Generating the texture of symmetric fermion mass matrices and anomalous hierarchy patterns for the neutrinos from an extra abelian symmetry

Abstract

Assuming that a horizontal abelian (gauge) symmetry is at the origin of texture zeros in the fermion mass matrices we show how realistic mass patterns can be generated stepwise with a small number of effective operators from GUT's and string theory. It is interesting to note that, in the minimal scenario, if the up quark and the down quark mass matrices are generated simultaneously their texture is formaquivalent and contains only two zeros. Textures with more zeros (and thus more predictability) emerge if the up and down sectors are generated stepwise. This last possibility leads to rather anomalous neutrino patterns with mass degenerate neutrinos and large $\nu_{\mu} - \nu_{\tau}$ or $\nu_e - \nu_{\tau}$ mixing even in the absence of hierarchy in $M_R$, the mass matrix of the righthanded neutrinos, and as required by the LSND results if they were to be confirmed by future experiments. In contrast if the quark mass matrices have two zero entries (or less) the neutrino mass-mixing spectrum is independent of the texture structure of $M_R$ -if the latter does not contain any hierarchy of scales- and obeys the quadratic seesaw.