Paper
On the physical running of the electric charge in a dimensionless theory of gravity
Authors
M. Gomes, A. C. Lehum, A. J. da Silva
Abstract
We revisit the renormalization of the gauge coupling in massless QED coupled to a scaleless quadratic theory of gravity. We compare two alternative prescriptions for the running of the electric charge: (i) the conventional -running in minimal subtraction, and (ii) a ''physical'' running extracted from the logarithmic dependence of amplitudes on a hard scale (e.g., or a Mandelstam invariant) after removing IR effects. At one loop, using dimensional regularization with an IR mass regulator , we compute the photon vacuum polarization. We find a clean separation between UV and soft logarithms: the former is gauge and process independent and fixes the beta function, whereas the latter encodes nonlocal, IR-dominated contributions that may depend on gauge parameters and must not be interpreted as UV running. In the quadratic-gravity sector, the photon self-energy is UV finite--the pieces cancel--leaving only soft logs. Consequently, quadratic gravity does not modify the one-loop UV coefficient and thus does not alter . Therefore, the physical running coincides with the -running in QED at one loop. Our analysis clarifies how to extract a gauge and process independent running in the presence of gravitational interactions and why soft logs from quadratic gravity should not contribute to .