Test of Lorentz invariance: exploiting the potential of air showers at ultra-high energy

In extensive air showers induced by ultra-high-energy (UHE) cosmic rays, secondary particles are produced with energies far above those accessible by other means. These extreme energies can be used to search for new physics beyond the current Standard Model of particle physics. In this work, the effects of isotropic, nonbirefringent Lorentz violation in the photon sector are investigated. In the case of a photon velocity smaller than the maximum attainable velocity of standard Dirac fermions, vacuum Cherenkov radiation becomes possible. For photon velocities greater than the maximum attainable velocity of standard Dirac fermions, photon decay is introduced together with a change in the decay time of neutral pions. Implementing these Lorentz-violating effects in air-shower simulations, a significant reduction of the average atmospheric depth of the shower maximum ⟨Xmax⟩ is obtained in both cases. Based on measurements of ⟨Xmax⟩ and its shower-to-shower fluctuations σ(Xmax), a new two-sided bound on Lorentz violation exploiting the high energies of particles in air showers is presented. The impact of Lorentz violation on the number of muons in air showers is also discussed.