Nonrelativistic Effective Field Theory for Axions

TL;DR

This paper develops a nonrelativistic effective field theory for axions, enabling simplified descriptions of low-energy axion phenomena, including dense Bose-Einstein condensates, by systematically expanding and approximating the effective potential.

Contribution

It derives the effective potential coefficients up to fifth order and introduces a systematic approach for including all orders in dense axion condensates.

Findings

Coefficients of the effective potential are determined up to fifth order.

A method for approximating the potential in dense condensates is developed.

The approach allows for systematic improvements in modeling axion interactions.

Abstract

Axions can be described by a relativistic field theory with a real scalar field $\phi$ whose self-interaction potential is a periodic function of $\phi$. Low-energy axions, such as those produced in the early universe by the vacuum misalignment mechanism, can be described more simply by a nonrelativistic effective field theory with a complex scalar field $\psi$ whose effective potential is a function of $\psi^*\psi$. We determine the coefficients in the expansion of the effective potential to fifth order in $\psi^*\psi$ by matching low-energy axion scattering amplitudes. In order to describe a Bose-Einstein condensate of axions that is too dense to expand the effective potential in powers of $\psi^*\psi$, we develop a sequence of systematically improvable approximations to the effective potential that include terms of all orders in $\psi^*\psi$.