Large solar neutrino mixing and radiative neutrino mechanism

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 fh+∼fh− and μ+∼μ−, where fh+ (fh−) and μ+ (μ−) stand for h+ (h′+) couplings, respectively, to leptons and to Higgs scalars.