Non-Abelian Proca-Dirac-Higgs theory: particle-like solutions and their energy spectrum

We study a system consisting of a non-Abelian SU(2) Proca field interacting with nonlinear scalar (Higgs) and spinor fields. For such a system, it is shown that particle-like solutions with finite energy do exist. It is demonstrated that the solutions depend on three free parameters of the system, including the central value of the scalar field $\xi_0$. For some fixed values of $\xi_0$, we find energy spectra of the solutions. It is shown that for each of the cases under consideration there is a minimum value of the energy $\Delta=\Delta(\xi_0)$ (the mass gap $\Delta(\xi_0)$ for a fixed value of $\xi_0$). The behavior of the function $\Delta(\xi_0)$ is studied for some range of $\xi_0$.