Percolation and de-confinement in relativistic nuclear collisions

TL;DR

The paper applies the Color String Percolation Model to $pp$, $Pb$-$Pb$, and $Xe$-$Xe$ collisions at LHC energies to extract the initial temperature $T(\xi)$ and energy density $\varepsilon$ from charged-particle spectra. By connecting cluster overlap via the percolation parameter $\xi$ to thermodynamic observables, it reveals a sharp rise in $\varepsilon/T^{4}$ above $T\approx 210$ MeV, approaching the ideal Quark-Gluon Plasma limit near $T\approx 230$ MeV. The results suggest a two-stage deconfinement with a lower transition around $T \sim 160$ MeV and a higher transition near $T \sim 220$ MeV, and they engage with broader QCD phase scenarios, including possible intermediate phases like SQGB. These findings provide a framework linking microscopic color connectivity to macroscopic thermal behavior in high-energy collisions, with implications for the nature of thermal transitions in QCD.

Abstract

In the present work we have analyzed the transverse momentum spectra of charged particles in high multiplicity $pp$ collisions at LHC energies $\sqrt s $ = 5.02 and 13 TeV using the Color String Percolation Model (CSPM). For heavy ions $Pb-Pb$ at $\sqrt {s_{NN}} $ = 2.76 and 5.02 TeV along with $Xe-Xe$ at $\sqrt {s_{NN}} $= 5.44 TeV have been analyzed. The initial temperature is extracted both in low and high multiplicity events in ${\it pp}$ collisions. For $A-A$ collisions the temperature is obtained as a function of centrality. From the measured energy density $ \varepsilon$ and the temperature T the dimensionless quantity $ \varepsilon/T^{4}$ is obtained. Our results for Pb-Pb and Xe-Xe collisions show a sharp increase in $\varepsilon/T^{4}$ above T $\sim$ 210 MeV and reaching the ideal gas of quarks and gluons value of $ \varepsilon/T^{4} \sim$ 16 at temperature $\sim $ 230 MeV. At this temperature there is a transition from the fluid behavior of QCD matter strongly interacting to a quasi free gas of quarks and gluons.

Figures (6)

• Figure 1: Partonic cluster structure in the transverse collision plane at low (left) and (right) high parton density satzbook.
• Figure 2: Color Suppression Factor $F(\xi)$ in ${\it pp}$, Pb-Pb and Xe-Xe collisions vs $dN_{ch}/d\eta$ scaled by the transverse area $S_{\perp}$. For ${\it pp}$ collisions $S_{\perp}$ is multiplicity dependent as obtained from IP-Glasma model cross. In case of Pb-Pb and Xe-Xe collisions the nuclear overlap area was obtained using the Glauber model glauber.
• Figure 3: Temperature vs $dN_{ch}/d\eta$ scaled by $S_{\perp}$ from ${\it pp}$, Pb-Pb and Xe-Xe collisions. The horizontal line at $\sim 165$ MeV is the universal hadronization temperature bec1.
• Figure 4: Energy density ($\epsilon$) as a function of the percolation density parameter ($\xi$). Upper panel shows the pp collision data at $\sqrt s$ = 5.02 and 13 TeV. Lower panel shows the data for Pb-Pb at $\sqrt {s_{NN}}$ = 2.76 and 5.02 TeV and Xe-Xe data at $\sqrt {s_{NN}}$ = 5.44 TeV.
• Figure 5: Dimensionless quantity $\varepsilon/T^{4}$ as a function of temperature from CSPM and LQCD calculation from HotQCD Collaboration lattice14. The CSPM values at higher temperature T > 200 MeV are obtained extrapolating from lower temperature.