Understanding <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Q</mml:mi></mml:math>-balls beyond the thin-wall limit
Julian Heeck, Arvind Rajaraman, Rebecca Riley, Christopher B. Verhaaren
Abstract
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.