The higher order corrections are proportional to $Gq^2$, and $q^2$ refers to a four-vector which can take both positive and negative values. A renormalization condition defined at one sign of $q^2$ produces a charge definition that fails to be applicable in the crossed reaction with the opposite sign of $q^2$. We will refer to this as the [*crossing problem*]{}. (In the above schematic example, this is visible in the ambiguity between renormalizing at $q^2=+E^2$ or $q^2=-E^2$.) The other obstruction is process dependence or [*non-universality*]{}. Because there are in general multiple higher order operators that are possible, and because these enter into different processes in different ways, the divergences and finite parts of different reactions will not be the same. A definition of the charge that is appropriate for one reaction will not work for another. To be useful, a running coupling must capture at least a significant or common portion of the quantum corrections. (In the preceding schematic example, problems would arise if the ratio $b_i/a_i$ is highly process dependent.) We have demonstrated these obstacles in Yukawa theories [@Anber:2010uj], and the same problems arise in the attempts to define gravitational corrections to running gauge charges.

In renormalizable theories these obstacles 