Neutrino Phenomenology from Unconventional E$_6$ models

Abstract

Superstring derived $\E$ models can accommodate small neutrino masses if a discrete symmetry is imposed which forbids tree level Dirac neutrino masses but allows for radiative mass generation. The only possible symmetries of this kind are known to be generation dependent. We explore the possibility that, as a consequence of such a symmetry, the three sets of light states in each generation do not have the same assignments with respect to the {\bf 27} of $E_6$, implying that the gauge interactions under the additional $U(1)^\pr$ factors are non universal. Models realising such a scenario are found to be viable, and by requiring the number of light neutral states to be minimal, an almost unique pattern of neutrino masses and mixings arises. We briefly discuss a model in which, with a natural choice of the parameters, $m_{ν_τ}\sim 0.1-10\,$eV is generated at one loop, $m_{ν_μ} \sim 10^{-3}\,$eV is generated at two loops and ${ν_e}$ remains massless.