Non-Abelian Proca theories with extra fields: particlelike and flux tube solutions

Abstract

We consider non-Abelian Proca theories with extra fundamental fields included. In the case of SU(2) Proca theory with nonlinear scalar and spinor fields, we obtain spherically symmetric regular solutions describing particlelike configurations with finite energy. For such systems, we find the energy spectrum and show the presence of a mass gap. In the case of SU(3) Proca theory with a nonlinear scalar field, we obtain cylindrically symmetric solutions describing tubes either with the flux of a longitudinal electric field or with the energy flux or with both of them. It is shown that the tubes with the energy flux may contribute considerably to the Proca proton spin. Consistent with all of this, we have argued that non-Abelian Proca theories containing extra fields may approximately describe some phenomena in QCD.

Linear Energy Density and the Flux of an Electric Field in Proca Tubes

“…Another interesting feature of QCD is that gluon fields give a considerable contribution to the proton spin. As we demonstrated in [4,5] and in the present paper, in SU(3) non-Abelian Proca theory, there are two types of tube solutions: (i) those with the flux of color electric field (in Proca theory, where such tubes connect "quarks" and may lead to confinement in massive Yang-Mills theories); (ii) those with the momentum directed along the tube (if such tubes connect "quarks" in a Proca proton, they will contribute to the Proca proton spin). This means that massive non-Abelian Yang-Mills theories (non-Abelian Proca theories) have some similarities to quantum chromodynamics; this gives a good reason for the detailed study of such theories.…”

“…In the present paper, we continued our investigations that we began in [4,5] concerning tube solutions within SU(3) non-Abelian-Proca-Higgs theory. Our purpose was to obtain the integral characteristics of those solutions.…”

“…where ρ, z, and ϕ are cylindrical coordinates. In [4,5], it was shown that solutions describing such configurations do exist. Here, we study the dependence of the flux of the electric field along the tube on the parameters determining the solutions in more detail.…”

“…with the following components of the Proca field mass matrix: µ 2 1 = µ 2 22,t t and µ 2 2 = µ 2 55,z z . Substituting the potentials (5) in Equations ( 2) and (3) and introducing the dimension-…”

“…For example, in [3], it was shown that there exist gravitating and nongravitating Q-tubes supported by a complex vector field with nonlinear terms which can in some sense imitate the selfinteraction in non-Abelian Yang-Mills theory. In [4,5], the existence of tubes within SU(3) Proca theory coupled to a Higgs scalar field has been demonstrated. In those papers, two types of tube solutions have been found.…”