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

A bstract 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 $$(\langle {p}_{\text{T}}\rangle )$$ of produced charged hadrons and the number of charged hadrons as a measure for the speed of sound, c s . This speed is related to the rate at which compression waves travel in the QGP and is determined by fitting the relative increase in $$\langle {p}_{\text{T}}\rangle $$ with respect to the relative change in the average charged-particle density $$(\langle \text{d}{N}_{\text{ch}}/\text{d}\eta \rangle )$$ measured at mid-rapidity. This study reports the event-average $$\langle {p}_{\text{T}}\rangle $$ of charged particles as well as the variance, skewness, and kurtosis of the event-by-event transverse momentum per charged particle $$([{p}_{\text{T}}])$$ 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 and their potential effects on the rise of the mean transverse momentum is tested. The measured $${c}_{\text{s}}^{2}$$ is found to strongly depend on the exploited centrality estimator and ranges between 0 . 1146±0 . 0028 (stat . )±0 . 0065 (syst . ) and 0 . 4374±0 . 0006 (stat . )±0 . 0184 (syst . ) in natural units. The self-normalized variance shows a steep decrease towards ultracentral collisions, while the self-normalized 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 [ p T ] distribution.