are properly done. Dimensional regularization is a good regulator for the gravitational interaction because it has a clear and direct interpretation. For this reason, we use dimensional regularization throughout this paper.

Pure gravity: The graviton propagator
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Let us first consider the purely gravitational sector. At one loop, pure gravity is finite for on-shell amplitudes, because the higher order counterterms, $R^2$ and $R_{\mu\nu} R^{\mu\nu}$ vanish by the equation of motion $R_{\mu\nu}=0$. Finite one-loop corrections do exist. These are higher order in the momentum variables, and do not have the same kinematic dependence as the lowest order effects governed by the gravitational constant $G$. However, by working at a high energy renormalization scale, we will see if we can attempt to package these loop effects as a running coupling $G(E)$.

Even though our primary focus in this paper involves on-shell physical reactions, it is useful to start by consideration of the vacuum polarization diagram and the graviton propagator. The only quantum correction that is demonstrably universal is that involving the vacuum polarization. Every graviton exchange receives a correction from the vacuum polarization. Because each end of the propagator carries a factor of $\kappa$, a modification of the propagator could be interpreted 