Gravitational Contact Interactions -- Does the Jordan Frame Exist?

Abstract: Scalar--tensor theories, with Einstein Hilbert and non-minimal interactions, $\sim M^2R/2 -\alpha\phi^2R/12 $, have graviton exchange induced contact interactions. These always pull the theory back into a formal Einstein frame in which $\alpha$ does not exist. In the Einstein frame, contact terms are induced, that are then absorbed back into other couplings to define the effective potential (or equivalently, the renormalization group). We show how these effects manifest themselves in a simple model by computing the effective potential in both frames displaying the discrepancy.