Shower formation constraints on cubic Lorentz Invariance Violation parameters in quantum electrodynamics

Abstract

We present shower formation constraints on the Lorentz Invariance Violation (LIV) energy scale for photons with cubic dispersion relation from recent gamma ray observations in $100$ TeV -- PeV energy range by LHAASO observatory. We assume Myers-Pospelov effective field theory framework, and calculate the suppression for the Bethe-Heitler process which is mainly responsible for the formation of photon-initiated atmosphere showers. Comparing the high-energy photon events with the suppressed flux predictions we obtain $95\%$ CL constraints on the LIV energy scale. The obtained shower constraint $E_{\rm LIV} \gtrsim \mathcal{O} \left( 10^{20} \mbox{ GeV}\right)$ is significantly weaker than existing birefringence constraints but is independent.