Leading quantum gravitational corrections to scalar QED

TL;DR

This work treats general relativity as an effective quantum field theory and computes the leading post-Newtonian and quantum corrections to the non-relativistic scattering of charged scalars in the combined GR+scalar QED theory. Using the background-field method and the full set of 1-loop diagrams, the authors extract the non-analytic long-range parts that determine the quantum corrections to the two-body potential, then sum these contributions to obtain a corrected potential that includes Newtonian, Coulomb, classical PN, and leading quantum terms: $V(r) = -\dfrac{G m_1 m_2}{r} + \dfrac{\tilde{\alpha} \tilde{e}_1 \tilde{e}_2}{r} + \cdots$. The results reproduce known gravitational vertex corrections and reveal explicit yet extremely small quantum gravitational corrections, with the dominant Newtonian and electromagnetic terms swamping the quantum effects. The findings illustrate the viability of EFT methods for gravity at low energies and provide explicit expressions for quantum corrections to the two-body potential, informing both theoretical understanding and the search for possible experimental or null-signature tests of quantum gravity.

Abstract

We consider the leading post-Newtonian and quantum corrections to the non-relativistic scattering amplitude of charged scalars in the combined theory of general relativity and scalar QED. The combined theory is treated as an effective field theory. This allows for a consistent quantization of the gravitational field. The appropriate vertex rules are extracted from the action, and the non-analytic contributions to the 1-loop scattering matrix are calculated in the non-relativistic limit. The non-analytical parts of the scattering amplitude, which are known to give the long range, low energy, leading quantum corrections, are used to construct the leading post-Newtonian and quantum corrections to the two-particle non-relativistic scattering matrix potential for two charged scalars. The result is discussed in relation to experimental verifications.

Figures (9)

• Figure 1: The set of tree diagrams contributing to the potential.
• Figure 2: The set of box and crossed box diagrams contributing to the non-analytical parts of the potential.
• Figure 3: The set of triangular diagrams contributing to the non-analytical terms of the potential.
• Figure 4: The circular diagram with non-analytic contributions.
• Figure 5: The class of the graviton 1PR vertex corrections which yield non-analytical corrections to the potential.