Lepton Mass Matrix Models

The smallness and hierarchy in fermion parameters could be the result of selection rules due to an Abelian horizontal symmetry broken by a small parameter. When applied to the lepton sector, then for a large class of models, a number of interesting order of magnitude relations arise: with i < j, m(ν i)/m(ν j) ∼ sin 2 θ ij ; m(ℓ − i)/m(ℓ − j) < ∼ sin θ ij ; m(ν i)/m(ν j) > ∼ m 2 (ℓ − i)/m 2 (ℓ − j); m(ν e) < ∼ m(ν µ) < ∼ m(ν τ). The relations between neutrino masses and mixings may become exact if the horizontal symmetry together with holomor-phy induce certain zero entries in the lepton mass matrices. A full high energy theory is likely to include scalars with flavor changing couplings and heavy leptons in vector representations ; however, the masses of these particles are too heavy to be directly observed in experiment. Indirect evidence for the horizontal symmetry may arise from other sectors of the theory: non-degenerate sleptons are allowed as the symmetry aligns lepton and slepton mass matrices; light leptoquarks are allowed as the symmetry can make their couplings diagonal and chiral.