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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2512.11742 |
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| _version_ | 1866911659996479488 |
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| author | Gomes, M. Lehum, A. C. da Silva, A. J. |
| author_facet | Gomes, M. Lehum, A. C. da Silva, A. J. |
| contents | 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 $\lnμ^{2}$ 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 $β(e)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_11742 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the physical running of the electric charge in a dimensionless theory of gravity Gomes, M. Lehum, A. C. da Silva, A. J. High Energy Physics - Theory High Energy Physics - Phenomenology 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 $\lnμ^{2}$ 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 $β(e)$. |
| title | On the physical running of the electric charge in a dimensionless theory of gravity |
| topic | High Energy Physics - Theory High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2512.11742 |