Probing Lorentz Invariance Violation at High Energies Using LHAASO Observations of GRB221009A via DisCan Algorithm

TL;DR

This work tests Lorentz invariance by searching for energy-dependent photon dispersion in TeV photons from GRB221009A using the dispersion-cancellation (DisCan) algorithm. By minimizing Shannon entropy of the reconstructed intrinsic time profile over LIV parameters for first- and second-order scenarios, and by combining LHAASO KM2A and WCDA data with energy-resolution Monte Carlo treatment, the authors derive stringent 95% confidence-level lower limits on the quantum-gravity energy scale: $E_{\rm QG}/10^{19}\text{ GeV} > 13.8$ (superluminal) and $>21.1$ (subluminal) for 1st order, and $E_{\rm QG}/10^{11}\text{ GeV} > 13.7$ (superluminal) and $>14.9$ (subluminal) for 2nd order. The energy-weighted profile proves more powerful than the count-based one, and the bounds are consistent with prior analyses, highlighting the viability of TeV-scale LIV tests with LHAASO data.

Abstract

The Lorentz invariance violation (LIV) predicted by some quantum gravity theories would manifest as an energy-dependent speed of light, which may potentially distort the observed temporal profile of photons from astrophysical sources at cosmological distances. The dispersion cancellation (DisCan) algorithm offers a powerful methodology for investigating such effects by employing quantities such as Shannon entropy, which reflects the initial temporal characteristics. In this study, we apply the DisCan algorithm to search for LIV effects in the LHAASO observations of GRB 221009A, combining data from both the WCDA and KM2A detectors that collectively span an energy range of $\sim 0.2-13$ TeV. Our analysis accounts for the uncertainties from both energy resolution and temporal binning. We derive $95\%$ confidence level lower limits on the LIV energy scale of $E_{\rm{QG}}/10^{19}~\text{GeV}>21.1$ (13.8) for the first-order subluminal (superluminal) scenario, and $E_{\rm{QG}}/10^{11}~\text{GeV}> 14.9$ (13.7) for the second-order subluminal (superluminal) scenario.

Figures (11)

• Figure 1: The distributions of Shannon entropy for the photons concerning the 1st-order LIV parameter $\tau_1$ with time bin widths of 0.3 s, 3 s, and 15 s. The photons are randomly generated over a uniform time interval from 0 to 100 s, incorporating the LIV effects with a parameter value of $\tau_1^* = -0.537$. The red and blue curves correspond to the results derived with the energy-weighted and photon-count profiles, respectively. The red and blue vertical dashed lines indicate the optimal $\tau_1$ values that minimize the Shannon entropy for the two cases, respectively.
• Figure 2: The same as Fig. \ref{['3-1']}, but for the arrival time profile of photons generated with a normal distribution.
• Figure 3: The same as Fig. \ref{['3-1']}, but for the photons generated using the time profile and energy spectrum reported by the LHAASO collaboration.
• Figure 4: The dependence of the optimal parameter $\tau$ on $\Delta t$. The left, middle and right panels correspond to the cases shown in Fig. \ref{['3-1']}, Fig. \ref{['3-2']} and Fig. \ref{['3-3']}, respectively.
• Figure 5: The variation of Shannon entropy with the 1st-order LIV parameters $\tau_1$ for time binning intervals of 0.5 s, 2 s, 5 s, and 20 s, respectively. The red (blue) and green (yellow) curves correspond to the results in the [230,400] s and [230,500] s intervals analyzed using the count-based (energy-weighted) profile, respectively.