usual theoretical framework for running couplings, the renormalization group, does not by itself define a running $G$. And while a definition generally can be made that is useful within a given process, the quantum effects are so non-universal that this definition will not be usefully applied to other reactions.

We have illustrated a series of reactions with one-loop corrections which differ significantly. Perhaps lost in the variety of signs and magnitudes is the key point that quantum corrections do not organize themselves into a running coupling. This is the expected behavior of an effective field theory. The relevant higher order operators are process dependent and decoupled from the renormalization of the lowest order operator. The kinematic variation of the one loop corrections are more complex than just mirroring the leading behavior because they involve higher powers of the momentum invariants and there are many allowed kinematic factors present at higher order. Attempts to repackage this larger kinematic variation as if it were a modification of the lowest order amplitude, i.e. a running coupling, will then in general fail because the running coupling cannot mimic the richer kinematics of the higher order terms. This leads directly to the crossing problem and 