Search for Lorentz Invariance Violation with spectral lags of GRB 190114C using profile likelihood

TL;DR

The paper addresses testing Lorentz invariance violation (LIV) using GRB spectral lag data. It employs a frequentist profile likelihood approach to profile over astrophysical nuisance parameters, applied to GRB 190114C, and compares the results to prior Bayesian analyses. The authors find best-fit LIV scales $E_{QG}$ for linear and quadratic models that lie below the Planck scale, with tight 68% and 95% confidence intervals, and they report a good fit quality while noting no evidence for LIV given stronger bounds from other observations. The work demonstrates a complementary analysis framework, provides open-source code for replication, and discusses caveats related to Wilks' theorem applicability and the interpretation of results within the broader LIV landscape.

Abstract

We search for Lorentz invariance violation (LIV) by re-analyzing the spectral lag data for GRB 190114C \rthis{from Fermi-GBM} using frequentist analysis, where we deal with the astrophysical nuisance parameters using profile likelihood. For this use case, we find a global minima for the $χ^2$ as a function of energy scale of LIV ($E_{QG}$), well below the Planck scale. The best-fit $1σ$ central intervals for $E_{QG}$ are given by $2.81^{+0.50}_{-0.37}\times 10^{14}$ GeV and $9.85^{+0.84}_{-0.60}\times 10^{5}$ GeV for linear and quadratic LIV, respectively, and agree with the Bayesian estimates obtained so far in a previous work. Therefore, the results from the frequentist analysis of GRB 190114C agree with Bayesian analysis.

Figures (4)

• Figure 1: $\Delta \chi^2$, defined as ($\chi^2-\chi^2_{min}$), plotted against $E_{QG}$ for a linearly-dependent LIV, corresponding to $n = 1$. The horizontal magenta dashed line represents $\Delta\chi^2 = \textcolor{black}{3.84}$ and the horizontal red dashed line represents $\Delta\chi^2 = 1$. The corresponding X-intercepts, provide us the both the 68.3% confidence interval ($\Delta\chi^2 = 1$) for $E_{QG,1} = 2.81^{+0.50}_{-0.37}\times 10^{14}$ GeV and the 95% confidence interval ($\Delta\chi^2 = 3.84$) for $E_{QG,1} = 2.81^{+0.99}_{-0.73}\times 10^{14}$ GeV.
• Figure 2: $\Delta \chi^2$, defined as ($\chi^2-\chi^2_{min}$), plotted against $E_{QG}$ for a quadratically-dependent LIV, corresponding to $n = 2$. The horizontal indigo dashed line represents $\Delta\chi^2 = \textcolor{black}{3.84}$ and the horizontal sienna dashed line represents $\Delta\chi^2 = 1$. The corresponding x-intercepts, provide us the both the 68.3% confidence interval ($\Delta\chi^2 = 1$) for $E_{QG,2} = 9.85^{+0.84}_{-0.60}\times 10^{5}$ GeV and the 95% confidence interval ($\Delta\chi^2 = 3.84$) for $E_{QG,2} = 9.85^{+1.62}_{-1.25}\times 10^{5}$ GeV.
• Figure 3: $\Delta \chi^2$, defined as ($\chi^2-\chi^2_{min}$), plotted against $E_{QG}$ for a linearly-dependent LIV, obtained from generating synthetic data samples. The input value of $E_{QG}$ used to generate the synthetic samples, is the best-fit obtained earlier in Fig.\ref{['fig:linearLIV']}, $E_{QG}=2.81 \times 10^{14}$. The horizontal dashed line represents $\Delta\chi^2 = 1$ and gives us the 68.3% confidence interval for $E_{QG,1,synt} = 2.72^{+0.43}_{-0.40}\times 10^{14}$ GeV.
• Figure 4: $\Delta \chi^2$, defined as ($\chi^2-\chi^2_{min}$), plotted against $E_{QG}$ for a quadratically-dependent LIV, obtained from generating synthetic data samples. The input value of $E_{QG}$ used to generate the synthetic samples, is the best-fit obtained earlier in Fig.\ref{['fig:quadLIV']}, $E_{QG}=9.85 \times 10^{5}$. The horizontal dashed line represents $\Delta\chi^2 = 1$ and gives us the 68.3% confidence interval for $E_{QG,2,synt} = 1.05^{+0.07}_{-0.09}\times 10^{6}$ GeV.