We investigate the Friedberg-Lee (FL) symmetry and its promotion to include
the μ−τ symmetry, and call that the twisted FL symmetry.Based on the
twisted FL symmetry, two possible schemes are presented toward the realistic
neutrino mass spectrum and the tri-bimaximal mixing.In the first scheme, we
suggest the semi-uniform translation of the FL symmetry.The second one is based
on the S3 permutation family symmetry.The breaking terms, which are twisted
FL symmetric, are introduced.Some viable models in each scheme are also
presented.Comment: 14 pages, no figure. v2: 16 pages, modified some sentences, appendix
added, references added. v3: 14 pages, composition simplified, accepted
version in EPJ