Neutrino 2-3 Symmetry and Inverted Hierarchy

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Neutrino oscillation data indicate the presence of a 2-3 symmetry for the left-handed neutrinos. We show that this symmetry between the second and third generations cannot be extended to include the charged leptons, no matter what basis we use. We point out that if this symmetry is also independently valid for the right-handed neutrinos, then the active neutrino spectrum is inverted, with m₃=0. This conclusion remains valid even when the left-handed 2-3 symmetry is broken by a non-maximal atmospheric mixing angle θ₂₃, or a non-zero reactor angle θ₁₃. As previously shown by Mohapatra, Nasri, and Yu, such a symmetry also gives rise to interesting consequences on the leptogenesis asymmetry parameter ε₁.