Two Categories of Approximately μ-τ Symmetric Neutrino Mass Textures

TOKAI-HEP/TH-0602 with Kenichi Fuki, published in Nucl. Phys. B 783 No.1-2 (2007) 31-56 (Received date: 8 August, 2006).

$Our approximately $\mu$-$\tau$ symmetric neutrino mass textures fall into two different categories, whose behaviors in the $\mu$-$\tau$ symmetric limit are characterized by either $\sin\theta_{13}\rightarrow 0$ (referred to as C1)), or $\sin\theta_{12}\rightarrow 0$ (referred to as C2)), where $\theta_{12}$ and $\theta_{13}$, respectively stand for the $\nu_e$-$\nu_\mu$ and $\nu_e$-$\nu_\tau$ mixing angles. 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 $\mu$-$\tau$ symmetry breaking ensures that $\sin^2\theta_{13}\ll 1$ for C1), and $\Delta m^2_\odot/\Delta m^2_{atm} (\equiv R) \ll 1$ for C2), where $\Delta m^2_\odot = m^2_2-m^2_1$ for solar neutrinos, and $\Delta m^2_{atm}=\vert m^2_3-(m^2_1+m^2_2)/2\vert$ for atmospheric neutrinos with $m_{1,2,3}$ being neutrino masses. A correlation among small quantities is provided by $\cos 2\theta_{23}\sim\sin\theta_{13}$ for C1), and by either $\cos 2\theta_{23}\sim R$, or $\cos 2\theta_{23}\sin\theta_{13}\sim R$ for C2), where $\theta_{23}$ is the $\nu_\mu$-$\nu_\tau$ mixing angle. It is further shown that $\tan 2\theta_{12}\sim\cos 2\theta_{23}/\sin\theta_{13}$ is satisfied for C2). We find the following properties for each mass ordering: 1) For the normal mass hierarchy, the other smallness of $R$ (or $\sin^2\theta_{13}$) in the case of C1) (or C2)) can be ascribed to an approximate electron number conservation; 2) For the normal and inverted mass hierarchies and for the quasi degenerate mass pattern II (with $m^2_{1,2,3}\gg \Delta m^2_{atm}$) exhibiting $m_1\sim m_2 \sim m_3$, all in the case of C2), either $R\sim\tan 2\theta_{12}\sin^2\theta_{13}$ or $R\sim\tan 2\theta_{12}\sin\theta_{13}$ is satisfied; 3) For the inverted mass hierarchy and the quasi degenerate mass pattern I (with $\vert m_{1,2,3}\vert\sim \sqrt{\Delta m^2_{atm}}$), both in the case of C1) with $m_1\sim -m_2$, the relation $R\sim \sin^2\theta_{13}$ arises from the contribution of ${\mathcal{O}}(\sin^2\theta_{13})$ in the estimation of neutrino masses; and 4) For the quasi degenerate mass pattern II, we observe that $m_{\beta\beta}$ can be as large as 0.5 eV, where $m_{\beta\beta}$ is the effective neutrino mass in $(\beta\beta)_{0\nu}$-decay, and that larger values of $m_{\beta\beta}$ favor larger values of $\sin \theta_{13}$ in the case of C1) for $m_1\sim m_2 \sim m_3$ and smaller values of $\sin \theta_{13}$ in the cases of C1) for $m_1\sim m_2 \sim -m_3$ and C2) for $m_1\sim m_2 \sim \pm m_3$.$

This Web site is maximally optimized for Internet Explorer of Version 3.0 or higher versions.

If you have any comments on this Web site (since Dec. 1st, 1997), please let us know:

yasue.
Copyright (c) 1997-2020/06 M. Yasue, Department of Physics, Tokai University.
Last update: 2020/06/05