Abstract
We find that the presence of a global $L_e-L_\mu-L_\tau$ ($\equiv L^\prime$) symmetry and an $S_2$ permutation symmetry for the $\mu$- and $\tau$-families supplemented by a discrete $Z_4$ symmetry naturally leads to almost maximal atmospheric neutrino mixing and large solar neutrino mixing, which arise, respectively, from type II seesaw mechanism initiated by an $S_2$-symmetric triplet Higgs scalar $s$ with $L^\prime=2$ and from radiative mechanism of the Zee type initiated by two singly charged scalars, an $S_2$-symmetric $h^+$ with $L^\prime=0$ and an $S_2$-antisymmetric $h^{\prime +}$ with $L^\prime=2$. The almost maximal mixing for atmospheric neutrinos is explained by the appearance of the democratic coupling of $s$ to neutrinos ensured by $S_2$ and $Z_4$ while the large mixing for solar neutrinos is explained by the similarity of $h^+$- and $h^{\prime +}$-couplings described by $f^h_+\sim f^h_-$ and $\mu_+\sim\mu_-$, where $f^h_+$ ($f^h_-$) and $\mu_+$ ($\mu_-$) stand for $h^+$ ($h^{\prime +}$)-couplings, respectively, to leptons and to Higgs scalars.
Highlights
3-20-1 Orido, Shimizu, Shizuoka 424-8610, Japan and Department of Physics, Tokai University 1117 KitaKaname, Hiratsuka, Kanagawa 259-1292, Japan (TOKAI-HEP/TH-0106, October, 2001)
We find that the presence of a global Le − Lμ − Lτ (≡ L′) symmetry and an S2 permutation symmetry for the μ- and τ -families supplemented by a discrete Z4 symmetry naturally leads to almost maximal atmospheric neutrino mixing and large solar neutrino mixing, which arise, respectively, from type II seesaw mechanism initiated by an S2-symmetric triplet Higgs scalar s with L′ = 2 and from radiative mechanism of the Zee type initiated by two singly charged scalars, an S2-symmetric h+ with L′ = 0 and an S2-antisymmetric h′+ with L′ = 2
The almost maximal mixing for atmospheric neutrinos is explained by the appearance of the democratic coupling of s to neutrinos ensured by S2 and Z4 while the large mixing for solar neutrinos is explained by the similarity of h+and h′+-couplings described by f+h ∼ f−h and μ+ ∼ μ−, where f+h (f−h ) and μ+ (μ−) stand for h+ (h′+)-couplings, respectively, to leptons and to Higgs scalars
Summary
In the limit of δmνμτ = 0, t23 is given by t23 = (1 − tα)/(1 + tα) from f = d + (t−231 − t23)e, which ensures the almost maximal atmospheric neutrino mixing characterized by t23 ≈ 1 because |sα| ≪ 1 for the hierarchical μ and τ mass texture. Summarizing our discussions, in the radiative mechanism based on the conservation of L′ and the invariance under the S2-transformation as well as under the discrete Z4-transformation, we have demonstrated that the almost maximal atmospheric neutrino mixing is guaranteed by the S2-symmetric coupling of s to neutrinos and the large solar neutrino mixing is derived by the radiative effects only, where the tree-level contributions from s vanish owing to the presence of S2.
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