Two-sided constraints on Lorentz Invariance violation from Tibet-AS$γ$ and LHAASO Very-High-Energy photon observations

Abstract: We present new two-sided constraints on Lorentz Invariance violation energy scale for photons with quartic dispersion relation from recent gamma ray observations by Tibet-AS$\gamma$ and LHAASO experiments. The constraints are based on the consideration of the processes of photon triple splitting (superluminal scenario) and the suppression of shower formation (subluminal). The constraints in subluminal scenario are better than the pair production constraints and are the strongest in the literature.