Color field configuration between three static quarks

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.

Figures (9)

• Figure 1: A sketch of distribution of static quarks and charge/current densities creating color electric, $\vec{E}^a$, and magnetic, $\vec{H}^a$, fields.
• Figure 2: A sketch of the Y-like distribution of the color electric field obtained in lattice calculations in Ref. Bornyakov:2004uv.
• Figure 3: Force lines of the electric fields $\vec{E}^{3,6,8}$ in the $z = 0$ plane.
• Figure 4: Potentials $A^{3,6,8}_t = h^{3,6,8}$ in the $z = 0$ plane.
• Figure 5: Force lines of the vector potentials $\vec{A}^{6,7}$ in the $z = 0$ plane and the spatial distribution of the potential $\vec{A}^{6}$.