Understanding Q-balls beyond the thin-wall limit

Complex scalar fields charged under a global U(1) symmetry can admit nontopological soliton configurations called Q-balls, which are stable against decay into individual particles or smaller Q-balls. These Q-balls are interesting objects within quantum field theory, but are also of phenomenological interest in several cosmological and astrophysical contexts. The Q-ball profiles are determined by a nonlinear differential equation, and so they generally require solution by numerical methods. In this work, we derive analytical approximations for the Q-ball profile in a polynomial potential and obtain simple expressions for the important Q-ball properties of charge, energy, and radius. These results improve significantly on the often-used thin-wall approximation and make it possible to describe Q-balls to excellent precision without having to solve the underlying differential equation.

Automated summary

Nontopological soliton configurations called Q-balls, which are stable against decay, are studied under global U(1) symmetry. Analytical approximations for the Q-ball profiles in a polynomial potential are derived, allowing for precise description without solving the underlying differential equation. Results significantly improve on thin-wall approximation and provide simple expressions for important Q-ball properties like charge, energy, and radius.