Addendum: Ultrahigh-energy cosmic-ray bounds on nonbirefringent   modified-Maxwell theory
  Nonbirefringent modified-Maxwell theory, coupled to standard Dirac particles, involves nine dimensionless parameters, which can be bounded by the inferred absence of vacuum Cherenkov radiation for ultrahigh-energy cosmic rays (UHECRs). With selected UHECR events, two-sided bounds on the eight nonisotropic parameters are obtained at the 10^{-18} level, together with an improved one-sided bound on the single isotropic parameter at the 10^{-19} level. 
F.R. Klinkhamer, M. Risse