Constraints on Lorentz Invariance Violation from Gamma-ray Burst rest-frame spectral lags using Profile Likelihood

We reanalyze the spectral lag data for 56 Gamma-Ray Bursts (GRBs) in the cosmological rest frame to search for Lorentz Invariance Violation (LIV) using frequentist inference. For this purpose, we use the technique of profile likelihood to deal with the nuisance parameters, corresponding to a constant time lag in the GRB rest frame and an unknown intrinsic scatter, while the parameter of interest is the energy scale for LIV ($E_{QG}$). With this method, we do not obtain a global minimum for ${\chi }^2$ as a function of $E_{QG}$ up to the Planck scale. Thus, we can obtain one-sided lower limits on $E_{QG}$ in a seamless manner. Therefore, the 95% c.l. lower limits which we thus obtain on $E_{QG}$ are then given by: $E_{QG}\ge 2.07\times {10}^{14}$ GeV and $E_{QG}\ge 3.71\times {10}^5$ GeV, for linear and quadratic LIV, respectively.