Role of Regularization in Quantum Corrections to the Scalar-Tensor Theories of Gravity

We show that regularizing divergent integrals is crucially important when applied to the loop diagrams corresponding to quantum corrections to the coupling of the “gravitational” scalar field due to the interaction among matter fields. We use the method of continuous spacetime dimensions to demonstrate that WEP is a robust property of the Brans-Dicke theory beyond the classical level, hence correcting our previous assertion of the contrary. The same technique can be used to yield the violation of WEP when applied to the scale-invariant theory, thus providing another reason for expecting fifth-force-type phenomena. In our previous paper [1] we argued that a type of quantum correction to the Brans-Dicke (BD) theory [2] results in a rather large effect of violating composition-independence of the scalar-matter coupling. It was claimed that precision tests of WEP constrain the parameter ω much more strongly than those derived from the solar-system experiments. Subsequently, however, we came to realize that the effect is an artifact of our neglect of “regularizing” basically divergent integrals, thus re-establishing WEP as a robust property of the theory beyond the classical level. The revised analysis to be presented here is essentially revisiting the lesson which was learned in such historic issues as self-stress [3] and trace anomaly [4]. It seems, however, that the same care might be crucially important in studying other quantum effects to some of the matter-gravity interaction. For this reason we try to explain essential ingredients of the discussion briefly but in a somewhat self-contained manner, hence allowing minimum overlapping with Ref. [1]. According to the “lesson,” the fact that an integral which is divergent judged from power-counting turns out to be finite does not necessarily mean that no Electronic address: [email protected]