# Vortex solutions in the Abelian Higgs Model with a neutral scalar

## TL;DR

This paper extends the Abelian Higgs model by adding a neutral scalar field, leading to richer vortex solutions and a phase diagram showing conditions for scalar condensation within vortices.

## Contribution

It introduces a new extended Abelian Higgs model with a neutral scalar, analyzing its vortex solutions and phase structure, which was not previously explored.

## Key findings

- Richer vortex structures due to additional ground states
- Identification of parameter regions with scalar condensation in vortices
- Phase diagram mapping scalar condensation conditions

## Abstract

We construct an extension of the Abelian Higgs model, which consists of a complex scalar field by including an additional real, electromagnetically neutral scalar field. We couple this real scalar field to the complex scalar field via a quartic coupling and investigate $U(1)$ vortex solutions in this "extended Abelian Higgs Model". Since this model has two additional homogeneous ground states, the $U(1)$ vortices that can form in this model have a richer structure than in the Abelian Higgs Model. We also find the "phase diagram" of the model showing the parameter space in which the real scalar particle condenses in the vortex state while having a zero vacuum expectation value in the homogeneous ground state.