Neutrino masses in $E_6$ model

Abstract

A neutrino mass model in supersymmetric extended gauge theories is constructed. Particle contents belong to the 27 of $E_6$ and gauge group is extended to include additional U(1) is one of the subgroups of $E_6$. Then there are five neutrinos in each generation. In the unconventional charge embedding, two neutrinos are remained light. The mixing of these two neutrinos can explain the solar neutrino problem if the mass scales of exotic particles are suitably chosen. At the same time Hot Dark Matter (HDM) can be explained by these neutrinos. To avoid the phenominological problems, discrete $Z_2$ symmetry is introduced. This discrete symmetry is broken a little to give the mixing of two light neutrinos. Through these schemes, a successful model is obtained.