Abstract
In this paper, we develop a phenomenological model inspired by QCD that mimics the QCD theory. We use the gauge theory in color dielectric medium (Gϕ) coupled with fermion fields to produce scalar and vector confinements in the chromoelectric flux tube scenario. The Abelian theory will be used to approximate the non-Abelian QCD theory in a consistent manner. We will calculate vector and scalar glueballs and compare the result to the existing simulation and experimental results and projections. The QCD-like vacuum associated with the model will be calculated and its behavior studied relative to changing quark masses. We will also comment on the relationship between tachyon condensation, dual Higgs mechanism, QCD monopole condensation, and their association with confinement. The behavior of the QCD string tension obtained from the vector potential of the model will be studied to establish vector dominance in confinement theories.
Highlights
Scalar and vector confinements [1] in 3 + 1 dimensional world have been predicted by hadron spectroscopy [2], by confinement in string picture, and by QCD lattice simulation, but no success has been made in solving it analytically from “first principle” of QCD
It has been shown in quarkonia phenomenology in 3 + 1 dimensional world that the best fit for meson spectroscopy is found for a convenient mixture of vector and scalar potentials
The coupling of the scalar potential, ξ = 2, exposes its weakness relative to the vector potential in Equation (48) by a ratio of 0 : 2. By simple interpretation, the scalar potential energy must be coupled strongly in order to coexist with the vector potential energy which needs no coupling as seen in our model framework and presented in expression Equation (54)
Summary
Scalar and vector confinements [1] in 3 + 1 dimensional world have been predicted by hadron spectroscopy [2], by confinement in string picture, and by QCD lattice simulation, but no success has been made in solving it analytically from “first principle” of QCD. We will use a dilaton in gauge theories [19, 20] to determine the coupling constants of the colored particles by transforming the exponential dilaton potential to conform with our chosen tachyon potential considered in this work We show that both scalar and vector confinements coincide with the tachyon condensation. The color dielectric function G is responsible for the long distance dynamics that bring about confinement in the IR regime of the model It facilitates the strong interactions between quarks and gluons. We are able to apply the phenomenological effective field theory to identify the color dielectric function with the tachyon potential in a simple form This approach makes it easy to observe how the QCD vacuum is modified by the dielectric function resulting in gluon condensation.
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