Lepton pair Čerenkov radiation emitted by tachyonic neutrinos: Lorentz-covariant approach and IceCube data

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 Cerenkov radiation (LPCR), that is, by the decay channel , which proceeds via a virtual boson. 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 for PeV, due to the potential onset of LPCR, is discussed.