the quantum corrections to the scattering of heavy objects - let us call them planets. Are the gravitational corrections here similar to those of massless scalars or gravitons? This tests the universality property of a running coupling. This scattering amplitude is closest to the situations that we are familiar with defining the running couplings in QED or QCD

The gravitational interaction at one-loop is the result of several Feynman diagrams that vary in magnitude and sign. Written in coordinate space, the total loop correction changes the interaction to that quoted above in Eq. 1. Written in its original momentum space for this corresponds to $$V(q) = -4\pi\frac{GMm}{\mathbf{q}^2}\left[1+\frac{41}{20\pi}G{\mathbf{q}}^2\ln \left( \frac{\mu^2}{{\mathbf q}^2}\right)\right]\,.
\label{potential}$$ Note that in this case, we have written this result in terms of the spatial part of $q^2$, i.e. $q^2=-{\mathbf q}^2$ because the results were derived in the non-relativistic approximation. We should not consider crossing this amplitude to timelike $q^2$ because the planet masses could be well above the Planck scale. This result corresponds to an increase in the gravitational strength with increasing energy. Ascribing it to a a running $G$ would yield Eq. 2, or equivalently the momentum factor in square brackets in Eq. \[potential\]. Note that the 