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The present article is the follow-up of our work Bottomonium suppression in quasi-particle model, where we have extended the study for charmonium states using quasi-particle model in terms of quasi-gluons and quasi quarks/antiquarks as an equation of state. By employing medium modification to a heavy quark potential thermodynamic observables,

The primary goal of heavy-ion experiment at the RHIC and the LHC is to search a new state of matter, i.e., the Quark Gluon Plasma. To study the properties of the Quark Gluon Plasma (QGP) heavy quarks are considered to be a suitable tool. Initially, the heavy quarks can be calculated in pQCD, which are produced in primary hard N N collisions [

At sufficiently large energy densities, lattice QCD calculations predict that hadronic matter undergoes a phase transition of deconfined quarks and gluons, called Quark Gluon Plasma (QGP). In order to reveal the existence and to analyze the properties of this phase transition several researches in this direction have been done. In the high-energy heavy-ion collision field, the study of charmonium production and suppression is the most interesting investigations, since the charmonium yield would be suppressed in the presence of a QGP due to color Debye screening [

In heavy-ion collisions, charmonium suppression study has been carried out first at the Super Proton Synchrotron (SPS) by the NA38 [

This strongly suggests that QGP may lie in the nonperturbative domain of QCD which is very hard to address both analytically and computationally. Similar conclusion about QGP and perfect fluidity of QGP have been reached from recent lattice studies and from the AdS/CFT studies [

The bag model, confinement models, and quasi-particle models are the several models for studying the EoS of strongly interacting quark gluon plasma [

The central theme of our work is that the potential which we are considering in the deconfined phase could have a nonvanishing confining (string) term, in addition to the Coulomb term [

In our previous work [

The paper is organized as follows. In Section

The interaction potential between a heavy quark and antiquark gets modified in the presence of a medium. The static interquark potential plays vital role in understanding the fate of quark-antiquark bound states in the hot QCD/QGP medium. In the present analysis, we preferred to work with the Cornell potential [

Next, substituting (

In the limiting case

Now we employ the Debye mass computed from the effective fugacity quasi-particle model (EQPM) [

Now, we obtain quasi particle debye mass for full QCD/QGP medium by considering quasi-parton distributions and EoS1 is the

Binding energy is defined as the distance between peak position and continuum threshold at finite temperature. The medium modified potential has similar appearance to the hydrogen atom problem [

In our analysis, the quark masses

We listed the values of dissociation temperature in Tables

Dissociation temperature

State | | | | | | |
---|---|---|---|---|---|---|

| 0.89 | 1.60 | 0.330 | 1/3 | 9.94 | 9.84 |

| 1.50 | 1.29 | 0.302 | 1/3 | 4.10 | 4.09 |

| 2.00 | 1.40 | 0.320 | 1/3 | 5.63 | 5.61 |

Dissociation temperature

State | | | | | | |
---|---|---|---|---|---|---|

| 0.89 | 1.64 | 0.331 | 1/3 | 11.05 | 10.93 |

| 1.50 | 1.36 | 0.316 | 1/3 | 4.99 | 4.98 |

| 2.00 | 1.46 | 0.322 | 1/3 | 6.75 | 6.72 |

An extensive study of strong-coupled plasma in QED with proper modifications to include colour degrees of freedom and the strong running coupling constant gives an expression for the energy density as a function of the plasma parameter can be written as

At sufficiently high temperature one must expect hadrons to melt, deconfining quarks and gluons. The exposure of new (color) degrees of freedom would then be manifested by a rapid increase in entropy density, hence in pressure, with increasing temperature, and by a consequent change in the equation of state (EOS) [

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Variation of

Variation of

Variation of

Variation of

To obtain the charmonium survival probability for an expanding QGP/QCD medium in the presence of viscous forces, the solution of equation of motion gives the time

Now we will discuss the physical understanding of charmonium suppression due to screening in the deconfined medium produced in relativistic nucleus-nucleus collisions. This involves a competition of various time-scales involved in expanding plasma. From Tables

In our analysis, we have employed the quasi-particle debye mass to determine the dissociation temperatures for the charmonium states (

We have shown the variation of

The variation of

The variation of

The variation of

The variation of

We find that the survival probability of sequentially produced

We studied the equation of state for strongly interacting quark-gluon plasma in the framework of strongly coupled plasma with appropriate modifications to take account of color and flavor degrees of freedom and QCD running coupling constant. In addition, we incorporate the nonperturbative effects in terms of nonzero string tension in the deconfined phase, unlike the Coulomb interactions alone in the deconfined phase beyond the critical temperature. Our results on thermodynamic observables,

At LHC energies, the inclusive

No data were used to support this study.

The authors declare that they have no conflicts of interest.

Vineet Kumar Agotiya acknowledge the Science and Engineering Research Board (SERB) Project No.

_{c}< T < 4T

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_{c}in the deconfined plasma from lattice QCD