Friedberg-Lee symmetry breaking and its prediction for θ13

We consider an effective Majorana neutrino mass operator with the Friedberg-Lee symmetry; i.e., it is invariant under the transformation να→να+z (for α=e,μ,τ) with z being a space-time independent constant element of the Grassmann algebra. We show that this new flavor symmetry can be broken in such a nontrivial way that the lightest neutrino remains massless but an experimentally-favored neutrino mixing pattern is achievable. In particular, we get a novel prediction for the unknown neutrino mixing angle θ13 in terms of two known angles: sinθ13=tanθ12|(1−tanθ23)/(1+tanθ23)|. The model can simply be generalized to accommodate CP violation and be combined with the seesaw mechanism.