The Tunneling Potential Approach to Q-Balls

TL;DR

This paper introduces a tunneling potential approach to Q-balls, simplifying the process of finding solutions by reformulating their differential equations, which are analogous to vacuum-decay bounce solutions.

Contribution

It adapts the tunneling potential method to Q-balls, providing a new, more efficient way to analyze their solutions compared to traditional methods.

Findings

Simplified the calculation of Q-ball solutions.

Established the analogy between Q-balls and vacuum-decay bounce solutions.

Provided a reformulation that facilitates approximate and exact solutions.

Abstract

Q-balls are bound-state configurations of complex scalars stabilized by a conserved Noether charge Q. They are solutions to a second-order differential equation that is structurally identical to Euclidean vacuum-decay bounce solutions in three dimensions. This enables us to translate the recent tunneling potential approach to Q-balls, which amounts to a reformulation of the problem that can simplify the task of finding approximate and even exact Q-ball solutions.