Color field configuration between three static quarks

TL;DR

This paper presents finite energy solutions for three static quarks in Yang-Mills-Proca theory, revealing a Y-shaped electric field distribution and toroidal magnetic field lines, aligning with lattice QCD results.

Contribution

It demonstrates the existence of regular solutions with specific field configurations in Yang-Mills-Proca theory and connects these findings to lattice QCD results.

Findings

Color electric field exhibits Y-like spatial distribution.

Color magnetic field lines form a torus surface.

Results agree with lattice QCD calculations.

Abstract

Within Yang-Mills-Proca theory with external sources in the form of three static quarks, regular, finite energy solutions are obtained. It is shown that color electric/magnetic fields have two components: the first part is a gradient/curl component, respectively, and the second part is a nonlinear component. It is shown that the color electric field has a Y-like spatial distribution provided by three static quarks. Such a Y-like behavior arises because the gradient component of the electric field is present. The nonlinear component of the electric field is a curl one, and it appears because the vector potential sourced by a solenoidal current is present. The color magnetic field is purely curl one, since its nonzero color components do not contain a nonlinear component; this results in the fact that its force lines lie on the surface of a torus. It is shown that the results obtained are in satisfactory agreement with the results obtained in lattice calculations in quantum chromodynamics. To discuss such an agreement, we have shown that the Yang-Mills-Proca equation can be obtained from the Lagrangian describing a gluon condensate varying in space. Also, we compare the energy profile obtained by us with that obtained in lattice calculations with a static potential.