Lorentz Invariance Violation and IceCube Neutrino Events

TL;DR

This paper proposes that Planck-scale Lorentz violation could explain the observed cutoff in IceCube neutrino energies around a few PeV, accounting for the absence of expected high-energy events like the Glashow resonance.

Contribution

It introduces a specific Lorentz violation model affecting neutrino dispersion relations to explain IceCube neutrino energy cutoff and the non-observation of certain decay signatures.

Findings

Neutrino energy cutoff can be explained by Lorentz violation parameter choice.

Certain meson and muon decays are suppressed or enhanced at PeV energies.

The absence of Glashow resonance events supports the Lorentz violation hypothesis.

Abstract

The IceCube neutrino spectrum shows a flux which falls of as $E^{-2}$ for sub PeV energies but there are no neutrino events observed above $\sim 3$ PeV. In particular the Glashow resonance expected at 6.3 PeV is not seen. We examine a Planck scale Lorentz violation as a mechanism for explaining the cutoff of observed neutrino energies around a few PeV. By choosing the one free parameter the cutoff in neutrino energy can be chosen to be between 2 and 6.3 PeV. We assume that neutrinos (antineutrinos) have a dispersion relation $E^2=p^2 - (\xi_3/M_{Pl})~p^3$, and find that both $\pi^+$ and $\pi^-$ decays are suppressed at neutrino energies of order of few PeV. We find that the $\mu^-$ decay being a two-neutrino process is enhanced, whereas $\mu^+$ decay is suppressed. The $K^+\rightarrow \pi^0 e^+ \nu_e$ is also suppressed with a cutoff neutrino energy of same order of magnitude, whereas $K^-\rightarrow \pi^0 e^- \bar \nu_e$ is enhanced. The $n \rightarrow p^+ e^- \bar \nu_e$ decay is suppressed (while the $\bar n \rightarrow p^- e^+ \nu_e$ is enhanced). This means that the $\bar \nu_e$ expected from $n$ decay arising from $p+\gamma \rightarrow \Delta \rightarrow \pi^+ n$ reaction will not be seen. This can explain the lack of Glashow resonance events at IceCube. If no Glashow resonance events are seen in the future then the Lorentz violation can be a viable explanation for the IceCube observations at PeV energies.