# The sign of the dipole-dipole potential by axion exchange

## TL;DR

This paper clarifies the sign of the axion-mediated dipole-dipole potential between fermions, emphasizing its importance for experimental detection and correcting common sign errors in previous literature.

## Contribution

It provides a detailed analysis of the sign of the axion-mediated potential and highlights a sign change related to the spin of the mediating particle.

## Key findings

- Confirmed the physical sign of the axion-mediated potential
- Identified a sign change due to the mediating particle's spin
- Clarified sign conventions to aid experimental searches

## 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.