Linear Energy Density and the Flux of an Electric Field in Proca Tubes

Vladimir Dzhunushaliev,Abylaikhan Tlemisov,Vladimir Folomeev

doi:10.3390/sym13040640

Abstract

In this work, we study cylindrically symmetric solutions within SU(3) non-Abelian Proca theory coupled to a Higgs scalar field. The solutions describe tubes containing either the flux of a color electric field or the energy flux and momentum. It is shown that the existence of such tubes depends crucially on the presence of the Higgs field (there are no such solutions without this field). We examine the dependence of the integral characteristics (linear energy and momentum densities) on the values of the electromagnetic potentials at the center of the tube, as well as on the values of the coupling constant of the Higgs scalar field. The solutions obtained are topologically trivial and demonstrate the dual Meissner effect: the electric field is pushed out by the Higgs scalar field.

Highlights

In quantum chromodynamics (QCD), it is assumed that the color non-Abelian fields between quark and anti-quark are confined in a tube due to a strong nonlinear interaction between different components of such fields
We were interested in obtaining the dependencies of the flux of the longitudinal electric field and linear momentum/energy densities on the system parameters
For tubes of the first type, possessing the flux of the longitudinal color electric field, we have obtained the dependencies of the flux and of the linear energy density on the value of the coupling constant Λ and on the values of the fields at the center of the tube

Summary

Introduction

In quantum chromodynamics (QCD), it is assumed that the color non-Abelian fields between quark and anti-quark are confined in a tube due to a strong nonlinear interaction between different components of such fields. The properties of this tube are such that outside the tube, all fields, and the energy density, decrease exponentially with distance. We calculate integral characteristics of the solutions such as the total flux of the non-Abelian longitudinal Proca electric field, the linear energy density and the total momentum passing across the cross section of the tube, depending on the system parameters.

Proca Tube with the Flux of the Electric Field

Proca Tubes with the Momentum Density

Abelian Proca Tubes

Non-Abelian Proca Tubes

Conclusions