Calculation of the Decay Rate of Tachyonic Neutrinos against Charged-Lepton-Pair and Neutrino-Pair Cerenkov Radiation

TL;DR

This paper calculates the decay rates of hypothetical superluminal neutrinos with tachyonic properties, focusing on lepton and neutrino pair Cerenkov radiation, to constrain their lifetime and energy loss, with implications for high-energy astrophysical neutrinos.

Contribution

It provides detailed decay rate calculations for tachyonic neutrinos, including threshold conditions and energy loss rates, using the tachyonic Dirac equation, and compares results with IceCube observations.

Findings

Decay rates depend on tachyonic mass parameter and energy thresholds.

Constraints on neutrino lifetime from high-energy cosmic neutrino observations.

Energy loss rates influence the propagation of superluminal neutrinos over cosmological distances.

Abstract

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.