  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.
