Axion-modified photon propagator, Coulomb potential and Lamb-shift

TL;DR

This paper develops a renormalized quantum theory of axion-electrodynamics, deriving the axion-modified Coulomb potential and exploring its implications for atomic physics and axion searches.

Contribution

It provides a second-order accurate self-energy calculation and establishes the axion-modified Coulomb potential, addressing the theory's renormalization and experimental implications.

Findings

Axion-like particles are unlikely to explain the proton radius puzzle.

The axion-modified Coulomb potential affects atomic energy levels.

High-precision spectroscopy can constrain axion-like particles.

Abstract

A consistent renormalization of a quantum theory of axion-electrodynamics requires terms beyond the minimal coupling of two photons to a neutral pseudoscalar field. This procedure is used to determine the self-energy operators of the electromagnetic and the axion fields with an accuracy of second-order in the axion-diphoton coupling. The resulting polarization tensor is utilized for establishing the axion-modified Coulomb potential of a static pointlike charge. In connection, the plausible distortion of the Lamb-shift in hydrogenlike atoms is established and the scopes for searching axionlike particles in high-precision atomic spectroscopy and in experiments of Cavendish-type are investigated. Particularly, we show that these hypothetical degrees of freedom are ruled out as plausible candidates for explaining the proton radius anomaly in muonic hydrogen. A certain loophole remains, though, which is linked to the nonrenormalizable nature of axion-electrodynamics.