Lorentz Violation Footprints in the Spectrum of High-Energy Cosmic Neutrinos—Deformation of the Spectrum of Superluminal Neutrinos from Electron-Positron Pair Production in Vacuum

José Manuel Carmona,Maykoll Anthonny Reyes,José Javier Relancio,José Luis Cortés

doi:10.3390/sym11111419

José Manuel Carmona, Maykoll Anthonny Reyes + Show 2 more

Open Access

https://doi.org/10.3390/sym11111419

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Journal: Symmetry	Publication Date: Nov 16, 2019
Citations: 8	License type: CC BY 4.0

Affiliation: Universidad de Zaragoza

Abstract

The observation of cosmic neutrinos up to 2 PeV is used to put bounds on the energy scale of Lorentz invariance violation through the loss of energy due to the production of e + e - pairs in the propagation of superluminal neutrinos. A model to study this effect, which allows us to understand qualitatively the results of numerical simulations, is presented.

Highlights

Special relativity (SR) postulates Lorentz invariance as an exact symmetry of Nature
We have used the detection of high energy neutrinos as an example where a breaking of Lorentz invariance with an energy scale much larger than the energy scale of any observation can lead to observable effects, thanks to the amplification due to the propagation of a particle over very large distances
If one has a modification of the energy-momentum relation of SR such that the energy of a particle with a given momentum is increased due to the breaking of Lorentz invariance, for sufficiently high energies, the lightest neutrino becomes unstable since it can decay through weak interactions into a neutrino and an e+ e− pair

Summary

Introduction

Special relativity (SR) postulates Lorentz invariance as an exact symmetry of Nature. The existence of a violation of Lorentz invariance implies a privileged system of reference, for which the cosmic background radiation is usually assumed to be isotropic In this way, Lorentz symmetry would be only a good long-distance, or low-energy, approximation to the true symmetries of a QGT, which should be parametrized by a certain high-energy scale Λ. The possible existence of an energy dependent velocity for massless particles could be observed in measurements of the time of arrival of photons emitted by very distant sources, since there is an amplification effect due to the long distance they travel Another possible observable effect could appear in the spectrum of the detected neutrinos in the IceCube experiment [10,11,12].

Neutrino Flux

Energy Loss in the Propagation of a Superluminal Neutrino

Expansion of the Universe

Vacuum Pair Emission

Evolution in Case of VPE

Deformation of the Spectrum of High-Energy Neutrinos

Discussion and Conclusions