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We present a QCD motivated model that mimics QCD theory. We examine the characteristics of the gauge field coupled with the color dielectric function (

Quantum chromodynamics (QCD) is a theory that attempts to explain the strong interactions carried by gluons that keep quarks and gluons in a confined state in hadrons. The success of this theory depends on asymptotic freedom [

It has been realized that owing to the gluon confinement, the QCD vacuum shows a characteristic of a dielectric medium [

There exists some similarity between QCD and QED (

In this paper, we will establish that the phenomenon of confinement is achievable with an electric field immersed in a color dielectric medium (

Many works have been done on determining the potentials for quark confinement as a function of temperature, commonly called thermal QCD, by using a number of different approaches including Wilson and Polyakov loop corrections [

The main purpose of this paper is to determine analytically the net static potential for the quarks, and gluons confinement in

The motivation for using this approach is twofold, firstly, because we are able to study QCD phenomenologically by identifying the color dielectric function naturally with the tachyon potential; secondly, one can apply such phenomenological approach to obtain models that mimic QCD in stringy models where temperature effects in tachyon potentials [

Thus, we choose a tachyon potential which is expected to condense at some value [

The paper is organized as follows. In Sections

In this section we will review the theory of electromagnetism in a

Consider the gauge field in dielectric medium,

We begin with (

The coupling between electromagnetism and scalar field dynamics at finite temperature is given by the effective Lagrangian

The behavior of the dielectric function

To establish strong interaction and its resultant confinement, our dielectric function needs to asymptotically satisfy these conditions:

In this section we analyze the gluodynamics in the tachyon matter. The Lagrangian for gluodynamics is given as

In this section we will establish the relationship between tachyon condensation and confinement. Tachyons are particles that are faster than light, have negative masses, and are unstable. Their existence is presumed theoretically in the same way as

From (

To start, let us consider the Lagrangian at (

For the tachyon Lagrangian in (

Now, disregarding the term with

Now perturbing the tachyon fields around its true vacuum

Writing (

The QCD string tension can be written as

Plotting the results from (

A plot of a potential

A plot of the string tension

The static potential for the confinement regimes is depicted in Figure

The color dielectric function in (

A plot of the color dielectric function

The search for glueballs has been on for a while now; unfortunately, the only evidence of its existence is a “possible” candidate because it has not been confirmed experimentally. They are known to be bound states of pure gluons, mixture of quark and gluon states (hybride), multiquark bound states, etc. Their presence is the consequence of gluon self-interactions in QCD theory. In this section we will be focusing on scalar glueballs. They are known to be the lightest in glueball mass; they have QCD degrees of freedom with isospin quantum state of

From our model, the glueball masses are expected to appear as excitations around the vacuum and are given by [

We start with (

We may now establish a relationship between string tension and glueball masses through (

To end this section, few comments in connection with Section

In our investigations we find the net static potential for confinement phase of quarks and gluons as a function of temperature. We used the Abelian QED theory to approximate the non-Abelian QCD theory. We do this by employing a phenomenological effective field theory involving tachyon field dynamics coupled to electromagnetism via color dielectric function. The color dielectric function is responsible for the long distance interactions to bring about confinement in the infrared (IR) regime. It also modifies the gluon condensate

The QCD string tension and scalar glueball mass were also computed as a function of temperature. They both decrease rapidly with temperature and break (vanish) at

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that they have no conflicts of interest.

The authors would like to thank CNPq and CAPES for partial financial support.