairly well
described in this first approximation.
We briefly discuss the nature of the perturbations which are the analogs of
the Gell-Mann Okubo perturbations but confine our attention for the most part
to the invariant model. We postulate that the invariant mass
spectrum consists of non zero masses for the and zero masses for
the other charged fermions but approximately degenerate masses for the three
neutrinos. The mixing matrices are assumed to be trivial for the charged
fermions but of tribimaximal type for the neutrinos in the first approximation.
It is shown that this can be implemented by allowing complex entries for the
mass matrix and spontaneous breakdown of the invariance of the
Lagrangian.Comment: 24 pages, 1 figure, minor corrections and acknowledgment added. To
appear in IJM
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