Parton-model calculation of a nonstandard decay process in isotropic modified Maxwell theory

We have performed a calculation in the parton-model approximation of a nonstandard decay process in isotropic modified Maxwell theory coupled to standard Dirac theory, with a single Lorentz-violating parameter $\kappa$ in the photonic sector. Previous calculations of this process (vacuum Cherenkov radiation by a proton for the theory with $\kappa >0$) were performed for pointlike particles, and an upper bound on $\kappa$ at the ${10}^{-19}$ level was obtained from experimental data on ultra-high-energy cosmic rays. The parton-model results change the decay rate by about an order of magnitude but give the same upper bound on $\kappa$ because the threshold energy is unchanged. The previous point-particle calculation of photon decay into an electron-positron pair for the theory with $\kappa <0$ remains valid, and experimental results on cosmic gamma rays provide a lower bound on $\kappa$ at the $-{10}^{-15}$ level.