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 $κ$ in the photonic sector. Previous calculations of this process (vacuum Cherenkov radiation by a proton for the theory with $κ>0$) were performed for pointlike particles, and an upper bound on $κ$ 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 $κ$ because the threshold energy is unchanged. The previous point-particle calculation of photon decay into an electron-positron pair for the theory with $κ<0$ remains valid, and experimental results on cosmic gamma rays provide a lower bound on $κ$ at the $-10^{-15}$ level.

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