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${}_{\hat{I}{½}_{\ddot{I}}„}\sim$m${}_{\hat{I}{½}_{\hat{I}}¼}\sim$M${}_L^2$/M${}_H$, m${}_{\hat{I}{½}_e}=0$, where M${}_L\sim 10^2$ 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${}_H^2$/M${}_R$ is predicted. First order radiative corrections will produce m${}_{\hat{I}{½}_e}\ne 0$ which is at least two orders of magnitude smaller than the other two neutrino masses.