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

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 $N_{\text{tot}}$ and average energy $E_{\text{tot}}/N_{\text{tot}}$ is related to the speed of sound $c_s$ by $c_s^2=d\ln (E_{\text{tot}}/N_{\text{tot}})/d\ln N_{\text{tot}}$ 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.

Comments: 21 pages, 8 figures, v2 -- published version, associated git-hub repository: https://github.com/gabriel-sr151/cylindrical-sym-CF