The Generational Seesaw Mechanism in [SU(6)]$^{3}\times$Z$_{3}$}

Abstract

In the context of the left-right symmetric gauge group [SU(6)]$^3\times$ Z$_3$ which unifies nongravitational forces with flavors, we analyze the generational seesaw mechanism. At tree level we get m$_{\nu_\tau}\sim$m$_{\nu_\mu}\sim$M$^2_L$/M$_H$, m$_{\nu_e}=0$, where M$_L\sim10^2$ GeVs and M$_H\ge 100$ TeVs is the mass scale at which the horizontal interactions get spontaneously broken. The right handed neutrinos get a Majorana mass M$_R\gg $M$_H$ of the order of the scale where SU(2)$_R$ is broken. An exotic neutral lepton with a mass of the order of M$^2_H$/M$_R$ is predicted. First order radiative corrections will produce m$_{\nu_e}\neq0$ which is at least two orders of magnitude smaller than the other two neutrino masses.