Study of $\langle p_{\rm T} \rangle$ and its higher moments, and extraction of the speed of sound in Pb-Pb collisions with ALICE

TL;DR

The paper uses ultracentral Pb--Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV to study event-by-event fluctuations of the mean transverse momentum $\langle p_{\rm T}\rangle$ and higher-order moments of the $[p_{\rm T}]$ distribution. By correlating $\langle p_{\rm T}\rangle^{\mathrm{norm}}$ with the normalized charged-particle density $\langle \mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta \rangle^{\mathrm{norm}}$ and fitting to a hydrodynamic-inspired form, the speed of sound squared $c_s^2$ is extracted, with strong dependence on the centrality estimator used due to jet-fragmentation and volume-balance biases. A two-component model separating Geometrical and Intrinsic fluctuations describes the non-Gaussian features of the $[p_{\rm T}]$ distribution, with Geometrical contributions dominating for transverse-energy-based centrality and diminishing toward ultracentral collisions. Comparisons to HIJING and the Trajectum hydrodynamic model show that hydrodynamics is essential to describe the data, while jet fragmentation biases must be accounted for when interpreting $c_s^2$ as a direct measure of the QGP speed of sound; the results motivate a reevaluation of extraction methods for $c_s^2$ in heavy-ion data.

Abstract

Ultrarelativistic heavy-ion collisions produce a state of hot and dense strongly interacting QCD matter called quark--gluon plasma (QGP). On an event-by-event basis, the volume of the QGP in ultracentral collisions is mostly constant, while its total entropy can vary significantly due to quantum fluctuations, leading to variations in the temperature of the system. Exploiting this unique feature of ultracentral collisions allows for the interpretation of the correlation of the mean transverse momentum of produced charged hadrons and the number of charged hadrons as a measure for the speed of sound. It is determined by fitting the relative increase in transverse momentum with respect to the relative change in the average charged-particle density measured at midrapidity. This study reports the event-average transverse momentum of charged particles as well as the self-normalized variance, skewness, and kurtosis of the event-by-event transverse momentum distribution in ultracentral Pb-Pb collisions at a center-of-mass energy of 5.02 TeV per nucleon pair using the ALICE detector. Different centrality estimators based on charged-particle multiplicity or the transverse energy of the event are used to select ultracentral collisions. By ensuring a pseudorapidity gap between the region used to define the centrality and the region used to perform the measurement, the influence of biases on the rise of the mean transverse momentum is tested. The measured values are found to strongly depend on the exploited centrality estimator. The variance shows a steep decrease towards ultracentral collisions, while the skewness variables show a maximum, followed by a fast decrease. These non-Gaussian features are understood in terms of the vanishing of the impact-parameter fluctuations contributing to the event-to-event transverse momentum distribution.

Figures (10)

• Figure 1: Average number of participating nucleons $(\langle N_\mathrm{part}\rangle\xspace)$ as a function of centrality percentile in Pb--Pb collisions at $\sqrt{s_{\mathrm{NN}}}~=~5.02$ TeemV. Data points are shown for centrality estimators based on $N_{\mathrm{ch}}$, $E_{\mathrm{T}}$, $N_{\mathrm{tracklets}}$ within $|\eta|\leq 0.8$, and $N_{\mathrm{ch}}$ within $-3.7<\eta<-1.7$ and $2.8 < \eta <5.1$. Uncertainty bars represent the sum of statistical and systematic uncertainties, with the latter being the dominant source. The systematic uncertainty is determined by varying the acceptance correction factors within their uncertainties and assigning the maximum deviation from the nominal $N_\mathrm{part}$ value as the systematic uncertainty.
• Figure 2: Normalized spectra ratios as a function of the transverse momentum in Pb--Pb collisions at $\sqrt{s_{\mathrm{NN}}}~=~5.02$ TeemV. Results are shown for centrality estimators based on $N_{\mathrm{ch}}$ (top left), $E_{\mathrm{T}}$ (top right), $N_{\mathrm{tracklets}}$ (bottom left) within $0.5 \leq |\eta| \leq 0.8$, and $N_{\mathrm{ch}}$ within $-3.7<\eta<-1.7$ and $2.8 < \eta <5.1$ (bottom right). Each panel displays normalized ratios for selected centrality classes. The centrality percentile legend in the bottom left panel applies to midrapidity estimators, while the legend in the bottom right panel applies to the forward estimator. Error bars represent statistical uncertainties. Systematic uncertainties, which are largely canceled due to their common origin in both the numerator and denominator, are not shown.
• Figure 3: Event fraction distribution as a function of the normalized charged-particle density in Pb--Pb collisions at $\sqrt{s_{\mathrm{NN}}}~=~5.02$ TeemV. Centrality classification is based on $N_{\mathrm{ch}}$ (red circles) and $E_{\mathrm{T}}$ (blue squares) in $|\eta|\leq0.8$, and on forward $N_{\mathrm{ch}}$ for the V0 (black crosses). $\langle\mathrm{d}N_\mathrm{ch}/\mathrm{d}\eta\xspace\rangle\xspace^{\mathrm{norm}}$ is derived from the extrapolated spectra in $|\eta|\leq0.8$. Gray curves represent fits using the model from Ref. Das:2017ned. The positions of $\langle\mathrm{d}N_\mathrm{ch}/\mathrm{d}\eta\xspace\rangle\xspace^{\mathrm{norm}}_{\mathrm{knee}}$, indicated by dashed vertical lines, are 1.137, 1.120, and 1.111 for the $N_{\mathrm{ch}}$-, $E_{\mathrm{T}}$-, and V0-based centrality estimators, respectively.
• Figure 4: Correlation between $\langle p_{\mathrm{T}}\rangle^{\mathrm{norm}}$ and $\langle\mathrm{d}N_\mathrm{ch}/\mathrm{d}\eta\xspace\rangle\xspace^{\mathrm{norm}}$ in Pb--Pb collisions at $\sqrt{s_{\mathrm{NN}}}~=~5.02$ TeemV. Each panel shows the results for different centrality estimators defined in Table \ref{['tab:centrality_definition']}. $\langle p_{\mathrm{T}}\rangle^{\mathrm{norm}}$ and $\langle\mathrm{d}N_\mathrm{ch}/\mathrm{d}\eta\xspace\rangle\xspace^{\mathrm{norm}}$ are derived from the $p_{\rm T}$ spectra within the 0--10 $\mathrm{GeV}/c$ interval for all centrality estimators. For $E_{\mathrm{T}}$-based centrality estimators, the $y$-axis scale should be read from the axis located to the right of the bottom right panel. Lines on top of the data represent fits using Eq. \ref{['eq:fitmeanpt']}. The fit range spans from 1 to the last point. Each panel displays the corresponding $c_{\mathrm{s}}^{2}$ values with their total uncertainty, determined by summing the statistical and systematic uncertainties in quadrature. Vertical uncertainty bars in each point represent the combined statistical and systematic uncertainty. The total uncertainty in the $\langle\mathrm{d}N_\mathrm{ch}/\mathrm{d}\eta\xspace\rangle\xspace^{\mathrm{norm}}$ is negligible and therefore not visible.
• Figure 5: Correlation between $\langle p_{\mathrm{T}}\rangle^{\mathrm{norm}}$ and $\langle\mathrm{d}N_\mathrm{ch}/\mathrm{d}\eta\xspace\rangle\xspace^{\mathrm{norm}}$ in Pb--Pb collisions at $\sqrt{s_{\mathrm{NN}}}~=~5.02$ TeemV. Each panel shows the results for different centrality estimators defined in Table \ref{['tab:centrality_definition']}. The data are compared with predictions from the HIJING PhysRevD.44.3501 and Trajectum Nijs:2023yabNijs:2020rocNijs:2021clz models, represented by continuous and dashed lines, respectively. The bands around the Trajectum predictions represent the sum in quadrature of the statistical and systematic uncertainties, with the latter being the dominant source. For the HIJING predictions, only the statistical uncertainty is shown (not visible in the plot).