What Does mu-tau Symmetry Imply about Neutrino Mixings?

Abstract

The requirement of the mu-tau symmetry in the neutrino sector that yields the maximal atmospheric neutrino mixing is shown to yield either sin(θ_{13})=0 (referred to as C1)) or sin(θ_{12})=0 (referred to as C2)), where θ_{12(13)} stands for the solar (reactor) neutrino mixing angle. We study general properties possessed by approximately mu-tau symmetric textures. It is argued that the tiny mu-tau symmetry breaking generally leads to cos(2θ_{23}) \simsin(θ_{13}) for C1) and cos(2θ_{23}) \sim Δm^2_\odot/Δm^2_{atm}(\equiv R) for C2), which indicates that the smallness of cos(2θ_{23}) is a good measure of the mu-tau symmetry breaking, where Δm^2_{atm} (Δm^2_\odot) stands for the square mass differences of atmospheric (solar) neutrinos. We further find that the relation R \sim sin^2(θ_{13}) arises from contributions of O(sin^2(θ_{13})) in the estimation of the neutrino masses (m_{1,2,3}) for C1), and that possible forms of textures are strongly restricted to realize sin^2(2θ_{12})=O(1) for C2). To satisfy R \sim sin^2(θ_{13}) for C1), neutrinos exhibit the inverted mass hierarchy, or the quasi degenerate mass pattern with | m_{1,2,3}| \sim O(\sqrt{Δm^2_{atm}}), and, to realize sin^2(2θ_{12})=O(1) for C2), there should be an additional small parameter ηwhose size is comparable to that of the mu-tau symmetry breaking parameter ε, giving tan(2θ_{12}) \sim ε/ηwith η\sim εto be compatible with the observed large mixing.

arXiv comment10 pages, title slightly modified, comments added in the introdction, typos corrected, references updated, version to appear in Physical Reviews D

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