Uniqueness of gravitational constant at low energies from the connection between spin-2 and spin-0 sectors

TL;DR

This paper demonstrates that the gravitational constant remains unique at low energies despite the complex structure of the graviton propagator, through a subtle connection between its spin-2 and spin-0 sectors, especially when quantum fields are involved.

Contribution

It reveals a non-trivial equivalence between the residues of the propagator's components, ensuring a consistent gravitational constant at large distances in quantum-corrected gravity with non-minimal coupling.

Findings

The residues of the propagator components are equivalent, supporting the decoupling theorem.

Quantum-corrected potentials share the same gravitational constant at large distances.

Experimental data constrains the non-minimal coupling parameter .

Abstract

The fact that graviton propagator contains not only one but two tensorial components excludes a unique definition of the running behavior of the gravitational constant, while at low energies gravitation is characterized solely by Newton's constant. How these two facts are reconciled when massive quantum fields are present remains unanswered. In this work, by non-minimally coupling gravity to a one-loop massive scalar, we show that this potential conflict is resolved by the non-trivial equivalence between the residues of the two propagator components. Such equivalence, crucial for the validity of the Appelquist-Carazzone decoupling theorem, is based on a rather subtle connection between the spin-2 and spin-0 sectors of the propagator. It is verified that this connection also makes the two quantum-corrected gravitational potentials be characterized by the same gravitational constant at large distances. In addition, we find that the potentials in our case as well as the quantum-corrected Coulomb potential can be expressed concisely in a unified formulation. By comparing these results with experiments, we establish a new upper bound on the magnitude of the non-minimal coupling parameter $\xi$.