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.

Comments: 19 pages, 14 figures