Fifth forces from QCD axions scale differently

TL;DR

This paper shows that the potential for a fifth force mediated by QCD axions scales differently than previously thought, due to higher-order symmetry-breaking terms, impacting experimental search sensitivities.

Contribution

It reveals that higher-order effects in the QCD axion Lagrangian alter the expected force law from 1/r^5 to 1/r^3, changing the theoretical understanding of axion-mediated forces.

Findings

Potential scales as 1/r^3 due to symmetry-breaking terms.

Different force behavior for nucleons and leptons.

Implications for experimental searches for fifth forces.

Abstract

We reexamine the low-energy potential for a macroscopic fifth force generated from the exchange of two axions. The shift-symmetry of the linear axion interactions leads to a potential falling off as $V(r) \sim 1/r^5$. We find that in the case of the QCD axion higher-order terms in the Lagrangian break the shift symmetry and lead to the dominant contribution to the potential scaling as $V(r) \sim 1/r^3$. These terms are generated by the same physics responsible for the axion mass and therefore the new contributions to the potential induce a different force for external nucleons and leptons. We demonstrate how this result affects the sensitivity of searches for new long-range forces.