Improved bound on isotropic Lorentz violation in the photon sector from extensive air showers

Cosmic rays have extremely high particle energies (up to $10^{20} \; \text{eV}$) and can be used to search for violations of Lorentz invariance. We consider isotropic nonbirefringent Lorentz violation in the photon sector for the case of a photon velocity larger than the maximum attainable velocity of the standard fermions. Up to now, Earth-based bounds on this type of Lorentz violation have been determined from observations of TeV gamma rays. Here, we elaborate on a novel approach to test Lorentz invariance with greatly improved sensitivity. This approach is based on investigating extensive air showers which are induced by cosmic-ray particles in the Earth's atmosphere. We study the impact of two Lorentz-violating decay processes on the longitudinal development of air showers, notably the atmospheric depth of the shower maximum $X_\text{max}$. Specifically, the two Lorentz-violating decay processes considered are photon decay into an electron-positron pair and modified neutral-pion decay into two photons. We use Monte Carlo simulations performed with the CONEX code which was extended to include these two Lorentz-violating decay processes at a magnitude allowed by the best previous Earth-based bound. Compared to standard physics, these Lorentz-violating decay processes reduce the average $X_\text{max}$ for showers with primary energies above $10^{18}\;\text{eV}$ by an amount that is significantly larger than the average resolution of current air shower experiments. Comparing the simulations of the average $X_\text{max}$ to observations, new Earth-based bounds on this type of Lorentz violation are obtained, which are better than the previous bounds by more than three orders of magnitude. Prospects of further studies are also discussed.