Neutrino Pair Cerenkov Radiation for Tachyonic Neutrinos

Ulrich D Jentschura,István Nándori

doi:10.1155/2017/9850312

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 q2 threshold for the production of a tachyonic neutrino-antineutrino 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.

Highlights

After early attempts at the construction of tachyonic neutrino theories [1,2,3,4,5,6,7], progress in the theoretical development was hindered by difficulties in the construction of a viable field theory involving tachyons
A very interesting hypothesis was brought forward by Chodos et al [13], who developed a tachyonic neutrino model based on the so-called tachyonic Dirac equation
They recognized that a simple modification of the mass term in the Dirac equation, according to the replacement m → γ5m, induces a dispersion relation of the form E = √→󳨀p 2 − m2, while preserving the spin-1/2 character of the equation

Summary

Introduction

After early attempts at the construction of tachyonic neutrino theories [1,2,3,4,5,6,7], progress in the theoretical development was hindered by difficulties in the construction of a viable field theory involving tachyons (a interesting argument was presented in [8]). A very interesting hypothesis was brought forward by Chodos et al [13], who developed a tachyonic neutrino model based on the so-called tachyonic Dirac equation They recognized that a simple modification of the mass term, according to the replacement m → γ5m, induces a dispersion relation of the form E = √→󳨀p 2 − m2 (with the “tachyonic” sign in front of the mass term), while preserving the spin-1/2 character of the equation. Lepton pair Cerenkov radiation has been analyzed as an energy loss mechanism for high-energy tachyonic neutrinos [35] The kinematics in this case implies that the oncoming, decaying neutrino decays into a tachyonic state of lower energy, emitting an electron-positron pair (see Figure 1(a)).

Pair Production Threshold

Calculation of the Pair Production

Discussion and Conclusions