A New Limit on Planck Scale Lorentz Violation from Gamma-ray Burst   Polarization
  Constraints on possible Lorentz invariance violation (LIV) to first order in $E/M_{\rm Planck}$ for photons in the framework of effective field theory (EFT) are discussed, taking cosmological factors into account. Then, using the reported detection of polarized soft $\gamma$-ray emission from the $\gamma$-ray burst GRB041219a that is indicative of an absence of vacuum birefringence, together with a very recent improved method for estimating the redshift of the burst, we derive constraints on the dimension 5 Lorentz violating modification to the Lagrangian of an effective local QFT for QED. Our new constraints are more than five orders of magnitude better than recent constraints from observations of the Crab Nebula. We obtain the upper limit on the Lorentz violating dimension 5 EFT parameter $|\xi|$ of $2.4 \times 10^{-15}$, corresponding to a constraint on the dimension 5 standard model extension parameter, $k^{(5)}_{(V)00} \le 4.2 \times 10^{-34}$ GeV$^{-1}$. 
Floyd W. Stecker
astro-ph.HE astro-ph.CO gr-qc hep-ph