Horizontal symmetries of leptons with a massless neutrino

الأصل · EN

Residual symmetry Gν of neutrino mass matrix with a massless neutrino and embedding of Gν and the residual symmetry Gₗ of the charged lepton mass matrix into finite discrete groups G is discussed. Massless neutrino results if Gν and hence G are subgroups of U(3) rather than of SU(3). Structure of the resulting leptonic mixing matrix UPMNS is discussed in three specific examples based on groups (a) Σ(3N³), (b) Σ(2N²) and (c) S₄(2) ≡ A₄ Z₄. Σ(3N³) groups are able to reproduce either the second or the third column of UPMNS correctly. Σ(2N²) groups lead to prediction θ₁₃=0, θ₂₃=π4 for the reactor and atmospheric mixing angles respectively if neutrino mass hierarchy is inverted. Solar angle remains undetermined in this case. This also gets determined when G=S₄(2) which can give bi-maximal mixing for inverted hierarchy. Examples (b) and (c) provide a good zeroth order approximation to realistic leptonic mixing with a massless neutrino. We also present an example of the specific model based on S₄(2) symmetry in which a massless neutrino and viable leptonic mixing angles are obtained.