Perturbations to \mu-\tau\ symmetry in neutrino mixing

Abstract

Many neutrino mixing scenarios that have \mu-\tau symmetry with \theta_{13}=0 are in disagreement with recent experimental results that indicate a nonzero value for \theta_{13}. We investigate the effect of small perturbations on Majorana mass matrices with \mu-\tau symmetry and derive analytic formulae for the corrections to the mixing angles. We find that since m_1 and m_2 are nearly degenerate, \mu-\tau symmetry mixing scenarios are able to explain the experimental data with about the same size perturbation for most values of \theta_{12}. This suggests that the underlying unperturbed mixing need not have \theta_{12} close to the experimentally preferred value. One consequence of this is that a new class of models with \mu-\tau symmetry is possible, with unperturbed \theta_{12} equal to zero or 90 degrees for arbitrary unperturbed \theta_{13}.