Generic Friedberg-Lee Symmetry of Dirac Neutrinos

We write out the generic Dirac neutrino mass operator which possesses the Friedberg-Lee (FL) symmetry and find that its corresponding neutrino mass matrix is asymmetric. Following a simple way to break the FL symmetry, we calculate the neutrino mass eigenvalues and show that the resultant neutrino mixing pattern is nearly tri-bimaximal. Imposing the Hermitian condition on the neutrino mass matrix, we also show that the simplified ansatz is consistent with current experimental data and favors the normal neutrino mass hierarchy.