Unified pictures of Q-balls and Q-tubes

TL;DR

This paper provides a comparative analysis of Q-balls and Q-tubes, exploring their equilibrium solutions across different potentials, and introduces an analytical method to understand their stability and charge-energy relations.

Contribution

It presents a unified framework for understanding Q-balls and Q-tubes, including an analytical approach to determine their stability and solution domains based on shape and potential.

Findings

Charge-energy relations can be similar or different between Q-balls and Q-tubes depending on the model.

An analytical method to find the energy and charge limits of solutions is developed.

The stability and existence domains depend on the shape and potential of the solutions.

Abstract

While Q-balls have been investigated intensively for many years, another type of nontopological solutions, Q-tubes, have not been understood very well. In this paper we make a comparative study of Q-balls and Q-tubes. First, we investigate their equilibrium solutions for four types of potentials. We find, for example, that in some models the charge-energy relation is similar between Q-balls and Q-tubes while in other models the relation is quite different between them. To understand what determines the charge-energy relation, which is a key of stability of the equilibrium solutions, we establish an analytical method to obtain the two limit values of the energy and the charge. Our prescription indicates how the existent domain of solutions and their stability depends on their shape as well as potentials, which would also be useful for a future study of Q-objects in higher-dimensional spacetime.