Gluon tubes in the non-Abelian theory of Proca + scalar Higgs field

Abstract

The non-Abelian Proca theory + scalar Higgs field is considered, possibly being some approximation for quantum chromodynamics. In the Lagrangian of this theory, a mass term and a term describing the interaction between the Proca field and the scalar Higgs field are proposed. In SU (3) of the non-Abelian Proca + scalar Higgs field, cylindrically symmetric solutions (gluon tubes) are obtained, in which there is a longitudinal non-Abelian electric field, leading to an electric field flow along the tube. This field is created by quarks located at ± ∞ and, due to the strong nonlinear interaction between the fields, it is concentrated in a finite region near the center of the tube. The corresponding equations are solved numerically as a nonlinear eigenvalue problem, where the eigenvalues are the masses of the scalar and Proca fields. It is shown that gauge potentials, field strengths, and energy density fall exponentially at spatial infinity, which leads to a finite flux of a longitudinal electric field through the tube, as well as to a finite linear energy density concentrated in this tube. The energy spectrum of solutions is obtained depending on the values of the parameters that determine the solutions.