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arXiv · 2510.10270

Newtonian potential from scattering amplitudes in super-renormalizable gravity

Haiyuan Feng·Rong-Jia Yang·Jinjun Zhang
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Abstract

Based on the classical limit of relativistic scattering amplitudes, we compute the coupling between a general super-renormalizable gravity and massive scalar particles. This allows us to derive the $D$-dimensional metric corrections at both tree-level and one-loop level-the latter containing the first calculation by using newly derived three-graviton Feynman rules. By introducing Newtonian potential function $\Phi\equiv\frac{h_{00}}{2}$, we reproduce at tree level, $\mathcal{O}(G)$, the well-known result proportional to the error function in four-dimensional spacetime. Furthermore, we obtain the loop-level contributions to the potential function at order $\mathcal{O}(G^2)$ and perform a numerical analysis of its behavior at large distances. Our results indicate that, at the one-loop level, the magnitude of the potential increases gradually with distance in the asymptotic regime.

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Haiyuan Feng, Rong-Jia Yang, Jinjun Zhang. 2025-10-11. Newtonian potential from scattering amplitudes in super-renormalizable gravity. https://arxiv.org/abs/2510.10270

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