Lepton mass matrix models Original Research Article

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(νi)/m(νjj) ∼ sin2 θ ij; m(ℓ−i)/m(ℓ−j)≲sinθij;m(νi)/m(νj) ≳m2(ℓ−i/m2(ℓ−j; m(νe ≲ m(νμ) ≲(ντ). 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.