Three sterile neutrinos inE6

Abstract

Candidates for unification of the electroweak and strong interactions include the grand unified groups SU(5), SO(10), and the exceptional group ${\mathrm{E}}_{6}$. The 27-dimensional fundamental representation of ${\mathrm{E}}_{6}$ contains exotic fermions, including weak isosinglet quarks of charge $\ensuremath{-}1/3$, vectorlike weak isodoublet leptons, and neutral leptons which are singlets under both left-handed and right-handed SU(2). These last are candidates for light ``sterile'' neutrinos, hinted at by some recent short-baseline neutrino experiments.In order to accommodate three families of quarks and charged leptons, an ${\mathrm{E}}_{6}$ model must contain three 27-plets, each of which contains a sterile neutrino candidate $n$. The mixing pattern within a 27-plet is described, and experimental consequences are discussed.