Abstract
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 $\xi_0$.
Highlights
By Proca theories one means gauge theories where the gauge invariance is violated explicitly by introducing a mass term
We have considered non-Abelian SU(2) Proca-Dirac-Higgs theory where a massive vector field interacts with nonlinear scalar and spinor fields
The main reason why such solutions can exist is the presence of the mass of the non-Abelian Proca field, and because of the structure of the Dirac equation leading to the existence of regular solutions of this equation
Summary
By Proca theories one means gauge theories (both Abelian and non-Abelian ones) where the gauge invariance is violated explicitly by introducing a mass term. In the present paper we study a non-Abelian SU(2) Proca field interacting with nonlinear scalar and spinor fields. The purpose of the present paper is to (i) obtain particlelike solutions within a theory with a non-Abelian SU(2) Proca field plus a Higgs scalar field plus a nonlinear Dirac field, (ii) study energy spectra of these solutions, (iii) search for a minimum of the spectrum (a mass gap), and (iv) understand the mechanism of the occurrence of a mass gap within the theory under investigation and, on this basis, to suggest a similar mechanism for QCD. II, using which the corresponding complete set of equations is written down
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