Calculation of the decay rate of tachyonic neutrinos against charged-lepton-pair and neutrino-pair Cerenkov radiation

We consider in detail the calculation of the decay rate of high-energy superluminal neutrinos against (charged) lepton pair Cerenkov radiation (LPCR), and neutrino pair Cerenkov radiation (NPCR), i.e., against the decay channels nu -> nu e+ e- and nu -> nu nubar nu. Under the hypothesis of a tachyonic nature of neutrinos, these decay channels put constraints on the lifetime of high-energy neutrinos for terrestrial experiments as well as on cosmic scales. For the oncoming neutrino, we use the Lorentz-covariant tachyonic relation E_nu = (p^2 - m_nu^2)^(1/2), where m_nu is the tachyonic mass parameter. We derive both threshold conditions as well as decay and energy loss rates, using the plane-wave fundamental bispinor solutions of the tachyonic Dirac equation. Various intricacies of rest frame versus lab frame calculations are highlighted. The results are compared to the observations of high-energy IceCube neutrinos of cosmological origin.