Examining Lorentz invariance violation with three remarkable GRB photons

Lorentz invariance violation in photons can be quantified by measuring the difference in arrival times between high- and low-energy photons originating from gamma-ray bursts (GRBs). When analyzing data, it is crucial to consider the inherent time delay in the emission of these photons at the source of the GRB. In a recent study, three distinct models were evaluated to explain the intrinsic emission times of high-energy photons by analyzing 14 multi-GeV photon events detected from 8 GRBs using the Fermi Gamma-ray Space Telescope (FGST). In this study, we examine three remarkable GRB photons recorded by different observatories: the 99.3~GeV photon from GRB 221009A observed by FGST, the 1.07~TeV photon from GRB 190114C detected by the Major Atmospheric Gamma Imaging Cherenkov (MAGIC) telescope, and the 12.2~TeV photon from GRB 221009A observed by the Large High Altitude Air-shower Observatory (LHAASO). Our analysis indicates that the newly proposed model with a linear relationship between photon energy and intrinsic emission time can offer a consistent framework to explain the behavior of all three exceptional photons with a Lorentz violation scale $E_{\rm LV}\sim 3\times 10^{17}$~GeV.