On the physical running of the electric charge in a dimensionless theory of gravity

M. Gomes; A. C. Lehum; A. J. da Silva

doi:10.1103/gc68-584n

paper

On the physical running of the electric charge in a dimensionless theory of gravity

arXiv:2512.11742 · doi:10.1103/gc68-584n

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 $μ$ -running in minimal subtraction, and (ii) a ''physical'' running extracted from the logarithmic dependence of amplitudes on a hard scale $Q^{2}$ (e.g., $p^{2}$ or a Mandelstam invariant) after removing IR effects. At one loop, using dimensional regularization with an IR mass regulator $m$ , 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 $ln μ^{2}$ pieces cancel--leaving only $ln (Q^{2} / m^{2})$ soft logs. Consequently, quadratic gravity does not modify the one-loop UV coefficient and thus does not alter $β (e)$ . Therefore, the physical running coincides with the $μ$ -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 $β (e)$ .

13 pages, 1 figure

On the physical running of the electric charge in a dimensionless theory of gravity

Abstract

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