New Limits on Planck Scale Lorentz Violation in QED

Constraints on possible Lorentz symmetry violation (LV) of order $E/M_{\mathrm{P}\mathrm{l}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{k}}$ for electrons and photons in the framework of effective field theory (EFT) are discussed. Using (i) the report of polarized MeV emission from GRB021206 and (ii) the absence of vacuum Čerenkov radiation from synchrotron electrons in the Crab Nebula, we improve previous bounds by ${10}^{-10}$ and ${10}^{-2}$, respectively. We also show that the LV parameters for positrons and electrons are different, discuss electron helicity decay, and investigate how prior constraints are modified by the relations between LV parameters implied by EFT.

Figure 1

Constraints on the photon ($\xi$) and electron ($\eta$) LV parameters. The birefringence constraint uses the observed polarization of MeV photons from GRB021206. The synchrotron and IC Čerenkov constraints use the observation of 0.1 GeV synchrotron and 50 TeV inverse Compton radiation from the Crab Nebula, respectively. For the origin of other constraints, see the text. For negative parameters the negative of the logarithm of the absolute value is plotted, and a region of width ${10}^{-18}$ is excised around each axis. The synchrotron and Čerenkov constraints are known to apply only for at least one ${\eta }_{R,L}$. The IC and synchrotron Čerenkov lines are truncated where they cross. Prior photon decay and absorption constraints are shown in dashed lines since they do not account for the EFT relations between the LV parameters.