Abstract
In the effective field theory of quantum gravitation coupled to Ns scalars, Nf fermions, and NV vectors, tree unitarity is violated at an energy squared of ECM2=20(GNN)−1, where N≡23Ns+Nf+4NV and GN is Newton's constant. This is related to radiative corrections proportional to GNNE2 (where E is the typical energy), due to loops of such particles. New physics must enter before ECM≈6×1018 GeV in the standard model, and 4×1018 GeV in the minimal supersymmetric standard model.
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