Speaker
Description
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 $\phi_0$. For some fixed values of $\phi _0$, 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 $\Delta=\Delta(\phi_0)$ (the mass gap $\Delta(\phi_0)$ for a fixed value of $\phi_0$). The behavior of the function $\Delta(\phi_0)$ is studied for some range of $\phi_0$.
We show that the energy spectrum has a minimum, at least for some values of $\phi_0$, and we argue that this will also take place for any value of $\phi_0$ lying in the range $0< \phi_0 <\infty$. The behaviour of this minimum as $\phi_0 \rightarrow \infty$ is of great interest: if in this limit the minimum is nonzero, one can say that there is a mass gap $\Delta \neq 0$ in non-Abelian Proca-Dirac-Higgs theory.
If such a mass gap does exist, this would be of great significance. The reason is that in quantum field theory there is a problem to prove the existence
of a mass gap in quantum chromodynamics. This problem is highly nontrivial and any examples of its existence (even within a classical theory)
would be very useful for an understanding of the nature of existence of the mass gap.
If there is a mass gap in the theory we are investigating, it is possible that this is due to the fact that non-Abelian Proca-Dirac-Higgs theory is some approximation for nonperturbative quantization in QCD. In this case, it can be assumed that the Proca field describes a $SU(2)$ subgroup of $SU(3)$, the Higgs scalar field describes sea gluons and the Dirac nonlinear field describes sea quarks.
Thus, the purpose of the investigation is to (i) obtain particle-like 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; and (iii) search for a minimum of the spectrum (a mass gap).
The talk is based on Phys.Rev. D99 (2019) no.7, 076009