Broken $S_3$ Symmetry in the Neutrino Mass Matrix

Understand

We explore the feasibility of the discrete flavor symmetry $S_3$ to explain the pattern of neutrino masses and mixings.

• In the flavor basis, the neutrino mass matrix is taken to be invariant under $S_3$ symmetry at the zeroth order.
• The effects of breaking $S_3$ symmetry by matrices invariant under different $S_2$ subgroups of $S_3$ are studied.
• The resulting retrocirculant perturbation matrix leads to the perturbed $S_3$ neutrino mass matrix having a trimaximal eigenvector as suggested by the solar neutrino data.