Ultraviolet Modifications of Dispersion Relations in Effective Field Theory

The existence of a fundamental ultraviolet scale, such as the Planck scale, may lead to modifications of the dispersion relations for particles at high energies in some scenarios of quantum gravity. We apply effective field theory to this problem and identify dimension-5 operators that do not mix with dimensions 3 and 4 and lead to cubic modifications of dispersion relations for scalars, fermions, and vector particles. Further we show that, for electrons, photons and light quarks, clock comparison experiments bound these operators at ${10}^{-5}/M_{\mathrm{P}\mathrm{l}}$.