Lepton mass matrix models

Abstract

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 j ) ∼ sin 2 θ ij ; m(ℓ − i )/ m(ℓ − j )≲sinθ ij ; m(ν i )/ m(ν j ) ≳m 2(ℓ − i/m 2(ℓ − j; m(ν e ≲ m(ν μ) ≲(ν τ). The relations between neutrino masses and mixings may become exact if the horizontal symmetry together with holomorphy 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.