Search for Lorentz Invariance breaking with a likelihood fit of the PKS 2155-304 flare data taken on MJD 53944

Several models of Quantum Gravity predict Lorentz Symmetry breaking at energy scales approaching the Planck scale (10^{19} GeV). With present photon data from the observations of distant astrophysical sources, it is possible to constrain the Lorentz Symmetry breaking linear term in the standard photon dispersion relations. Gamma-ray Bursts (GRB) and flaring Active Galactic Nuclei (AGN) are complementary to each other for this purpose, since they are observed at different distances in different energy ranges and with different levels of variability. Following a previous publication of the High Energy Stereoscopic System (H.E.S.S.) collaboration, a more sensitive event-by-event method consisting of a likelihood fit is applied to PKS 2155-304 flare data of MJD 53944 (July 28, 2006) as used in the previous publication. The previous limit on the linear term is improved by a factor of ~3 up to M^{l}_{QG} > 2.1x10^{18} GeV and is currently the best result obtained with blazars. The sensitivity to the quadratic term is lower and provides a limit of M^{q}_{QG} > 6.4x10^10 GeV, which is the best value obtained so far with an AGN and similar to the best limits obtained with GRB.
Comment: 24 pages, 9 figures. Accepted for publication in Astropart. Phys. Rev1 is the final accepted version (typo corrections)