TeV astrophysics constraints on Planck scale Lorentz violation

We analyze observational constraints from TeV astrophysics on Lorentz violating nonlinear dispersion for photons and electrons without assuming any a priori equality between the photon and electron parameters. The constraints arise from thresholds for vacuum Čerenkov radiation, photon decay and photo-production of electron-positron pairs. We show that the parameter plane for cubic momentum terms in the dispersion relations is constrained to an order unity region in Planck units. We find that the threshold configuration can occur with an asymmetric distribution of momentum for pair creation, and with a hard photon for vacuum Čerenkov radiation.