Leptonic mixing matrix in terms of Cabibbo angle

Abstract

We phenomenologically build a neutrino mass matrix obeying $μ-τ$ symmetry with only two parameters, Cabibbo angle $(λ)$ and a flavour twister parameter $(η)$. For vanishing $η$, the model assumes TBM mixing. When $η=λ$, 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 $ sinθ_{12}<\frac{1}{\sqrt{3}}$, $θ_{13}=0$ and $θ_{23}=π/4$. The corrections in $θ_{13}$ and $θ_{23}$ are conducted following the breaking of $μ-τ$ symmetry, by choosing a proper unitary diagonalizing charged lepton matrix, and this ensures that $θ_{23}$ lies within the first octant. The Cabibbo angle $(λ=\sinθ_{c})$ plays the role of a guiding parameter in both neutrino as well as leptonic sector. The effect of the Dirac CP violating phase $δ_{cp}$ is also studied when it enters either through the charged lepton diagonalizing matrix or through neutrino mixing matrix.