Two categories of approximately [formula omitted] symmetric neutrino mass textures

Abstract

We present ten phenomenologically viable neutrino mass textures, which are approximately μ – τ symmetric: two for the normal mass hierarchy, three for the inverted mass hierarchy, and five for the quasi-degenerate mass pattern. Each texture falls into two categories characterized by either sin θ 13 → 0 (referred to as (C1)), or sin θ 12 → 0 (referred to as (C2)) in the μ – τ symmetric limit, where θ 12 and θ 13 , respectively, stand for the ν e – ν μ and ν e – ν τ mixing angles. Our textures that depend on the signs of neutrino masses as well as on (C1) and (C2) are so constructed to satisfy general relations, which ensure that Δ m ⊙ 2 / Δ m atm 2 ( ≡ R ) ≪ 1 and sin 2 θ 13 ≪ 1 , where Δ m ⊙ 2 and Δ m atm 2 are neutrino mass differences squared, respectively, for solar and atmospheric neutrinos. Three textures are found to provide R ∼ sin 2 θ 13 .