Newtonian potential from scattering amplitudes in super-renormalizable gravity

Abstract

Using scattering amplitudes, we compute the coupling between a general super-renormalizable gravity theory and massive scalar particles. This allows us to derive the $D$-dimensional Newtonian potential at both tree-level and one-loop level-the latter containing the first calculation by using newly derived three-graviton Feynman rules. In four-dimensional spacetime, we numerically demonstrate that the Newtonian potential remains finite at the origin, providing compelling evidence that the singularity-free nature of super-renormalizable gravity persists at the one-loop level.

Figures (4)

• Figure 1: The tree-level contribution to the three-point vertex function involves the graviton momentum $q$, and the four-momentum $k$ of the on-shell particle, which satisfies the condition $k^2 = m^2$.
• Figure 2: The one-loop contribution to the three-point vertex function involves $q$, and $k$. The loop momentum is denoted by $l$.
• Figure 3: The Newtonian potential in $D = 4$ dimension as a function of distance.
• Figure 4: The Feynman diagram for the three-graviton vertex interaction with $2i\kappa V^{\mu\nu\alpha\beta\gamma\delta}_{h^3}$p,q,k$$.