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Register a new userClustering 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 exceeds the 2D percolation threshold a cluster is formed, which defines the onset of color deconfinement. These interactions also produce fluctuations in the string tension which transforms the Schwinger particle (gluon) production mechanism into a maximum entropy thermal distribution. The single string tension is determined by identifying the known value of the universal hadron limiting temperature $T_{c}$ = 167.7 $pm$ 2.6 MeV with the CSPM percolation temperature at the critical threshold $xi_{c}$ =1.2. At mid-rapidity the initial Bjorken energy density and the initial temperature determine the number of degrees of freedom consistent with the formation of a $sim$ 2+1 flavor QGP. An analytic expression for the equation of state, the sound velocity $C_{s}^{2}(xi)$ is obtained in CSPM. The CSPM $C_{s}^{2}(xi)$ and the bulk thermodynamic values $varepsilon /T^{4}$ and $s /T^{3}$ are in excellent agreement in the phase transition region with recent lattice QCD simulations (LQCD) by the HotQCD Collaboration.
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 Model (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 LHC. 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.
We discuss a non-perturbative $T$-matrix approach to investigate the microscopic structure of the quark-gluon plasma (QGP). Utilizing an effective Hamiltonian which includes both light- and heavy-parton degrees of freedoms. The basic two-body interaction includes color-Coulomb and confining contributions in all available color channels, and is constrained by lattice-QCD data for the heavy-quark free energy. The in-medium $T$-matrices and parton spectral functions are computed selfconsistently with full account of off-shell properties encoded in large scattering widths. We apply the $T$-matrices to calculate the equation of state (EoS) for the QGP, including a ladder resummation of the Luttinger-Ward functional using a matrix-log technique to account for the dynamical formation of bound states. It turns out that the latter become the dominant degrees of freedom in the EoS at low QGP temperatures indicating a transition from parton to hadron degrees of freedom. The calculated spectral properties of one- and two-body states confirm this picture, where large parton scattering rates dissolve the parton quasiparticle structures while broad resonances start to form as the pseudocritical temperature is approached from above. Further calculations of transport coefficients reveal a small viscosity and heavy-quark diffusion coefficient.
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 clusters 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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