It is shown that de-confinement can be achieved in high multiplicity non jet $bar{p}$p collisions at $sqrt{s}$= 1.8 TeV Fermi National Accelerator Laboratory(FNAL- E735) experiment. Previously the evidence for de-confinement was the demonstrated by t
he constant freeze out energy density in high multiplicity events. In this paper we use the same data but analyze the transverse momentum spectrum in the framework of the clustering of color sources. The charged particle pseudorapidities densities in the range 7.0 $leq langle dN_{c}/deta rangle leq$26.0 are considered. Results are presented for both thermodynamic and transport properties. The initial temperature and energy density are obtained and compared with the Lattice Quantum Chromo Dynamics(LQCD) simulations. The energy density ($varepsilon/T^{4}$) $sim$ 11.5 for $ langle dN_{c}/deta rangle sim $ 25.0 is close to the value for 0-10% central events in Au+Au collisions at $sqrt{s_{NN}}$= 200 GeV. The shear viscosity to entropy density ratio($eta/s$) is $sim$ 0.2 at the transition temperature. The result for the trace anomaly $Delta$ is in excellent agreement with LQCD simulations. These results confirm our earlier observation that the de-confined state of matter was created in high multiplicity events in $bar{p}$p collisions at $sqrt{s}$=1.8 TeV.
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.
Possible phase transition of strongly interacting matter from hadron to a quark-gluon plasma state have in the past received considerable interest. The clustering of color sources provides a framework of the the partonic interactions in the initial s
tage of the collisions. The onset of de-confinement transition is identified by the spanning percolation cluster in 2D percolation. In this talk results are presented both for the multiplicity and the elliptic flow at RHIC and LHC energies. The thermodynamic quantities temperature, equation of state and transport coefficient are obtained in the framework of clustering of color sources. It is shown that the results are in excellent agreement with the recent lattice QCD calculations(LQCD).
In heavy-ion ({it A-A}) collisions, the correlations among the particles produced across wide range in rapidity, probe the early stages of the reaction. The analyses of forward-backward multiplicity correlations in these collisions are complicated by
several effects, which are absent or minimized in hadron-hadron collisions. This includes effects, such as the centrality selection in the {it A-A} collisions, which interfere with the measurement of the dynamical correlations. A method, which takes into account the fluctuations in centrality selection, has been utilized to determine the forward-backward correlation strength {$b_{rm corr}$} in {itA-A} collisions. This method has been validated by using the HIJING event generator in case of Au-Au collisions at $sqrt{s_{NN}}$= 200 GeV and Pb-Pb collisions at $sqrt{s_{NN}}$= 2.76 TeV. It is shown that the effect of impact parameter fluctuations is to be considered properly in order to obtain meaningful results.
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.
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 col
or 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.
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.
Possible phase transition of strongly interacting matter from hadron to a Quark-Gluon Plasma (QGP) state have in the p ast received considerable interest. It has been suggested that this problem might be treated by percolation theory. Th e Color Stri
ng Percolation Model (CSPM) is used to determine the equation of state (EOS) of the QGP produced in central Au-Au collisions at RHIC energies. The bulk thermodynamic quantities- energy density, entropy density and t he sound velocity- are obtained in the framework of CSPM. It is shown that the results are in excellent agreement with the recent lattice QCD calculations(LQCD).
We present comments on the paper Observation of Long-Range, Near-Side Angular Correlations in proton-proton Collisions at the LHC.
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.
