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 $i<j$, $m({\nu }_i)/m({\nu }_j)\sim {\sin }^2{\theta }_{ij}$; $m({\ell }_i^{-})/m({\ell }_j^{-})\text{lsim}\sin {\theta }_{ij}$; $m({\nu }_i)/m({\nu }_j)\text{gsim}{m}^2({\ell }_i^{-})/m^2({\ell }_j^{-})$; $m({\nu }_e)\text{lsim}m({\nu }_{\mu })\text{lsim}m({\nu }_{\tau })$. 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.

Comments: 25 pages, uses harvmac; no figures