An Algebraic Analysis of Neutrino Masses and Mixings and its Implications on $\mu$-$\tau$ Symmetric Mass Matrix

We diagonalize Majorana neutrino mass matrix with the help of PMNS matrix and obtain analytical relations between the mass matrix elements and mixing parameters, viz., three mixing angles- ${\theta }_{12},{\theta }_{23},{\theta }_{13}$ and Dirac CP phase \delta. We analyse our results in a special $\mu$-$\tau$ symmetric mass matrix which corresponds to maximal atmospheric mixing (${\theta }_{23}=\pi \mathrm{/}4$) and maximal CP violation ($\delta =-\pi \mathrm{/}2$). The analysis shows that a deviation of ${\theta }_{23}$ from its maximal value can be correlated with the prediction of other two mixing angles.