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%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$95\\%$$\\end{document} CL constraints on the LIV energy scale. The obtained shower constraint ELIV≳O1020GeV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E_\ extrm{LIV} \\gtrsim \\mathcal {O} \\left( 10^{20} \ ext{ GeV }\\right) $$\\end{document} is significantly weaker than existing birefringence constraints but is independent.
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