LeptonicCPviolation induced by approximatelyμ-τsymmetric seesaw mechanism

Abstract

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