Shower formation constraints on cubic Lorentz invariance violation parameters in quantum electrodynamics

We present shower formation constraints on the Lorentz invariance violation (LIV) energy scale for photons with a cubic dispersion relation from recent gamma-ray observations in the 100 TeV–PeV energy range by the Large High Altitude Air Shower Observatory (LHAASO). We assume a 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 atmospheric showers. Comparing the high-energy photon events with the suppressed flux predictions, we obtain $$95%$$ 95 % CL constraints on the LIV energy scale. The obtained shower constraint ELIV O ( 10²⁰ GeV ) E LIV ≳ O 10 20 GeV is significantly weaker than existing birefringence constraints but is independent.