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Leptonic CP Violation Induced by Approximately μ-τ Symmetric Seesaw Mechanism

TOKAI-HEP/TTH-0701 with Teppei Baba, published in Phys. Rev. D 77 No.7 (2008) 075008 1-20 (Received date: October, 2007).

$Assuming a minimal seesaw model with two heavy neutrinos ($N$), we examine effects of leptonic CP violation induced by approximate $\mu$-$\tau$ symmetric interactions. As long as $N$ is subject to the $\mu$-$\tau$ symmetry, we can choose CP phases of Dirac mass terms without loss of generality in such a way that these phases arise from $\mu$-$\tau$ symmetry breaking interactions. In the case that no phase is present in heavy neutrino mass terms, leptonic CP phases are controlled by two phases $\alpha$ and $\beta$. The similar consideration is extended to $N$ blind to the $\mu$-$\tau$ symmetry. It is argued that $N$ subject (blind) to the $\mu$-$\tau$ symmetry necessarily describes the normal (inverted) mass hierarchy. We restrict ourselves to $\mu$-$\tau$ symmetric textures giving the tri-bimaximal mixing and calculate flavor neutrino masses to estimate CP-violating Dirac and Majorana phases as well as neutrino mixing angles as functions of $\alpha$ and $\beta$. Since $\alpha$ and $\beta$ are generated by $\mu$-$\tau$ symmetry breaking interactions, CP-violating Majorana phase tends to be suppressed and is found to be at most ${\mathcal O}(0.1)$ radian. On the other hand, CP-violating Dirac phase tends to show a proportionality to $\alpha$ or to $\beta$.$

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