Realistic tribimaximal neutrino mixing

We propose a generalized version of the tribimaximal (TBM) ansatz for lepton mixing, leading to a nonzero reactor angle ${\theta }_{13}$ and $CP$ violation. The latter is characterized by two $CP$ phases. The Dirac phase, affecting neutrino oscillations, is nearly maximal (${\delta }_{CP}\sim \pm \pi /2$), while the Majorana phase implies narrow allowed ranges for the neutrinoless double beta decay amplitude. The solar angle ${\theta }_{12}$ lies nearly at its TBM value, while the atmospheric angle ${\theta }_{23}$ has the TBM value for a maximal ${\delta }_{CP}$. Neutrino oscillation predictions can be tested in present and upcoming experiments.

Figure 1

Correlation between ${\sin }^2{\theta }_{13}$ and ${\sin }^2{\theta }_{12}$ given in Eq. (6). Notice that in the whole experimentally allowed range [2], the value of ${\sin }^2{\theta }_{12}$ remains very close to $1/3$.

Figure 2

$|m_{ee}|$ prediction for NO and IO when $\rho =0$. Here, $\theta$ is taken as a free parameter, and we require the three mixing angles to lie in their allowed $3\sigma$ regions [2, 3]. Note that $m_{ee}$ does not depend on $\sigma$.

Figure 3

The correlation between the atmospheric angle ${\theta }_{23}$ and the $CP$ phase ${\delta }_{CP}$ predicted by our generalized TBM matrix in Eq. (2) is given by the hatched band, while the 1, 2, and $3\sigma$ regions allowed by the current neutrino oscillation global fit are indicated by the shaded areas [2, 3].

Figure 4

The predicted dependence of $|{\sin }^2{\theta }_{23}-\frac{1}{2}|$ on the parameter $\sigma$ is indicated by the curved band. Its width comes from varying ${\theta }_{13}$ within its $3\sigma$ range, while the horizontal band gives the current determination of ${\theta }_{23}$ [2, 3].

Figure 5

$|m_{ee}|$ prediction for NO and IO in the most general GTBM ansatz. Here, the parameters $\rho$ and $\theta$ are varied within their allowed $3\sigma$ ranges [2, 3]. Note that $m_{ee}$ does not depend on $\sigma$.

Figure 6

The allowed range of electron neutrino appearance probability at T2K covers a more restricted region, thanks to the GTBM predictions. Here, the black line corresponds to the best fit, the cyan region is the general three-neutrino result, while the yellow region is the GTBM prediction.