Gravitational interaction to one loop in effective quantum gravity

TL;DR

This paper treats gravity as an effective field theory at energies well below the Planck scale and isolates the non-analytic one-loop quantum-gravity contributions to the long-range interaction between heavy scalars. It derives the leading corrections to the Newtonian potential, presents the lowest-order Feynman rules, and computes both vertex corrections and vacuum-polarization effects, yielding a corrected potential with a specific quantum term that differs in detail from prior results. The authors emphasize that these non-analytic corrections are finite and regulator-independent, valid only at low energies, and highlight discrepancies with previous work as well as limitations of the approach near the Planck scale. The work provides a concrete, calculable framework for quantum gravitational effects in a realistic, low-energy setting and lays groundwork for further exploration of gravity’s quantum corrections within effective field theory.

Abstract

We carry out the first step of a program conceived, in order to build a realistic model, having the particle spectrum of the standard model and renormalized masses, interaction terms and couplings, etc. which include the class of quantum gravity corrections, obtained by handling gravity as an effective theory. This provides an adequate picture at low energies, i.e. much less than the scale of strong gravity (the Planck mass). Hence our results are valid, irrespectively of any proposal for the full quantum gravity as a fundamental theory. We consider only non-analytic contributions to the one-loop scattering matrix elements, which provide the dominant quantum effect at long distance. These contributions are finite and independent from the finite value of the renormalization counter terms of the effective lagrangian. We calculate the interaction of two heavy scalar particles, i.e. close to rest, due to the effective quantum gravity to the one loop order and compare with similar results in the literature.