The Friedberg-Lee symmetry and minimal seesaw model

The Friedberg-Lee (FL) symmetry is generated by a transformation of a fermionic field q to q + xi z. This symmetry puts very restrictive constraints oil allowed terms in a Lagrangian. Applying this symmetry to N fermionic fields, we find that the number of independent fields is reduced to N - 1 if the fields have gauge interaction or the transformation is a local one. Using this property, we find that a seesaw model originally with three generations of left- and right-handed neutrinos, with the left-handed neutrinos unaffected but the right-handed neutrinos transformed under the local FL translation, is reduced to an effective theory of minimal seesaw which has only two right-handed neutrinos. The symmetry predicts that one of the light neutrino masses must be zero. (C) 2009 Elsevier B.V. All rights reserved.