Families of Q-balls in a deformed $O(4)$ linear sigma model

TL;DR

This paper analytically investigates families of $Q$-ball solutions in deformed $O(4)$ sigma models with two complex scalar fields, revealing single and composite rotating $Q$-balls with specific internal symmetries.

Contribution

It introduces new analytical solutions for $Q$-balls in deformed $O(4)$ models, including single and composite types with internal rotation.

Findings

Existence of two types of single $Q$-balls with internal rotations.

Discovery of a one-parameter family of composite $Q$-balls.

Composite solutions involve two $Q$-balls spinning around each complex field.

Abstract

In this paper the existence of analytical solutions describing $Q$-balls in a family of deformed $O(4)$ sigma models in (1+1) dimensions has been investigated. These models involve two complex scalar fields whose coupling breaks the $O(4)$ symmetry group to $U(1)\times U(1)$. It has been shown that there are two types of single $Q$-balls rotating around each of the components of the internal space and a one-parameter family of composite $Q$-balls. These composite solutions consist of two single $Q$-balls (separated by a distance determined by the family parameter) spinning around each complex field with the same internal rotation frequency.