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 $\mathrm{\Delta }=\mathrm{\Delta }({\xi }_0)$ (the mass gap $\mathrm{\Delta }({\xi }_0)$ for a fixed value of ${\xi }_0$). The behavior of the function $\mathrm{\Delta }({\xi }_0)$ is studied for some range of ${\xi }_0$.