Two categories of approximately μ-τ symmetric neutrino mass textures

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 sinθ13→0 (referred to as (C1)), or sinθ12→0 (referred to as (C2)) in the μ-τ symmetric limit, where θ12 and θ13, respectively, stand for the νe-νμ and νe-ντ 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 Δm⊙2/Δmatm2(≡R)≪1 and sin2θ13≪1, where Δm⊙2 and Δmatm2 are neutrino mass differences squared, respectively, for solar and atmospheric neutrinos. Three textures are found to provide R∼sin2θ13.