Neutrino Mixing : from the Broken μ - τ Symmetry to the Broken Friedberg - Lee Symmetry

I argue that the observed flavor structures of leptons and quarks might imply the existence of certain flavor symmetries. The latter should be a good starting point to build realistic models towards deeper understanding of the fermion mass spectra and flavor mixing patterns. The µ-τ permutation symmetry serves for such an example to interpret the almost maximal atmospheric neutrino mixing angle (θ 23 ∼ 45 •) and the strongly suppressed CHOOZ neutrino mixing angle (θ 13 < 10 •). In this talk I like to highlight a new kind of flavor symmetry, the Friedberg-Lee symmetry, for the effective Majorana neutrino mass operator. Luo and I have shown that this symmetry can be broken in an oblique way, such that the lightest neutrino remains massless but an experimentally-favored neutrino mixing pattern is achievable. We get a novel prediction for θ 13 in the CP-conserving case: sin θ 13 = tan θ 12 |(1 − tan θ 23)/(1 + tan θ 23)|. Our scenario can simply be generalized to accommodate CP violation and be combined with the seesaw mechanism. Finally I stress the importance of probing possible effects of µ-τ symmetry breaking either in terrestrial neutrino oscillation experiments or with ultrahigh-energy cosmic neutrino telescopes.