Fifth Forces from QCD Axions Scale Differently

This is the authors' abstract. We don't add key points for this paper.

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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>V</a:mi><a:mo stretchy="false">(</a:mo><a:mi>r</a:mi><a:mo stretchy="false">)</a:mo><a:mo>∼</a:mo><a:mn>1</a:mn><a:mo>/</a:mo><a:msup><a:mi>r</a:mi><a:mn>5</a:mn></a:msup></a:math>. 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 <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>V</e:mi><e:mo stretchy="false">(</e:mo><e:mi>r</e:mi><e:mo stretchy="false">)</e:mo><e:mo>∼</e:mo><e:mn>1</e:mn><e:mo>/</e:mo><e:msup><e:mi>r</e:mi><e:mn>3</e:mn></e:msup></e:math>. 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.