Astroparticle Physics Tests of Lorentz Invariance Violation

TL;DR

This paper analytically investigates how Lorentz invariance violation affects ultra-high energy cosmic ray interactions, especially proton propagation and photopion production, providing a framework to test LIV effects with cosmic ray data.

Contribution

It introduces an analytic method to calculate inelasticity for LIV-affected interactions, enabling detailed modeling of cosmic ray propagation under LIV scenarios.

Findings

LIV alters the phase space for photopion production

The inelasticity depends on LIV parameters and interaction geometry

Propagation lengths of cosmic rays are affected by LIV modifications

Abstract

Testing Lorentz invariance is essential as it is one of the pillars of modern physics. Moreover, its violation is foreseen in several popular Quantum Gravity models. Several authors study the effects of Lorentz invariance violation (LIV) in the propagation of ultra-high energy cosmic rays. These particles are the most energetic events ever detected and therefore represent a promising framework to test LIV. In this work we present an analytic calculation of the in-elasticity for any $a+b \rightarrow c+d$ interaction using first order perturbation in the dispersion relation that violates Lorentz invariance. The inelasticity can be calculated by solving a third-order polynomial equation containing: a) the kinematics of the interaction, b) the LIV term for each particle and c) the geometry of the interaction. We use the inelasticity we calculate to investigate the proton propagation in the intergalactic media. The photopion production of the proton interaction with the CMB is taken into account using the inelasticity and the attenuation length in different LIV scenarios. We show how the allowed phase space for the photopion production changes when LIV is considered for the interaction. The calculations presented here are going to be extended in order to calculated the modified ultra-high energy cosmic rays spectrum and compare it to the data.