Large $$\theta _{13}$$ and $$S_3$$S3 Perturbation with Neutrino Mass Matrix

In various recent neutrino experiments the mixing angle \(\theta _{13}\) has been measured. Interestingly, the mixing angle is found to be large and non-zero which has opened up the possibility of measurement of CP violation. The Tri-Bimaximal neutrino mass matrix, which has been very successful in describing the observed neutrino data so far gives \(\theta _{13}\) to be zero. In this work we have used the democratic neutrino mass matrix and \(S_3\) perturbation to obtain the large \(\theta _{13}\) value. We furthermore show the allowed parameter space of the flavor symmetry breaking parameters.