Changes in extensive air showers from isotropic Lorentz violation in the photon sector

We consider a theory with isotropic nonbirefringent Lorentz violation in the photon sector and explore the effects on the development of the electromagnetic component of extensive air showers in the Earth atmosphere. Specifically, we consider the case of a "fast" photon with a phase velocity larger than the maximum attainable velocity of a massive Dirac fermion (this case corresponds to a negative Lorentz-violating parameter $\kappa$ in the action). Shower photons with above-threshold energies decay promptly into electron-positron pairs, instead of decaying by the conventional production of electron-positron pairs in the background fields of atomic nuclei. This rapid production of charged leptons accelerates the shower development, decreasing the atmospheric depth of the shower maximum ($X_\text{max}$) by an amount which could be measured by cosmic-ray observatories. Precise measurements of $X_\text{max}$ could then improve existing limits on the negative Lorentz-violating parameter $\kappa$ by several orders of magnitude.