Two-loop Radiative Neutrino Mechanism in an $SU(3)_L\times U(1)_N$ Gauge Model

Abstract

By using the $L_e$ - $L_μ$ - $L_τ$ symmetry, we construct an $SU(3)_L\times U(1)_N$ gauge model that provides two-loop radiative neutrino masses as well as one-loop radiative neutrino masses. The generic smallness of two-loop neutrino masses leading to $Δm^2_\odot$ compared with one-loop neutrino masses leading to $Δm^2_{atm}$ successfully explains $Δm^2_{atm}$ $>>$ $Δm^2_{\odot}$ by invoking the $L_e$ - $L_μ$ - $L_τ$ breaking. The Higgs scalar ($h^+$) that initiates radiative mechanisms is unified into a Higgs triplet together with the standard Higgs scalar ($ϕ^+$, $ϕ^0$) to form ($ϕ^+$, $ϕ^0$, $h^+$), which calls for three families of lepton triplets: ($ν^i_L$, $\ell^i_L$, $ω^i_L$) (i = 1,2,3), where $ω^i$ denote heavy neutral leptons. The two-loop radiative mechanism is found possible by introducing a singly charged scalar, which couples to $\ell^i_Rω^j_R$ (i,j = 2,3).