Phased breaking ofμ−τsymmetry and leptogenesis

Nonvanishing $U_{e3}$ has been theoretically related to a certain flavor symmetry breaking in the neutrino sector. We propose a scenario to break the $\mu -\tau$ symmetry so as to accommodate the nonvanishing $U_{e3}$. Our scenario is constructed in the context of a seesaw model, and the $\mu -\tau$ symmetry breaking is achieved by introducing a $CP$ phase in the Dirac Yukawa matrix. We also show how the deviation of ${\theta }_{23}$ from the maximal mixing and nonvanishing $U_{e3}$ depend on the $CP$ phase. Neutrino mixings and the neutrino mass-squared differences are discussed, and the amplitude in neutrinoless double beta decay $m_{ee}$ are also predicted. We found that a tiny breaking of the $\mu -\tau$ symmetry due to mass splitting between two degenerate heavy Majorana neutrinos on top of the Dirac $CP$ phase can lead to successful leptogenesis. We examine how leptogenesis can be related with low energy neutrino measurement, and show that our predictions for $U_{e3}$ and $m_{ee}$ can be constrained by the current observation of baryon asymmetry.