Revelations of the E6/U(1)N Model: Two-Loop Neutrino Mass and Dark Matter

The E6/U(1)N gauge extension of the Supersymmetric Standard Model, first proposed by Ma, is shown to have exactly the requisite ingredients to realize the important new idea that dark matter is the origin of neutrino mass. With the implementation of a discrete Z2 × Z2 symmetry, and particle content given by three 27 representations of E6, neutrino masses are naturally generated in two loops, with candidates of dark matter in the loops. All particles of this model are expected to be at or below the TeV scale, allowing them to be observable at the LHC. The E6/U(1)N model was proposed in 1995 by one of us [1]. It is a supersymmetric model with matter content given by three 27 representations of E6, and gauge interactions of the Standard Model plus those of U(1)N , which is a linear combination of U(1)ψ and U(1)χ in the decomposition: E6 → SO(10)× U(1)ψ, (1) SO(10) → SU(5)× U(1)χ. (2) In terms of the maximal subgroup SU(3)C × SU(3)L × SU(3)R of E6, the U(1)N charge is given by [1] QN = 6YL + T3R − 9YR, (3) where T3L,3R and YL,R are the usual quantum numbers of the SU(2)× U(1) decompositions of SU(3)L,R. The particle content of a 27 multiplet of E6 is tabulated below. Table 1: Particle content of 27 of E6 under SU(3)C × SU(2)L × U(1)Y and U(1)N . Superfield SU(3)C × SU(2)L × U(1)Y U(1)N Q = (u, d) (3,2,1/6) 1 u (3, 1,−2/3) 1 e (1,1,1) 1 d (3, 1, 1/3) 2 L = (ν, e) (1, 2,−1/2) 2 h (3, 1,−1/3) −2 Ē = (E, N c E) (1, 2, 1/2) −2 h (3, 1, 1/3) −3 E = (νE, E) (1, 2,−1/2) −3 S (1, 1, 0) 5 N c (1,1,0) 0