Leptonic mixing matrix in terms of Cabibbo angle

Abstract

We phenomenologically build a neutrino mass matrix obeying $\mu -\tau$ symmetry with only two parameters, Cabibbo angle $(\lambda )$ and a flavour twister parameter $(\eta )$. For vanishing $\eta$, the model assumes TBM mixing. When $\eta =\lambda$, the model generates a solar mixing angle and solar mass squared difference that coincide with the experimental best-fits. It motivates us to propose a mixing matrix in the neutrino sector with $sin{\theta }_{12}<\frac{1}{\sqrt{3}}$, ${\theta }_{13}=0$ and ${\theta }_{23}=\pi /4$. The corrections in ${\theta }_{13}$ and ${\theta }_{23}$ are conducted following the breaking of $\mu -\tau$ symmetry, by choosing a proper unitary diagonalizing charged lepton matrix, and this ensures that ${\theta }_{23}$ lies within the first octant. The Cabibbo angle $(\lambda =\sin {\theta }_c)$ plays the role of a guiding parameter in both neutrino as well as leptonic sector. The effect of the Dirac CP violating phase ${\delta }_{cp}$ is also studied when it enters either through the charged lepton diagonalizing matrix or through neutrino mixing matrix.

13 pages, 4 figures

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• Indication for the disappearance of reactor electron antineutrinos in the Double Chooz experiment
• Global analysis of neutrino masses, mixings and phases: entering the era of leptonic CP violation searches
• Determination of neutrino masses from future observations of CMB B-mode polarization and the growth of structure