A Lorentz-Violating Origin of Neutrino Mass?
  We explore implications for neutrino physics of Very Special Relativity (VSR), wherein the symmetry group of nature includes only a 4-parameter subgroup of the Lorentz group. VSR can provide a natural origin to lepton-number conserving neutrino masses without need for sterile (right-handed) states. Neutrinoless double beta decay is forbidden if VSR is solely responsible for neutrino masses. For ultra-relativistic neutrinos, such as are ordinarily studied, VSR and conventional neutrino masses are indistinguishable. However, we show that VSR effects can be significant near the beta decay endpoint where neutrinos are not ultra-relativistic. 
Andrew G. Cohen and Sheldon L. Glashow