^{1}

^{,*}

^{2}

^{,†}

^{3}

^{,‡}

^{2}

^{,§}

^{2}

^{,∥}

^{3}.

We propose a generalized version of the tribimaximal (TBM) ansatz for lepton mixing, leading to a nonzero reactor angle

Ever since the discovery of neutrino oscillations, the structure of the leptonic mixing matrix has been an active topic of research. Over the last twenty years or so, there has been a flood of both theoretical and experimental activity aimed at determining and understanding the structure of the leptonic mixing matrix. Solar and atmospheric data, confirmed by accelerator and reactor data, made it clear that the structure of lepton mixing is quite at odds with that of quarks, given the large values of

Since it was first proposed, the TBM ansatz has been a popular benchmark for describing the pattern of lepton mixing, inspiring a flood of theory papers. It gives

Motivated by the need for departing from the simplest “first-order” form for the TBM ansatz, Eq.

This new ansatz is characterized by just one angle

The first is the limit

In the limit of

We now discuss the realistic limits of GTBM that lead to

Using the

Correlation between

In the

Notice that this matrix shares many properties of matrix in Eq.

So far, the limits we have discussed all lead to the maximal atmospheric mixing angle, i.e., they all predict

The correlation between the atmospheric angle

The mixing matrix of Eq.

Having discussed the various limits of our proposed GTBM matrix,

The predicted dependence of

The expression for the parameter

From these mixing angles and phases in Eq.

The predictions made by the GTBM ansatz can also be tested in currently running and upcoming neutrino oscillation experiments. The predictions made by GTBM to oscillation experiments is illustrated in Fig.

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.

In conclusion, we have proposed a realistic generalization of the TBM ansatz, which not only accounts for nonzero measured value of

Before closing, we comment on the theoretical origin of our GTBM matrix. We note that this ansatz may be derived systematically by the method of generalized

Imposing any three of the

For simplicity, we work in the basis of diagonal charged lepton mass matrix. In this basis, the whole leptonic mixing is solely due to the neutrino sector.

one recovers the complex TBM matrix of Eq.In order to generate realistic mass and mixing patterns, we add perturbation terms, preserving only the

Thus, the mixing matrix diagonalizing the full mass matrix

Work supported by the Spanish Grants No. FPA2017-85216-P and No. SEV-2014-0398 (MINECO), PROMETEOII/2014/084 (Generalitat Valenciana), and by the National Natural Science Foundation of China, Grant No. 11522546.