Here, we review searches for empirical evidence for the existence of tachyons, superluminal particles having $m^2<0.$ The review considers searches for new particles that might be tachyons, as well as evidence that neutrinos are tachyons from data that may have been gathered for other purposes. Much of the second half of the paper is devoted to the $3+3$ neutrino model including a tachyonic mass state, which has empirical support from a variety of areas. Although this is primarily a review article, it contains several newly identified results.

Current experiments do not exclude the possibility that one or more neutrinos are very slightly superluminal or that they have a very small tachyonic mass. Important bounds on the size of a hypothetical tachyonic neutrino mass term are set by lepton pair Čerenkov radiation (LPCR), that is, by the decay channelν→e+e-ν, which proceeds via a virtualZ0boson. Here, we use a Lorentz-invariant dispersion relation which leads to very tight constraints on the tachyonic mass of neutrinos; we also calculate decay and energy loss rates. A possible cutoff seen in the IceCube neutrino spectrum forEν>2 PeV, due to the potential onset of LPCR, is discussed.

A review is given of hypothetical faster-than-light tachyons and the development of the author’s 3+3 model of the neutrino mass states, which includes one tachyonic mass state doublet. Published empirical evidence for the model is summarized, including an interpretation of the mysterious Mont Blanc neutrino burst from SN 1987A as being due to tachyonic neutrinos having m2=-0.38eV2. This possibility requires an 8 MeV antineutrino line from SN 1987A, which a new dark matter model has been found to support. Furthermore, this dark matter model is supported by several datasets: γ-rays from the galactic center, and the Kamiokande-II neutrino data on the day of SN 1987A. The KATRIN experiment should serve as the unambiguous test of the 3+3 model and its tachyonic mass state.