interactions.

Dimensional cutoffs
===================

The comments of the preceding section are reasonably obvious when dimensional regularization is used. Indeed they are consistent with the portion of the literature concerning gravitational corrections to gauge couplings that employed dimensional regularization [@doesnot]. However, more recently there has been another subset of this literature which used dimensionful cutoffs in the analysis and which reached the opposite conclusion, i.e. that there was a universal gravitational correction to the running of the gauge charges [@does; @does2]. This dichotomy appears to violate a key principle that true physics is independent of the renormalization scheme. In fact, there is no disagreement between the schemes and the apparent difference arises from an incorrect interpretation of the dimensionful cutoff schemes. It is important for us to demonstrate the flaw of these cutoff calculations, because many attempts to define a running gravitational constant, $G(\Lambda)$ employ a similarly incorrect reasoning.

If we rescale the vector field, $A^\mu \to A^\mu/e_0$, then the electric charge appears only in the photon part of the Lagrangian $${\cal L} = -\frac{1}{4e_0^2}F_{\mu\nu}F^{\mu\nu} + \bar{\psi} i \slashed{D}\psi\,.$$ After including gravition loops regularized with a dimensional cutoff $\Lambda$, there is a quadratic cutoff dependence in the leading term, as well 