A new method of parametrisation of neutrino mass matrix through breaking of $μ-τ$ symmetry: Normal hierarchy

Abstract

In the first part of the present work the $μ-τ$ 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 $θ_{13}$ and maximal condition of $\tan^{2}θ_{23}=1$. 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 $η$ and $α$ take care of $θ_{12}$ and $θ_{13}$ respectively without any interference with mass eigenvalues. In the second part the deviation from maximal condition $\tan^{2}θ_{23}=1$, along with the nonzero value of $θ_{13}$, has been implemented with the introduction of a perturbing matrix which breaks the $μ-τ$ 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.