Probing Lorentz violation at ultra-high energies using air showers

In air showers initiated by ultra-high-energy cosmic rays in the Earth's atmosphere, even the secondary particles created in the start-up phase are produced at energies far above those accessible by other means. These high-energy particles can be used to search for New Physics, such as a violation of Lorentz invariance. We focus on isotropic, nonbirefringent Lorentz violation in the photon sector and consider the two cases kappa < 0 and kappa > 0 (i.e., the velocity of photons is larger/smaller than the maximum attainable velocity of standard Dirac fermions). In both cases, processes that are forbidden in the standard, Lorentz-invariant theory (kappa = 0) become allowed, in particular photon decay in the case kappa < 0 and vacuum-Cherenkov radiation for kappa > 0. Implementing these processes into air-shower simulations, we found that the development of an air shower at the highest energies can be significantly impacted, specifically the average atmospheric depth of the shower maximum < X-max > and its shower-to-shower fluctuations sigma(X-max). Comparing these simulations to actual measurements, we were able to obtain much stricter bounds on this specific type of LV in the case kappa < 0 than possible with previous methods. We discuss these limits and, in addition, present first results for the case kappa > 0.