# A one-dimensional soliton system of gauged Q-ball and anti-Q-ball

## TL;DR

This paper investigates one-dimensional gauge models with two interacting scalar fields forming Q-ball systems, revealing their properties, stability, and the effects of electromagnetic and scalar interactions through analytical and numerical methods.

## Contribution

It introduces and analyzes a new class of nontopological soliton solutions involving two Q-balls with opposite charges in a gauge field, highlighting their stability and interaction dynamics.

## Key findings

- Existence of symmetric and nonsymmetric Q-ball systems.
- Nonsymmetric systems are energetically more favorable.
- Both systems are stable against decay into scalar bosons.

## Abstract

The (1+1)-dimensional gauge model of two complex self-interacting scalar fields that interact with each other through an Abelian gauge field and a quartic scalar interaction is considered. It is shown that the model has nontopological soliton solutions describing soliton systems consisting of two Q-ball components possessing opposite electric charges. The two Q-ball components interact with each other through the Abelian gauge field and the quartic scalar interaction. The interplay between the attractive electromagnetic interaction and the repulsive quartic interaction leads to the existence of symmetric and nonsymmetric soliton systems. Properties of these systems are investigated by analytical and numerical methods. The symmetric soliton system exists in the whole allowable interval of the phase frequency, whereas the nonsymmetric soliton system exists only in some interior subinterval. Despite the fact that these soliton systems are electrically neutral, they nevertheless possess nonzero electric fields in their interiors. It is found that the nonsymmetric soliton system is more preferable from the viewpoint of energy than the symmetric one. Both symmetric and nonsymmetric soliton systems are stable to the decay into massive scalar bosons.