The sign of the dipole–dipole potential by axion exchange

Abstract

We calculate a dipole–dipole potential between fermions mediated by a light pseudoscalar, axion, paying a particular attention to the overall sign. While the sign of the potential is physical and important for experiments to discover or constrain the axion coupling to fermions, there is often a sign error in the literature. The purpose of this short note is to clarify the sign issue of the axion-mediated dipole–dipole potential. As a by-product, we find a sign change of the dipole–dipole potenital due to the different spin of the mediating particle.