Two Categories of Approximately mu-tau Symmetric Neutrino Mass Textures

Abstract

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.

31 pages, 15 figures (High-resolution figures can be downloaded from http://www.sp.u-tokai.ac.jp/~yasue/two_categories_of.pdf.tar.gz)

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• Soft breaking of $L_{\mu }-L_{\tau }$ symmetry: Light neutrino spectrum and Leptogenesis
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