Lorentz violation in simple QED processes
  We determine the effect of a CPT-even and Lorentz violating non-minimal coupling on the differential cross sections for some of the most important tree-level processes in QED, namely, Compton and Bhabha scatterings, as well as electron-positron annihilation. Experimental limits constraining the allowed deviation of the differential cross sections relative to pure QED allow us to place upper bounds on the Lorentz violating parameters. A constraint based on the decay rate of para-positronium is also obtained. 
G.P. de Brito, J.T. Guaitolini Junior, D. Kroff, P.C. Malta, C.   Marques
hep-ph hep-th