Lorentz Invariance Violation from Gamma-Ray Bursts

Lorentz invariance violation (LV) is examined through the time delay between high-energy and low-energy photons in gamma-ray bursts (GRBs). Previous studies determined the LV energy scale as $E_{\rm LV} \simeq 3.60 \times 10^{17}$~GeV using Fermi Gamma-ray Space Telescope (FGST) data. This study updates the time-delay model and reaffirms these findings with new observations. High-energy photons from GRBs at GeV and TeV bands are analyzed, including the 99.3 GeV photon from GRB 221009A (FGST), the 1.07 TeV photon from GRB 190114C (MAGIC), and the 12.2 TeV photon from GRB 221009A (LHAASO). Our analysis, in conjunction with previous data, consistently shows that high-energy photons are emitted earlier than low-energy photons at the source. By evaluating 17 high-energy photons from 10 GRBs observed by FGST, MAGIC, and LHAASO, we estimate the LV energy scale to be $E_{\rm LV} \simeq 3.00 \times 10^{17}$ GeV. The null hypothesis of dispersion-free vacuum $E=pc$ (or, equivalently, the constant light-speed $v_{\gamma}=c$) is rejected at a significance level of 3.1$\sigma$ or higher.