Leading quantum gravitational corrections to scalar QED

TL;DR

This paper calculates the leading quantum and post-Newtonian corrections to the scattering amplitude of charged scalars in a combined effective field theory of gravity and scalar QED, providing insights into quantum gravitational effects on charged particles.

Contribution

It introduces a method to compute the leading quantum and post-Newtonian corrections to scalar QED in a gravitational context using effective field theory, including explicit vertex rules and scattering amplitude analysis.

Findings

Derived the non-analytic parts of the 1-loop scattering amplitude.

Constructed the corrected two-particle potential including quantum effects.

Discussed potential experimental implications of the quantum corrections.

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.