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

Abstract

By using the $L_e$ - $L_{\mu }$ - $L_{\tau }$ 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 $\Delta m_{\odot }^2$ compared with one-loop neutrino masses leading to $\Delta m_{atm}^2$ successfully explains $\Delta m_{atm}^2$ $>>$ $\Delta m_{\odot }^2$ by invoking the $L_e$ - $L_{\mu }$ - $L_{\tau }$ breaking. The Higgs scalar ($h^{+}$) that initiates radiative mechanisms is unified into a Higgs triplet together with the standard Higgs scalar (${\varphi }^{+}$, ${\varphi }^0$) to form (${\varphi }^{+}$, ${\varphi }^0$, $h^{+}$), which calls for three families of lepton triplets: (${\nu }_L^i$, ${\ell }_L^i$, ${\omega }_L^i$) (i = 1,2,3), where ${\omega }^i$ denote heavy neutral leptons. The two-loop radiative mechanism is found possible by introducing a singly charged scalar, which couples to ${\ell }_R^i{\omega }_R^j$ (i,j = 2,3).

Comments: with 10 pages, revtex, including 2 figures, accepted for publication in Phys. Rev. D (with undefined latex citation indices removed)