Large Solar Neutrino Mixing in an Extended Zee Model

Abstract

The Zee model, which employs the standard Higgs scalar ($ϕ$) with its duplicate ($ϕ^\prime$) and a singly charged scalar ($h^+$), can utilize two global symmetries associated with the conservation of the numbers of $ϕ$ and $ϕ^\prime$, $N_{ϕ,ϕ^\prime}$, where $N_ϕ+N_{ϕ^\prime}$ coincides with the hypercharge while $N_ϕ-N_{ϕ^\prime}$ ($\equiv X$) is a new conserved charge, which is identical to $L_e-L_μ-L_τ$ for the left-handed leptons. Charged leptons turn out to have $e$-$μ$ and $e$-$τ$ mixing masses, which are found to be crucial for the large solar neutrino mixing. In an extended version of the Zee model with an extra triplet Higgs scalar (s), neutrino oscillations are described by three steps: 1) the maximal atmospheric mixing is induced by democratic mass terms supplied by $s$ with $X$=2 that can initiate the type II seesaw mechanism for the smallness of these masses; 2) the maximal solar neutrino mixing is triggered by the creation of radiative masses by $h^+$ with $X$ = 0; 3) the large solar neutrino mixing is finally induced by a $ν_μ$-$ν_τ$ mixing arising from the rotation of the radiative mass terms as a result of the diagonalization that converts $e$-$μ$ and $e$-$τ$ mixing masses into the electron mass.