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We have performed a calculation in the parton-model approximation of anonstandard decay process in isotropic modified Maxwell theory coupled tostandard Dirac theory, with a single Lorentz-violating parameter $\kappa$ inthe photonic sector. Previous calculations of this process (vacuum Cherenkovradiation by a proton for the theory with $\kappa>0$) were performed forpointlike particles, and an upper bound on $\kappa$ at the $10^{-19}$ level wasobtained from experimental data on ultra-high-energy cosmic rays. Theparton-model results change the decay rate by about an order of magnitude butgive the same upper bound on $\kappa$ because the threshold energy isunchanged. The previous point-particle calculation of photon decay into anelectron-positron pair for the theory with $\kappa<0$ remains valid, andexperimental results on cosmic gamma rays provide a lower bound on $\kappa$ atthe $-10^{-15}$ level.

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