Kenichi Fuki | Searcharxiv

arXiv2006

Two Categories of Approximately mu-tau Symmetric Neutrino Mass Textures

Our approximately μ-τsymmetric neutrino mass textures fall into two different categories, whose behaviors in the μ-τsymmetric limit are characterized by either \sin(theta_{13})->0 (referred to as C1)), or \sin(theta_{12})->0 (referred to as C2)). We present ten phenomenologically viable neutrino mass textures: two for the normal mass hierarchy, three for the inverted mass hierarchy, and five for the quasi degenerate mass pattern. Tiny μ-τsymmetry breaking ensures that \sin^2(theta_{13}) << 1 for C1), and Δm^2_\odot/Δm^2_{atm} (\equiv R) << 1 for C2). A correlation among small quantities is provided by \cos 2(theta_{23}) \sim \sin(theta_{13}) for C1), and by either \cos(2theta_{23}) \sim R, or \cos(2theta_{23})\sin(theta_{13}) \sim R for C2). It is further shown that \tan(2theta_{12}) \sim \cos(2theta_{23})/\sin(theta_{13}) is satisfied for C2). We find specific properties for each mass ordering, which are discussed in this article.

hep-ph↗

arXiv2006

What Does mu-tau Symmetry Imply about Neutrino Mixings?

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.

hep-ph↗