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تسجيل مستخدم جديدClustering of Color Sources and the Equation of State of the QGP
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Brijesh K. Srivastava
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Possible phase transition of strongly interacting matter from hadron to a quark-gluon plasma state have in the past received c onsiderable interest. It has been suggested that this problem might be treated by percolation theory. The clustering of color sources with percolation (CSPM) is used to determine the equation of state (EOS) and the transport coefficient of the Quark-Gl uon Plasma (QGP) produced in central A-A collisions at RHIC and LHC energies.
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The Color String Percolation Model (CSPM) is used to determine the equation of state (EOS) of the QGP produced in central Au-Au collisions at $sqrt{s_{NN}}$ = 200 A GeV using STAR data at RHIC. When the initial density of interacting colored strings
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The initial temperature $T_{i}$, energy density $varepsilon_{i}$, and formation time $tau_{i}$ of the initial state of the QGP formed in the heavy ion collisions at RHIC and LHC energies are determined using the data driven Color String Percolation M
odel (CSPM). Multiparticle production by interacting strings stretched between projectile and target form a spanning cluster at the percolation threshold. The relativistic kinetic theory relation for $eta/s$ is evaluated as a function of $it T$ and the mean free path ($lambda_{mfp}$) using data and CSPM. $eta/s$($T_{i}$, $lambda_{mfp}$) describes the transition from a strongly interacting QGP at $T/T_{c} sim 1$ to a weakly coupled QGP at $T/T_{c} ge 6$. We find that the reciprocal of $eta/s$ is equal to the trace anomaly $Delta = varepsilon-3P/T^{4}$ which also describes the transition. We couple this initial state of the QGP to a 1D Bjorken expansion to determine the sound velocity $c_{s}^{2}$ of the QGP for 0.85 $le T/T_{c} leq 3$. The bulk thermodynamic quantities and the equation of state are in excellent agreement with LQCD results.
The Color String Percolation Model (CSPM) is used to determine the shear viscosity to entropy ratio ($eta/s$) of the Quark-Gluon Plasma (QGP) produced in Au-Au collisions at $sqrt{s_{NN}}$ = 200 GeV at RHIC and Pb-Pb at $sqrt{s_{NN}}$ = 2.76 TeV at L
HC. The relativistic kinetic theory relation for $eta/s$ is evaluated using CSPM values for the temperature and the mean free path of the QGP constituents. The experimental charged hadron transverse momentum spectrum is used to determine the percolation density parameter $xi$ in Au-Au collisions (STAR). For Pb-Pb at $sqrt{s_{NN}}$ = 2.76 TeV $xi$ values are obtained from the extrapolation at RHIC energy. The value of $eta/s$ is 0.204$pm$0.020 and 0.262$pm$0.026 at the CSPM initial temperatures of 193.6$pm$3 MeV (RHIC) and 262.2 $pm$13 MeV (LHC) respectively. These values are 2.5 and 3.3 times the AdS/CFT conjectured lower bound $1/4pi$. We compare the CSPM $eta/s$ analytic expression with weak coupling (wQGP) and strong coupling (sQGP) calculations. This indicates that the QGP is a strongly coupled fluid in the phase transition region.
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A brief introduction of the relationship of string percolation to the Quantum Chromo Dynamics (QCD) phase diagram is presented. The behavior of the Polyakov loop close to the critical temperature is studied in terms of the color fields inside the clu
sters of overlapping strings, which are produced in high energy hadronic collisions. The non-Abelian nature of the color fields implies an enhancement of the transverse momentum and a suppression of the multiplicities relative to the non overlapping case. The prediction of this framework are compared with experimental results from the SPS, RHIC and LHC for $pp$ and AA collisions. Rapidity distributions, probability distributions of transverse momentum and multiplicities, Bose-Einstein correlations, elliptic flow and ridge structures are used to evaluate these comparison. The thermodynamical quantities, the temperature, and energy density derived from RHIC and LHC data and Color String Percolation Model (CSPM) are used to obtain the shear viscosity to entropy density ratio ($eta/s$). It was observed that the inverse of ($eta/s$) represents the trace anomaly $Delta =(varepsilon-3P)/T^{4}$. Thus the percolation approach within CSPM can be successfully used to describe the initial stages in high energy heavy ion collisions in the soft region in high energy heavy ion collisions. The thermodynamical quantities, temperature and the equation of state are in agreement with the lattice QCD calculations. Thus the clustering of color sources has a clear physical basis although it cannot be deduced directly from QCD.
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