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(nu(i))/m(nu(j)) similar to sin(2) theta(ij); m(l(i)(-))/m(l(j)(-))less than or equal to sin theta(ij); m(nu(i))/m(nu(j)) greater than or equal to m(2)(l(i)(-))/m(2)(l(j)(-)); m(nu(e)) less than or equal to m(nu(mu)) less than or equal to (nu(tau)). 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.