Universal leading quantum correction to the Newton potential

Ilya L Shapiro,Tibério De Paula Netto,Leonardo Modesto

doi:10.1140/epjc/s10052-022-10077-7

Abstract

The derivation of effective quantum gravity corrections to Newton’s potential is an important step in the whole effective quantum field theory approach. We hereby add new strong arguments in favor of omitting all the diagrams with internal lines of the massive sources, and we also recalculate the corrections to the Newtonian potential using functional methods in an arbitrary parametrization of the quantum fluctuations of the metric. The general proof of the gauge- and parametrization-independence within this approach is also explicitly given. On top of that, we argue that the universality of the result holds regardless of the details of the ultraviolet completion of quantum gravity theory. Indeed, it turns out that the logarithm quantum correction depends only on the low energy spectrum of the theory that is responsible for the analytic properties of loop’s amplitudes.

Highlights

Quantum corrections to Newton’s potential for the classical gravitational force is a kind of theoretical “standard candle” for the effective quantum gravity theory
The simplified model of scalar electrodynamics was used to prove that disregarding some of the diagrams is inconsistent as this procedure does not provide the gauge-fixing independence of the potential
In the calculations described below, we choose these sources as a massive point-like mass and a light point-like test particle, but in principle, the integral (1) can be explored for arbitrary massive sources, e.g., for the dark matter (DM), finite-size stars, or interstellar gas

Summary

Introduction

Quantum corrections to Newton’s potential for the classical gravitational force is a kind of theoretical “standard candle” for the effective quantum gravity theory. In the calculations described below, we choose these sources as a massive point-like mass and a light point-like test particle, but in principle, the integral (1) can be explored for arbitrary massive sources, e.g., for the dark matter (DM), finite-size stars, or interstellar gas In all these cases, the integration over is not included for the reasons described above. In the effective framework, in the IR only the massless fields are relevant, leaving only the effects of graviton and photon [2] In this effective setting, our antisemiclassical approach emerges naturally and the mixing of the massless degree of freedom with the ones of massive (macroscopic) degrees of freedom describing the classical sources does not look reasonable.

Derivation of effective action

Gravitational field in the Newtonian limit with quantum contributions

The motion of a test particle

General proof of gauge independence

Universality of the effective field theory result

Conclusions and discussions