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.
Dzhunushaliev et al. (Tue,) studied this question.