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In the standard model, the permutation symmetry among the three generationsof fundamental fermions is usually regarded to be broken by the Higgscouplings. It is found that the symmetry is restored if we include the massmatrix parameters as physical variables which transform appropriately under thesymmetry operation. Known relations between these variables, such as therenormalization group equations, as well as formulas for neutrino oscillations(in vacuum and in matter), are shown to be covariant tensor equations under thepermutation symmetry group.

Flavor Mixing and the Permutation Symmetry among Generations