Nonrelativistic Effective Field Theory for Axions

Abstract

Axions can be described by a relativistic field theory with a real scalar field $\varphi$ whose self-interaction potential is a periodic function of $\varphi$. 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 ${\psi }^{\ast }\psi$. We determine the coefficients in the expansion of the effective potential to fifth order in ${\psi }^{\ast }\psi$ 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 ${\psi }^{\ast }\psi$, we develop a sequence of systematically improvable approximations to the effective potential that include terms of all orders in ${\psi }^{\ast }\psi$.

Comments: 21 pages, 8 figures, Published Version