Scale of quantum gravity

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≈6×1018GeV in the standard model, and 4×1018GeV in the minimal supersymmetric standard model.