Search for Lorentz Invariance Violation with time-lag on gamma-ray Cherenkov Telescope data : From the data to the time lag constraints

Lorentz Invariance Violations (LIV) are allowed within some models of Quantum Gravity and can manifest as energy-dependent effects on photon propagation. This lecture notes aim to provide an overview of LIV data analysis in TeV gamma-ray astronomy, focusing on the estimation of the limits of quantum gravity energy scale using Cherenkov telescope data. The lecture covers various topics, from the production and propagation of gamma-ray signals, to the detection principles of TeV gamma rays with Imaging Air Cherenkov Telescopes. The importance of data reconstruction and considerations for instrumental effects that can mimic LIV effects are discussed. It particularly focus on the aspect of extraction of time from Cherenkov data, using a likelihood method. Finally, a concrete analysis example using the LIVelihood code is presented, showcasing the extraction of limits on quantum gravity energy.