String Percolation Research Articles

String percolation in AA and p+p collisions

A brief review of the string percolation model and its results are presented together with the comparison to experimental data. First, it is done an introduction to the quark-gluon phase diagram and the lattice results concerning the connement and the percolation of center domains. It is studied the interaction of the strings produced in nucleus-nucleus and proton-proton collisions showing how the string percolation arises. The main consequences of the string percolation, concerning the dependence on the energy and centrality, on the multiplicities and the mean transverse momentum are obtained comparing with experimental data. It is emphasized the non-abelian character of the color eld of the strings forming the cluster to reproduce the rise of the transverse momentum with multiplicity and the relative suppression of multiplicities. It is also studied dierent observables like multiplicity and transverse momentum distributions, dependence with multiplicity and transverse momentum correlations, forward-backward correlations, the strength of the Bose-Einstein correlations, dependence on the multiplicity of J/ψ production and its possible suppression in pp collisions at high multiplicity, strangeness enhancement, elliptic ow, and ridge structure. The comparison with the data shows an overall agreement. The thermodynamical properties of the extended cluster formed in the collision are discussed computingits energy and entropy density, shear viscosity over entropy density ratio, bulk viscosity, sound speed and trace anomaly as a function of temperature, showing a remarkable agreement with lattice QCD evaluations. The string percolation can be regarded as the initial frame able to describe the collective behavior produced in AA and pp collisions.

Universal scaling of meson and baryon spectra in p-Pb collisions at 5.02TeV

We systematically investigate the scaling property of mesons (pions and kaons) and baryons (protons, [Formula: see text], [Formula: see text] and [Formula: see text]) transverse momentum ([Formula: see text]) spectra at different centrality classes (0–5[Formula: see text], 5–10[Formula: see text], 10–20[Formula: see text], 20–40[Formula: see text], 40–60[Formula: see text], 60–80[Formula: see text] and 80–100[Formula: see text]) in proton-lead collisions with center of mass energy per nucleon pair 5.02[Formula: see text]TeV. In the low [Formula: see text] region with [Formula: see text][Formula: see text]GeV/c, a universal scaling independent of the centrality is observed in the pion (kaon, proton, [Formula: see text], [Formula: see text] and [Formula: see text]) spectra when a dilatation, [Formula: see text], is applied. Here, [Formula: see text] is a scaling parameter depending on the centrality class. We find that the rates at which ln[Formula: see text] changes with the logarithmic value of the average value of the number of participating nucleons, ln[Formula: see text], are stronger for baryons than those for mesons. In the high [Formula: see text] region, there is a deviation from the scaling. The more peripheral the collisions are, the more obvious the violation of the scaling is. In the framework of the color string percolation (CSP) model, we show that mesons and baryons are generated from the decay of clusters formed by strings overlapping in the transverse plane with the same size dispersion but with different mean size. The mean size of clusters for baryons is smaller than that of mesons. For the same hadrons at different centrality classes, the mean size of clusters decreases with the increase of centrality. The fragmentation functions for cluster decay are different for different hadrons, while they are universal for the same hadrons at different centrality classes. The universal scaling of the meson and baryon spectra in the low [Formula: see text] region can be quantitatively understood with the CSP model at the same time.

Hot Dense Matter: Deconfinement and Clustering of Color Sources in Nuclear Collisions

Within the first few microseconds from after the Big Bang, the hot dense matter was in the form of the Quark Gluon Plasm (QGP) consisting of free quarks and gluons. By colliding heavy nuclei at RHIC and LHC at a velocity close to the speed of light, we were able to create the primordial matter and observe the matter after expansion and cooling. In this report we present the thermodynamics and transport coefficients obtained in the framework of clustering of color sources in both hadron-hadron and nucleus-nucleus collisions at RHIC and LHC energies. Multiparticle production at high energies can be described in terms of color strings stretched between the projectile and target. At high string density single strings overlap and form color sources. This addition belongs to the non-perturbative domain of Quantum Chromo Dynamics (QGP) and manifests its most fundamental features. The Schwinger QED 2 mechanism produces color neutral q q ¯ pairs when color source strings break. Subsequent hardonization produces the observed hadrons. With growing energy and atomic number of the colliding nuclei the density of strings grows and more color sources form clusters in the transverse plane. At a certain critical density a macroscopic cluster appears, which marks the percolation phase transition. This is the Color String Percolation Model (CSPM). The critical density is identified as the deconfinement transition and happens at the hadronization temperature. The stochastic thermalization in p p and A-A is a consequence of the quantum tunneling through the event horizon introduced by the confining color fields, the Hawking-Unruh effect. The percolation approach within CSPM is successfully used to describe the crossover phase transition in the soft collision region. The same phenomenology when applied to both hadron-hadron and nucleus-nucleus collisions emphasizes the importance of color string density, creating a macroscopic cluster which identifies the connectivity required for a finite droplet of the QGP.

Electrical conductivity of hot and dense QCD matter created in heavy-ion collisions: A color string percolation approach

Recently, transport coefficients viz. shear viscosity, electrical conductivity etc. of strongly interacting matter produced in heavy-ion collisions have drawn considerable interest. We study the normalised electrical conductivity ($\sigma_{\rm el}$/T) of hot QCD matter as a function of temperature (T) using the Color String Percolation Model (CSPM). We also study the temperature dependence of shear viscosity and its ratio with electrical conductivity for the QCD matter. We compare CSPM estimations with various existing results and lattice Quantum Chromodynamics (lQCD) predictions with (2+1) dynamical flavours. We find that $\sigma_{\rm el}$/T in CSPM has a very weak dependence on the temperature. We compare CSPM results with those obtained in Boltzmann Approach to Multi-Parton Scatterings (BAMPS) model. A good agreement is found between CSPM results and predictions of BAMPS with fixed strong coupling constant.

Energy and centrality dependent study of deconfinement phase transition in a color string percolation approach at RHIC energies

We take the experimental data for transverse momentum spectra of identified charged hadrons in different centrality classes for nucleus-nucleus (A+A) collisions at various Relativistic Heavy-Ion Collider (RHIC) energies measured by the STAR collaboration. We analyse these data in the framework of color string percolation model (CSPM) in order to extract various percolation parameters at different centralities at RHIC energies to study the effect of collision geometry and collision energy. We use these parameters to study the centrality dependent behaviour of initial temperature of the percolation cluster, energy density, average transverse momentum, shear viscosity to entropy density ratio ($\eta/s$) and trace anomaly for different energies at RHIC from $\sqrt{s_{\rm NN}}$ = 19.6 to 200 GeV. These observables are found to strongly depend on centrality at various collision energies. The critical percolation density, which is related to the deconfinement phase transition is achieved in the most central nucleus-nucleus collisions, while it fails in the peripheral collisions. A universal scaling is observed in color suppression factor and initial temperatures when studied as a function of charged particle pseudorapidity distribution scaled by nuclear overlap area at RHIC energies. The minimum of $\eta/s$ is observed in the most central collisions at $\sqrt{s_{\rm NN}}$ = 130 and 200 GeV.

Universal scaling of the pion, kaon and proton pT spectra in Pb[sbnd]Pb collisions at 2.76 TeV

With the experimental data collected by the ALICE collaboration in PbPb collisions at a center-of-mass energy per nucleon pair 2.76 TeV for six different centralities (0–5%, 5–10%, 10–20%, 20–40%, 40–60% and 60–80%), we investigate the scaling property of the pion, kaon and proton transverse momentum (pT) spectra at these centralities. We show that in the low pT region with pT≤ 2.75 (3.10 and 2.35) GeV/c the pion (kaon and proton) spectra exhibit a scaling behaviour independent of the centrality of the collisions. This scaling behaviour arises when these spectra are presented in terms of a suitable variable, z=pT/K. The scaling parameter K is determined by the quality factor method and is parameterized by a〈Npart〉b, where 〈Npart〉 is the average value of the number of participating nucleons, a and b are free parameters, b characterizes the rate at which lnK changes with ln〈Npart〉. The values of b for pions and kaons are consistent within uncertainties, while they are smaller than that for protons. In the high pT region, due to the suppression of the spectra, a violation of the proposed scaling is observed going from central to peripheral collisions. The more peripheral the collisions are, the more clearly violated the proposed scaling becomes. In the framework of the colour string percolation model, we argue that the pions, kaons and protons originate from the fragmentation of clusters which are formed by strings overlapping and the cluster's fragmentation functions are different for different hadrons. The scaling behaviour of the pion, kaon and proton spectra in the low pT region can be simultaneously explained by the colour string percolation model in a qualitative way.

Universal scaling of strange particle pT spectra in pp collisions

As a complementary study to that performed on the transverse momentum ($p_{\rm T}$) spectra of charged pions, kaons and protons in proton-proton (pp) collisions at LHC energies 0.9, 2.76 and 7 TeV, we present a scaling behaviour in the $p_{\rm T}$ spectra of strange particles ($K_{S}^{0}$, $\rm \Lambda$, $\rm \Xi$ and $\phi$) at these three energies. This scaling behaviour is exhibited when the spectra are expressed in a suitable scaling variable $z=p_{\rm T}/K$, where the scaling parameter $K$ is determined by the quality factor method and increases with the center of mass energy ($\sqrt{s}$). The rates at which $K$ increases with $\mathrm{ln}\sqrt{s}$ for these strange particles are found to be identical within errors. In the framework of the colour string percolation model, we argue that these strange particles are produced through the decay of clusters that are formed by the colour strings overlapping. We observe that the strange mesons and baryons are produced from clusters with different size distributions, while the strange mesons (baryons) $K_{S}^{0}$ and $\phi$ ($\rm \Lambda$ and $\rm \Xi$) originate from clusters with the same size distributions. The cluster's size distributions for strange mesons are more dispersed than those for strange baryons. The scaling behaviour of the $p_{\rm T}$ spectra for these strange particles can be explained by the colour string percolation model in a quantitative way.

String percolation threshold for elliptically bounded systems

It has been shown that a hot and dense deconfined nuclear matter state produced in ultra-relativistic heavy-ion collisions, can be quantitatively described by the String Percolation phenomenological model. The model address the phase transition in terms of the two-dimensional continuum percolation theory over strings, which are schematic representations of the fundamental interactions among the partons of the colliding nuclei in the initial state. In this work, we present an extension of the critical string density results including the eccentricity dependence on the initial state geometry focus on small string number with different density profile, small deviations from the different profile densities are found. The percolation threshold shows consistency with the thermodynamic limit for the uniform density profile with a large number of strings in the case of circular boundary system. A significant dependence on the eccentricity for a small number of strings compared to high occupancy systems is exhibited, the implications may become relevant in hadron–hadron or hadron–nucleus collision systems.

The onset on the ridge structure in AA, pA and pp collisions

It is shown that the anomalous sharp increasing of the strength of the near-side ridge structures observed in Au-Au collisions at s=62 GeV and s=200 GeV and the onset of the ridge structure in pPb and in pp collisions can be naturally explained in the framework of string percolation. In all the cases the near-side strength reflects the collision area covered by the strings stretched between the colliding objects and therefore it is related to the shape of their profile functions. The dependence of the pseudorapidty and azimuthal widths on multiplicty and energy is qualitatively explained.

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.

Indication of change of phase in high-multiplicity proton-proton events at LHC in string percolation model

We analyze high multiplicity proton-proton ($pp$) collision data in the framework of the String Percolation Model (SPM) that has been successful in describing several phenomena of multiparticle production, including the signatures of recent discovery of strongly interacting partonic matter, the Quark Gluon Plasma (QGP), in relativistic heavy-ion collisions. Our study in terms of the ratio of shear viscosity and entropy density ($\eta/s$) and the (LQCD) predicted signature of QCD change of phase, in terms of effective number of degrees of freedom ($\epsilon /T^4$), reiterates the possibility of strongly interacting collective medium in these events.

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.

Onset of the ridge structure inAA,pA, andppcollisions

It is shown that the anomalous sharp increasing of the strength of the near-side ridge structures observed in Au-Au collisions at $\sqrt{s}=$ 62 GeV and $\sqrt{s}=$ 200 GeV and the onset of the ridge structure in pPb and in pp collisions can be naturally explained in the framework of string percolation. In all the cases the near-side strength reflects the collision area covered by the strings stretched between the colliding objects and therefore it is related to the shape of their profile functions. The dependence of the pseudorapidty and azimuthal widths on multiplicty and energy is qualitatively explained.

Scaling behaviour of charged hadron distributions in pp and collisions

We report on a scaling behaviour in the transverse momentum () distributions for charged hadrons produced in proton–proton (pp) collisions with different centre of mass energies ( = 0.9, 2.76 and 7 TeV) at the Compact Muon Solenoid detector. This scaling behaviour appears when the is replaced by , where K is a parameter and depends on . A similar scaling behaviour is observed in the pT distributions of charged hadrons produced in proton–antiproton () collisions with = 0.63, 1.8 and 1.96 TeV at the Collider Detector at Fermilab. The particle production mechanism behind the scaling behaviour in the pp or collisions could be explained by the model of percolation of strings.

Rapidity dependence of particle densities in pp and AA collisions in the string percolation approach

We use multiple scattering and energy conservation arguments to describe dn=dnNANA as a function of dn=dnpp in the framework of string percolation. As nuclei are made up of nucleons it is natural to look at nucleus-nucleus (A-A) collisions as resulting from the superposition of nucleon-nucleon (p-p) collisions, in the spirit of Glauber model approach. In the single scattering limit the average number of participating nucleons per nucleus, NA behave incoherently and the multiplicity at low energy corresponds to the wounded nucleon model

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.

Rapidity dependence of particle densities inppandAAcollisions

We use multiple scattering and energy conservation arguments to describe $dn/d\eta_{NANA}$ as a function of $dn/d\eta_{pp}$ in the framework of string percolation. We discuss the pseudo-rapidity $\eta$? and beam rapidity Y dependence of particle densities. We present our results for pp, Au- Au, and Pb-Pb collisions at RHIC and LHC.

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.

Multiplicity in pp and AA collisions: the same power law from energy–momentum constraints in string production

We show that the dependence of the charged particle multiplicity on the centre-of-mass energy of the collision is, in the String Percolation Model, driven by the same power law behavior in both proton–proton and nucleus–nucleus collisions. The observed different growths are a result of energy–momentum constraints that limit the number of formed strings at low energy. Based on the very good description of the existing data, we provide predictions for future high energy LHC runs.