Testing Lorentz Invariance with Ultra High Energy Cosmic Ray Spectrum

TL;DR

This study uses ultra high energy cosmic ray data to test Lorentz invariance, finding no significant violation and thus supporting the principle up to the highest observed energies.

Contribution

It provides the first constraints on Lorentz invariance violation parameters using UHECR spectra from HiRes and Auger experiments.

Findings

LIV parameters are constrained to near zero, consistent with Lorentz invariance.

The observed GZK cutoff aligns with Lorentz-invariant physics.

Data supports strict Lorentz invariance up to ultra high energies.

Abstract

The GZK cutoff predicted at the Ultra High Energy Cosmic Ray (UHECR) spectrum as been observed by the HiRes and Auger experiments. The results put severe constraints on the effect of Lorentz Invariance Violation(LIV) which has been introduced to explain the absence of GZK cutoff indicated in the AGASA data. Assuming homogeneous source distribution with a single power law spectrum, we calculate the spectrum of UHECRs observed on Earth by taking the processes of photopion production, $e^+e^-$ pair production and adiabatic energy loss into account. The effect of LIV is also taken into account in the calculation. By fitting the HiRes monocular spectra and the Auger combined spectra, we show that the LIV parameter is constrained to $\xi=-0.8^{+3.2}_{-0.5}\times10^{-23}$ and $0.0^{+1.0}_{-0.4}\times10^{-23}$ respectively, which is well consistent with strict Lorentz Invariance up to the highest energy.