Nearly tri-bimaximal neutrino mixing and CP violation from μ-τ symmetry breaking

Assuming the Majorana nature of massive neutrinos, we generalize the Friedberg-Lee neutrino mass model to include CP violation in the neutrino mass matrix Mν. We show that a favorable neutrino mixing pattern (with θ12≈35.3°, θ23=45°, θ13≠0° and δ=90°) can naturally be derived from Mν, if it has an approximate or softly-broken μ-τ symmetry. We point out a different way to obtain the nearly tri-bimaximal neutrino mixing with δ=0° and non-vanishing Majorana phases. The most general case, in which all the free parameters of Mν are complex and the resultant neutrino mixing matrix contains both Dirac and Majorana phases of CP violation, is also discussed.