Fifth forces from QCD axions scale differently

Understand

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.