Weakness of accelerator bounds on departures from Lorentz symmetry for the electron

Abstract

The reference laboratory bounds on departures from Lorentz symmetry for the electron are obtained from the absence of in vacuo Cherenkov processes and the determinations of synchrotron radiated power for LEP electrons. It is usually assumed that these analyses establish the validity of a standard special-relativistic description of the electron with accuracy of at least a few parts in 1014, and in particular this is used to exclude electron superluminality with such an accuracy. We observe that these bounds rely crucially on the availability of a preferred frame. In vacuo Cherenkov processes are automatically forbidden in any theory with “deformed Lorentz symmetry”, relativistic theories that, while different from Special Relativity, preserve the relativity of inertial frames. Determinations of the synchrotron radiated power can be used to constrain the possibility of Lorentz-symmetry deformation, but provide rather weak bounds, which in particular for electron superluminality we establish to afford us no more constraining power than for an accuracy of a few parts in 104.