Color String Percolation Model Research Articles

Transport coefficient to trace anomaly in the clustering of color sources approach

From our previously obtained shear viscosity to entropy density ratio ($\eta/s$) in the framework of clustering of color sources (Color String Percolation Model: CSPM), we calculate the jet quenching parameter $\hat {q}$ and trace anomaly $\Delta = (\varepsilon -3\it p)/T^{4}$ as a function of temperature. It is shown that the scaled $\hat {q}/T^{3}$ is in agreement with the recent JET Collaboration estimates. The inverse of $\eta/s$ is found to represent $\Delta$. The results for $\Delta$ are in excellent agreement with Lattice Quantum Chromo Dynamics (LQCD) simulations. From the trace anomaly and energy density $\epsilon$, the equation of state is obtained as a function of temperature and compared with LQCD simulations. It is possible that there is a direct connection between the $\eta/s$ and $\Delta$. Thus the estimate of transport coefficient $\eta/s$ provides $\hat {q}$ and $\Delta$ as a function of temperature. Both $\Delta$ and $\eta/s$ describe the transition from a strongly coupled QGP to a weakly coupled QGP.

Scaling behaviours of the pT spectra for identified hadrons in pp collisions

We extend the scaling behaviour observed in the inclusive charged hadron transverse momentum (pT) distributions to the pT spectra of pions, kaons and protons produced in proton–proton (pp) collisions with center of mass energies () at 0.9, 2.76 and 7 TeV. This scaling behaviour arises when a linear transformation, is applied on the pion, kaon or proton pT spectra. The scaling parameter K depends on and is determined by a new method, the quality factor method, which does not rely on the shape of the scaling function. We argue that the pions, kaons and protons originate from different distributions of clusters which are formed by strings overlapping, and the scaling behaviours of these identified particles pT spectra could be understood with the colour string percolation model in a quantitative way simultaneously.

De-Confinement and the Clustering of Color Sources

A brief review of the color string percolation model (CSPM) is presented. The clustering of color sources provides a framework of the the partonic interactions in the initial stage of the collisions. The CSPM has described several observables in agreement with the experimental results e.g. multiplicity, elliptic flow at RHIC and LHC energies. The thermodynamical quantities temperature and the Equation Of State (EOS) are obtained in agreement with the Lattice Quantum Chromo Dynamics (LQCD) calculations. The shear viscosity to entropy density ratio (·=s) is obtained at RHIC and LHC energies. It is also observed that the inverse of ·=s is equivalent to trace anomaly ¢ = ( i 3P)=T 4 in excellent agreement with the recent LQCD calculations.

Clustering of Color sources and the Equation of State in Heavy Ion Collisions at RHIC and LHC Energies

The initial temperature Ti, energy density εi, and formation time τi 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 η/s is evaluated as a function of T and the mean free path (λmfp) using data and CSPM. η/s(Ti, λmfp) describes the transition from a strongly interacting QGP at T/Tc ~ 1 to a weakly coupled QGP at T/Tc ≥ 6. We find that the reciprocal of η/s is equal to the trace anomaly Δ = ε − 3P/T4 which also describes the transition. We couple this initial state of the QGP to a ID Bjorken expansion to determine the sound velocity c2s of the QGP for 0.85 ≤ T/Tc ≤ 3. The bulk thermodynamic quantities and the equation of state are in excellent agreement with LQCD results.

Clustering of color sources and the shear viscosity of the QGP in heavy ion 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 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 $1/4\pi$. 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.

Percolation and Deconfinement

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 String 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).

Percolation of color sources and the equation of state of QGP in central Au–Au collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV

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.

Forward-backward multiplicity correlations for identified particles in Au+Au 200 GeV collisions

Preliminary STAR measurements of the forward-backward multiplicity correlation as a function of rapidity separation for pions and (anti)protons in Au+Au 200 GeV collisions are presented for 0–10% and 10–20% centralities. A strong, uniform correlation is shown for pions, and is smaller for (anti)protons. The Color String Percolation Model predicts the long-range correlation, and suggests a possible measurement to study a transition from percolation to the quark-gluon plasma.