
In the effective field theory of quantum gravitation coupled to N_s scalars, N_f fermions, and N_V vectors, tree unitarity is violated at an energy squared of E_{CM}^2 = 20(G_N N)^{-1}, where N = {2/3}N_s + N_f + 4N_V and G_N is Newton's constant. This is related to radiative corrections proportional to G_N N E^2 (where E is the typical energy), due to loops of such particles. New physics must enter before E_{CM}=5.6 x 10^{18} GeV in the standard model, and 4.6 x 10^{18} GeV in the minimal supersymmetric standard model.
6 pages. Accepted for publication in PLB
High Energy Physics - Theory, High Energy Physics - Phenomenology, High Energy Physics - Phenomenology (hep-ph), High Energy Physics - Theory (hep-th), FOS: Physical sciences, String and superstring theories in gravitational theory, General Relativity and Quantum Cosmology (gr-qc), Quantization of the gravitational field, quantum gravitation, General Relativity and Quantum Cosmology, Gravitational interaction in quantum theory
High Energy Physics - Theory, High Energy Physics - Phenomenology, High Energy Physics - Phenomenology (hep-ph), High Energy Physics - Theory (hep-th), FOS: Physical sciences, String and superstring theories in gravitational theory, General Relativity and Quantum Cosmology (gr-qc), Quantization of the gravitational field, quantum gravitation, General Relativity and Quantum Cosmology, Gravitational interaction in quantum theory
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