Analytical insights into the interplay of momentum, multiplicity and the speed of sound in heavy-ion collisions

TL;DR

This paper presents a minimal model linking the speed of sound in quark-gluon plasma to particle multiplicity and energy in ultracentral heavy-ion collisions, analyzing how rapidity cuts and initial conditions affect this relationship.

Contribution

It introduces an analytical framework to relate the speed of sound to measurable particle properties, accounting for rapidity cuts and initial temperature effects in heavy-ion collision models.

Findings

Finite rapidity cuts cause measurable deviations in the speed of sound estimates.

Deviations scale with the ratio of freezeout to initial temperature.

The model highlights the importance of initial conditions in interpreting experimental data.

Abstract

We introduce a minimal model of ultracentral heavy-ion collisions to study the relation between the speed of sound of the produced plasma and the final particles' energy and multiplicity. We discuss how the particles' multiplicity $N_{\textrm{tot}}$ and average energy $E_{\textrm{tot}}/N_{\textrm{tot}}$ is related to the speed of sound $c_s$ by $c_s^2=d \ln (E_{\textrm{tot}}/N_{\textrm{tot}})/d\ln N_{\textrm{tot}}$ if the fluid is inviscid, its speed of sound is constant and all final particles can be measured. We show that finite rapidity cuts on the particles' multiplicity $N$ and energy $E$ introduce corrections between $c_s^2$ and $d \ln (E/N)/d\ln N$ that depend on the system's lifetime. We study analytically these deviations with the Gubser hydrodynamic solution, finding that, for ultrarelativistic bosons, they scale as the ratio of the freezeout temperature $T_{\mathrm{FO}}$ over the maximum initial temperature of the fluid $T_{0}$; the non-thermodynamic aspect of these corrections is highlighted through their dependence on the system's initial conditions.