Breaking μ − τ symmetry of tri-bimaximal mixing.

The TBM neutrino mass matrix is invariant under the TM1, TM2, and μ − τ exchange symmetry. The prediction of vanishing θ13 by TBM is due to its invariance under μ − τ exchange symmetry. We can construct neutrino mass textures where TBM mass matrix is the main contributing matrix and a μ − τ symmetry breaking term is added as an additional contribution. The overall matrix will be invariant under either TM1 or TM2 symmetry only. We present eight such textures which are invariant under either TM1 or TM2 symmetry but are not invariant under the μ − τ exchange symmetry. These textures give definite predictions on the values of mβ, mββ, CP violating phase δ, and the octant of the mixing angle θ23. [ABSTRACT FROM AUTHOR]