# Non-Abelian Proca-Dirac-Higgs theory: particle-like solutions and their energy spectrum

## TL;DR

This paper investigates particle-like solutions in a non-Abelian SU(2) Proca-Dirac-Higgs system, revealing finite energy solutions, their dependence on parameters, and the existence of a mass gap in the energy spectrum.

## Contribution

It introduces and analyzes finite energy particle-like solutions in a non-Abelian Proca-Dirac-Higgs system, including the energy spectrum and mass gap dependence on system parameters.

## Key findings

- Existence of finite energy particle-like solutions.
- Energy spectra depend on three free parameters.
- Presence of a mass gap with a minimum energy value.

## Abstract

We study a system consisting of a non-Abelian SU(2) Proca field interacting with nonlinear scalar (Higgs) and spinor fields. For such a system, it is shown that particle-like solutions with finite energy do exist. It is demonstrated that the solutions depend on three free parameters of the system, including the central value of the scalar field $\xi_0$. For some fixed values of $\xi_0$, we find energy spectra of the solutions. It is shown that for each of the cases under consideration there is a minimum value of the energy $\Delta=\Delta(\xi_0)$ (the mass gap $\Delta(\xi_0)$ for a fixed value of $\xi_0$). The behavior of the function $\Delta(\xi_0)$ is studied for some range of $\xi_0$.