# Non-Abelian Proca-Dirac-Higgs theory: Particlelike solutions and their energy spectrum

Dzhunushaliev, Vladimir (Department of Theoretical and Nuclear Physics, Al-Farabi Kazakh National University, Almaty 050040, Kazakhstan) (Institute of Experimental and Theoretical Physics, Al-Farabi Kazakh National University, Almaty 050040, Kazakhstan) (Institute of Physicotechnical Problems and Material Science of the NAS of the Kyrgyz Republic, 265 a, Chui Street, Bishkek 720071, Kyrgyzstan) (Institute of Systems Science, Durban University of Technology, 4000 Durban, South Africa) ; Folomeev, Vladimir (Institute of Experimental and Theoretical Physics, Al-Farabi Kazakh National University, Almaty 050040, Kazakhstan) (Institute of Physicotechnical Problems and Material Science of the NAS of the Kyrgyz Republic, 265 a, Chui Street, Bishkek 720071, Kyrgyzstan) ; Makhmudov, Arislan (Institute of Systems Science, Durban University of Technology, 4000 Durban, South Africa)

16 April 2019

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 particlelike 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 $\Delta =\Delta \left({\xi }_{0}\right)$ [the mass gap $\Delta \left({\xi }_{0}\right)$ for a fixed value of ${\xi }_{0}$]. The behavior of the function $\Delta \left({\xi }_{0}\right)$ is studied for some range of ${\xi }_{0}$.

Published in: Physical Review D 99 (2019)