Is there a signal for Lorentz non-invariance in existing radioactive   decay data?
  Measurements of the beta decay rates of nuclei have revealed annual periodicities with approximately the same relative amplitude even though the half-lives range over nine orders of magnitude. Here we show that this can be explained if the emitted neutrinos behave as if they propagate in a medium with a refractive index which varies as the Earth orbits the sun. This refractive index may be due to fundamental Lorentz non-invariance (LNI), or apparent LNI arising from interactions with solar or relic neutrinos, or dark matter. Additionally, this medium could have consequences for experiments attempting to measure the neutrino mass. 
M. J. Mueterthies, D. E. Krause, A. Longman, V. E. Barnes, and E.   Fischbach
hep-ph