# Homogeneous Balls in a Spontaneously Broken U(1) Gauge Theory

## TL;DR

This paper demonstrates the existence of stable, homogeneous, spherically symmetric soliton solutions called homogeneous balls in a spontaneously broken U(1) gauge theory, with properties like charge screening and stability for large sizes.

## Contribution

It introduces and numerically verifies the existence of homogeneous ball solutions in a U(1) gauge theory with spontaneous symmetry breaking, highlighting their stability and physical properties.

## Key findings

- Homogeneous balls are stable and can be arbitrarily large.
- Charge density is screened by a counter charge cloud.
- Energy density behaves like a nonrelativistic gas.

## Abstract

We study the coupled system consisting of a complex matter scalar field, a U(1) gauge field, and a complex Higgs scalar field that causes spontaneously symmetry breaking. We show by numerical calculations that there are spherically symmetric nontopological soliton solutions. Homogeneous balls solutions, all fields take constant values inside the ball and in the vacuum state outside, appear in this system. It is shown that the homogeneous balls have the following properties: charge density of the matter scalar field is screened by counter charge cloud of the Higgs and gauge field everywhere; an arbitrary large size is allowed; energy density and pressure of the ball behave homogeneous nonrelativistic gas; a large ball is stable against dispersion into free particles and against decay into two smaller balls.