Cerenkov-Like Emission of Pions by Photons in a Lorentz-Violating Theory

In the presence of Lorentz violation, the Cerenkov-like process $\gamma \to \gamma +{\pi }^0$ may become allowed for sufficiently energetic photons. Photons above the threshold would lose energy rapidly through pion emission. The fact that propagating photons with energies of up to 80 TeV survive to be observed on Earth allows us to place a one-sided constraint on an isotropic Lorentz violating parameter at the $7\times {10}^{-13}$ level; this is more than an order of magnitude better than best previous result.