Understanding Q-Balls Beyond the Thin-Wall Limit

Complex scalar fields charged under a global U(1) symmetry can admit non-topological 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 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.