explicit calculation [@Toms:2011zz].

These same comments apply to dimensionful cutoffs and the gravitational coupling $G$. When using a scheme with a dimensionful cutoff, one will generate corrections to the gravitational constant $G=G_0(1+aG_0\Lambda^2)$. If this is done in a way that preserves general covariance, the same correction will be obtained in any process that involves $G$. This quadratic dependence will disappear from all observables once one identifies the physical renormalized parameter $G$ to be equal to its Newtonian value.

Note that the logarithmic $\ln \Lambda$ dependence can be useful in tracing the running of couplings. This is because at high energies the logarithm must also contain kinematic variables, i.e. $\ln (\Lambda^2/q^2)$. This is analogous to tracing the $\ln q^2 $ behavior from the $1/\epsilon$ dependence in dimensional regularization.

These features explain how dimensional regularization and cutoff regularization can agree in calculations involving gravity. There are no quadratic divergences in dimensional regularization, but we have seen that such divergences in cutoff schemes disappear from observables under renormalization. When considering gravitational corrections, the logarithmic cutoff dependence and the $1/\epsilon$ dependence are both associated with higher order terms of order $\kappa^2 q^2$, and the residual kinematic effects will be in agreement when the calculations 