Exploring Thermalization and Multi-Freeze-Out Effects in Pb-Pb collisions Based on Tsallis pT Distributions

TL;DR

This work analyzes identified-hadron $p_T$ spectra in Pb+Pb collisions at $\sqrt{s_{NN}}=2.76$ TeV with the thermodynamically consistent Tsallis distribution to extract the effective temperature $T$, non-extensivity parameter $q$, and mean $p_T$ across centralities. By linearizing $T$ versus hadron mass $m_0$ and $\langle p_T\rangle$ versus mean moving mass, the authors separately estimate the kinetic freeze-out temperature $T_0$ and average transverse flow $\langle \beta_T\rangle$, enabling a disentanglement of thermal and collective effects. The results show a mass-dependent (multi-freeze-out) hierarchy, with heavier hadrons decoupling earlier at higher temperatures and larger $\langle p_T\rangle$, and a centrality-driven progression toward near-equilibrium (smaller $q$) and stronger radial flow, which saturates for the most central collisions. These findings illuminate the thermalization and expansion dynamics of QCD matter at LHC energies and motivate direct comparisons with hydrodynamic models and phase-transition signatures.

Abstract

This study investigates transverse-momentum (pT) distributions of pi-, pi+, K-, K+, p, pbar, K0s, and Lambda in several centrality classes of Pb-Pb collisions at sqrt(sNN) = 2.76 TeV. The measured spectra are analyzed with the Tsallis non-extensive distribution, from which the effective temperature T, non-extensive parameter q, and the mean transverse momentum mean_pT are extracted for each particle species and centrality interval. To disentangle thermal and collective effects, the mean kinetic freeze-out temperature T0 is obtained from the intercept of the T-versus-mass relation, while the average transverse flow velocity betaT is extracted from the slope of mean_pT versus the mean moving mass for pions, kaons, and protons. The results show that T increases and q decreases with increasing centrality, indicating a hotter and more equilibrated system in central collisions. A clear mass dependence of T supports a multi-freeze-out scenario, with heavier particles decoupling earlier. Both T0 and betaT rise from peripheral to mid-central collisions before saturating toward central events, which may suggest the onset of collective behavior or changes in freeze-out dynamics. These observations provide new insights into the thermal and dynamical properties of the medium created in heavy-ion collisions at the LHC.

Figures (6)

• Figure 1: The $p_T$ distributions of $\pi^+$, $\pi^-$, $K^+$, $K^-$, $p$, and $\bar{p}$ are superimposed over the fit function across different centrality classes in Pb--Pb collisions at a collision energy of 2.76 TeV. Experimental data for various centrality values are shown with different coloured data points, while the solid lines give the fitting result, using Eq. (\ref{['eqTsallisConsistent']}). Each graph has been provided with a Data/Fit panel attached to the lower part.
• Figure 2: The outcome of the fit function on the $p_T$ distribution of $K_s^0$ and $\Lambda$ measured by ALICE collaboration at 2.76 TeV of Pb--Pb collisions in different centrality classes. Experimental data for various centrality values are shown with different coloured data points, while the solid lines represent the fitting result obtained through Eq. (\ref{['eqTsallisConsistent']}). Each graph has been provided with a Data/Fit panel attached to the lower part.
• Figure 3: The centrality dependence of (a) $T$, (b) $q$ and (c) $\langle p_T\rangle$.
• Figure 4: Correlation between (a) $T$ and $q$, (b) $T$ and $\langle p_T\rangle$ and (c) $q$ and $\langle p_T\rangle$.
• Figure 5: (a) Effective temperature $T$ as a function of rest mass $m_0$ and (b) $\langle p_T\rangle$ versus mean moving mass $\overline{m}$ for light flavoured particles produced in Pb-Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV. The solid lines are the linear fitting results.