Neutrino Pair Cerenkov Radiation for Tachyonic Neutrinos

Abstract

The emission of a charged light lepton pair by a superluminal neutrino has been identified as a major factor in the energy loss of highly energetic neutrinos. The observation of PeV neutrinos by IceCube implies their stability against lepton pair Cerenkov radiation. Under the assumption of a Lorentz-violating dispersion relation for highly energetic superluminal neutrinos, one may thus constrain the Lorentz-violating parameters. A kinematically different situation arises when one assumes a Lorentz-covariant, space-like dispersion relation for hypothetical tachyonic neutrinos, as an alternative to Lorentz-violating theories. We here discuss a hitherto neglected decay process, where a highly energetic tachyonic neutrino may emit other (space-like, tachyonic) neutrino pairs. We find that the space-like dispersion relation implies the absence of a 2 threshold for the production of a tachyonic neutrinoantineutrino pair, thus leading to the dominant additional energy loss mechanism for an oncoming tachyonic neutrino in the medium-energy domain. Surprisingly, the small absolute values of the decay rate and energy loss rate in the tachyonic model imply that these models, in contrast to the Lorentz-violating theories, are not pressured by the cosmic PeV neutrinos registered by the IceCube collaboration.

On the Time-Like and Space-Like Components of Majorana Field

“…The neutrino is a particle candidate for testing the Majorana field theory, at least according to the interpretation considered in this study. The neutrino propagates at a velocity very close to that of light and can reach energy in the order of PeV [38] under optimal conditions, because the ultrarelativistic particle interacts with the tachyonic field. The neutrino is the only particle for which the mass oscillation phenomenon is known [40][41], and recently the MiniBooNE experiment at the Fermilab detected an anomalous event that could be explained by a new neutrino flavour that is different from the three currently known flavours [42].…”

“…Recently, Jentschura explained various data collected by the Ice Cube Collaboration and proposed a similar mechanism, where a superluminal neutrino decays into two collinear tachyonic pairs [38]. In the case where the two collinearly emitted tachyons have different energies, the following relationships hold:…”