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

TL;DR

This study uses spectral lag data from 56 gamma-ray bursts to set lower limits on the energy scale of Lorentz Invariance Violation, employing a profile likelihood method to handle uncertainties and nuisance parameters.

Contribution

It introduces a profile likelihood approach to constrain LIV energy scales from GRB spectral lag data, providing robust lower limits without assuming a global minimum.

Findings

Lower limit on linear LIV scale: 2.07 x 10^{14} GeV

Lower limit on quadratic LIV scale: 3.71 x 10^{5} GeV

No evidence of LIV up to Planck scale

Abstract

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: $E_{QG}\geq 2.07 \times 10^{14}$ GeV and $E_{QG}\geq 3.71\times 10^{5}$ GeV, for linear and quadratic LIV, respectively.