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The requirement of the mu-tau symmetry in the neutrino sector that yields themaximal atmospheric neutrino mixing is shown to yield either sin(\theta_{13})=0(referred to as C1)) or sin(\theta_{12})=0 (referred to as C2)), where\theta_{12(13)} stands for the solar (reactor) neutrino mixing angle. We studygeneral properties possessed by approximately mu-tau symmetric textures. It isargued that the tiny mu-tau symmetry breaking generally leads tocos(2\theta_{23}) \simsin(\theta_{13}) for C1) and cos(2\theta_{23}) \sim\Delta m^2_\odot/\Delta m^2_{atm}(\equiv R) for C2), which indicates that thesmallness of cos(2\theta_{23}) is a good measure of the mu-tau symmetrybreaking, where \Delta m^2_{atm} (\Delta m^2_\odot) stands for the square massdifferences of atmospheric (solar) neutrinos. We further find that the relationR \sim sin^2(\theta_{13}) arises from contributions of O(sin^2(\theta_{13})) inthe estimation of the neutrino masses (m_{1,2,3}) for C1), and that possibleforms of textures are strongly restricted to realize sin^2(2\theta_{12})=O(1)for C2). To satisfy R \sim sin^2(\theta_{13}) for C1), neutrinos exhibit theinverted mass hierarchy, or the quasi degenerate mass pattern with | m_{1,2,3}|\sim O(\sqrt{\Delta m^2_{atm}}), and, to realize sin^2(2\theta_{12})=O(1) forC2), there should be an additional small parameter \eta whose size iscomparable to that of the mu-tau symmetry breaking parameter \epsilon, givingtan(2\theta_{12}) \sim \epsilon/\eta with \eta \sim \epsilon to be compatiblewith the observed large mixing.Comment: 10 pages, title slightly modified, comments added in the introdction,  typos corrected, references updated, version to appear in Physical Reviews

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

What does<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>μ</mml:mi><mml:mo>−</mml:mo><mml:mi>τ</mml:mi></mml:math>symmetry imply about neutrino mixings?

What doesμ−τsymmetry imply about neutrino mixings?