Possible gravitoelectric dipole moment of neutrinos and atmospheric and   solar neutrino anomalies
  Quantum-mechanical calculations of transitions dynamics between the left- and right-handed helicity states of the atmospheric muon Dirac neutrino,which has a gravitoelectrical dipole moment (GEDM) interacting with the gravitational field of the Earth have been carried out. It is shown that the asymmetry of the zenith-angle distribution of an atmospheric muon neutrino can be explained by the interference of two mutually perpendicular plain-wave neutrino states having different velocites inside the Earth in the presence of its gravitation field. The deficit of the solar neutrino can also be explained by the electron neutrino helicity flip transition due to the interaction of its GEDM with the gravitation field of the Sun. The characteristic mass for the gravitational dipole of the neutral and charged leptons have been estimated. 
Anatoli S. Kuznetsov