TeV Astrophysics Constraints on Planck Scale Lorentz Violation

Abstract

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 Cerenkov 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 Cerenkov radiation.

Figures (1)

• Figure 1: Combined constraints on the dimensionless photon and electron parameters for the case $n=3$ ($\eta,\,\xi=1$ corresponds to the dimensionful coefficient $M^{-1}=10^{-19}$ GeV${}^{-1}$ of the $n=3$ term in Eq. (\ref{['eq:pdr']})). The regions excluded by the photon decay and Ĉerenkov constraints are lined horizontally in blue and vertically in red respectively. The region between the two diagonal green lines corresponds to a threshold between one and two times the standard threshold (which is $10$ TeV for photon annihilation with an IR photon of energy 0.025 eV). The upper green line corresponds to the unmodified threshold. The shaded patch is the part of the allowed region that falls between these photon annihilation thresholds. The dashed line is $\xi=\eta$.