Planck-scale Lorentz violation constrained by Ultra-High-Energy Cosmic Rays

TL;DR

This study uses ultra-high-energy cosmic ray data to set stringent bounds on Lorentz violation parameters in the Standard Model, indicating symmetry breaking scales well above the Planck energy.

Contribution

It provides the first two-sided bounds on dimension five and six Lorentz-violating operators for protons and pions using cosmic ray observations.

Findings

Bounds on dimension five operators at $10^{-3} M_{Planck}^{-1}$

Dimension six proton coefficient constrained below $10^{-6} M_{Planck}^{-2}$

Constraints on pion coefficients are weaker but below $M_{Planck}^{-2}$

Abstract

We investigate the consequences of higher dimension Lorentz violating, CPT even kinetic operators that couple standard model fields to a non-zero vector field in an Effective Field Theory framework. Comparing the ultra-high energy cosmic ray spectrum reconstructed in the presence of such terms with data from the Pierre Auger observatory allows us to establish two sided bounds on the coefficients of the mass dimension five and six operators for the proton and pion. Our bounds imply that for both protons and pions, the energy scale of Lorentz symmetry breaking must be well above the Planck scale. In particular, the dimension five operators are constrained at the level of $10^{-3} M_{\rm Planck}^{-1}$. The magnitude of the dimension six proton coefficient is bounded at the level of $10^{-6} M_{Planck}^{-2}$ except in a narrow range where the pion and proton coefficients are both negative and nearly equal. In this small area, the magnitude of the dimension six proton coefficient must only be below $10^{-3} M_{\rm Planck}^{-2}$. Constraints on the dimension six pion coefficient are found to be much weaker, but still below $M_{\rm Planck}^{-2}$.