Scalar-tensor theories, trace anomalies and the QCD-frame

We consider the quantum effects of matter fields in scalar-tensor theories and clarify the role of trace anomaly when switching between conformally related `frames'. We exploit the property that the couplings between the scalar and the gauge fields are not frame-invariant in order to define a `QCD-frame', where the scalar is not coupled to the gluons. We show that this frame is a natural generalization of the `Jordan frame' in the case of non-metric theories and that it is particularly convenient for gravitational phenomenology: test bodies have trajectories that are as close as possible to geodesics with respect to such a metric and equivalence principle violations are directly proportional to the scalar coupling parameters written in this frame. We show how RG flow and decoupling work in metric and non-metric theories. RG-running commutes with the operation of switching between frames at different scales. When only matter loops are considered, our analysis confirms that metricity is stable under radiative corrections and shows that approximate metricity is natural in a technical sense.