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.