A new method of parametrisation of neutrino mass matrix through breaking of $\mu-\tau $ symmetry: Normal hierarchy

Abstract

In the first part of the present work the $\mu-\tau $ symmetry of the neutrino mass matrix is perturbed at its minimal level in order to produce deviation from Tri-bimaximal mixing (TBM), which includes nonzero value of reactor angle $\theta_{13}$ and maximal condition of $\tan^{2}\theta_{23}=1$. The parametrisation of neutrino mass matrix which describes Normal hierarchy (NH), has been addressed with minimum number of independent parameters, out of which two parameters $\eta$ and $\alpha$ take care of $\theta_{12}$ and $\theta_{13}$ respectively without any interference with mass eigenvalues. In the second part the deviation from maximal condition $\tan^{2}\theta_{23}=1$, along with the nonzero value of $\theta_{13}$, has been implemented with the introduction of a perturbing matrix which breaks the $\mu-\tau $ symmetric mass matrix. The model is found to be flexible enough to adjust itself with the changing precise experimental results. The method is also applicable for inverted hierarchy and quasi-degenerate cases.