Q-balls in polynomial potentials

TL;DR

This paper investigates Q-balls, stable bound states of bosons with conserved charge, in polynomial potentials, revealing universal features and providing numerical and analytical insights into their properties.

Contribution

The study offers a comprehensive analysis of Q-balls in arbitrary polynomial potentials, highlighting universal features and connecting to renormalizable models.

Findings

Q-balls exhibit universal properties largely independent of potential details.

Numerical and analytical methods effectively describe Q-ball characteristics.

Polynomial potentials can be realized in renormalizable scalar models.

Abstract

Bosons carrying a conserved charge can form stable bound states if their Lagrangian contains attractive self-interactions. Bound-state configurations with a large charge $Q$ can be described classically and are denoted as Q-balls, their properties encoded in a non-linear differential equation. Here, we study Q-balls in arbitrary polynomial single-scalar-field potentials both numerically and via various analytical approximations. We highlight some surprising universal features of Q-balls that barely depend on the details of the potential. The polynomial potentials studied here can be realized in renormalizable models involving additional heavy or light scalars, as we illustrate with several examples.