Exploring Lorentz Invariance Violation from Ultrahigh-Energy $\gamma$ Rays Observed by LHAASO

Recently, the LHAASO Collaboration published the detection of 12 ultrahigh-energy $\gamma$-ray sources above 100 TeV, with the highest energy photon reaching 1.4 PeV. The first detection of PeV $\gamma$ rays from astrophysical sources may provide a very sensitive probe of the effect of the Lorentz invariance violation (LIV), which results in decay of high-energy $\gamma$ rays in the superluminal scenario and hence a sharp cutoff of the energy spectrum. Two highest energy sources are studied in this work. No signature of the existence of the LIV is found in their energy spectra, and the lower limits on the LIV energy scale are derived. Our results show that the first-order LIV energy scale should be higher than about ${10}^5$ times the Planck scale $M_{\mathrm{Pl}}$ and that the second-order LIV scale is $>{10}^{-3}{M}_{\mathrm{Pl}}$. Both limits improve by at least one order of magnitude the previous results.

Figure 1

TS distributions of MC data with and without spectral cutoff, for the Crab Nebula and $E_{\mathrm{cut}}=250\mathrm{TeV}$. The red and blue lines are fitted results based on 700 000 MC simulations (showing as red and blue dots) for the LIV and LI cases, respectively. The fitting is to illustrate the $C{L}_s$ method, and the direct counting from the MC is used for the following calculation of the limits on $E_{\mathrm{cut}}$.

Figure 2

The probability $1-C{L}_s$ as a function of $E_{\mathrm{cut}}$ for the Crab Nebula (black line) and LHAASO $\mathrm{J}2032+4102$ (orange line). The red dots mark the $E_{\mathrm{cut}}$ value which are excluded at the 95% CL with the $C{L}_s$ method.

Figure 3

Comparison of the constraints on the $E_{\mathrm{LIV}}^{(1)}$ and $E_{\mathrm{LIV}}^{(2)}$ derived from LHAASO and other experiments [11, 19, 20, 22, 42]. We show constraints due to the photon decay ($e^{+}{e}^{-}$) and the photon splitting ($3\gamma$) processes for all experiments except for Fermi-LAT which adopted the time delay method ($\mathrm{\Delta }t$).