Feasibility of measuring the speed of sound of the quark-gluon plasma from the multiplicity and mean $p_T$ of ultracentral heavy-ion collisions

Abstract

The mean transverse momentum $⟨p_T⟩$ of hadrons has been observed experimentally and in numerical simulations to have a power-law dependence on the hadronic multiplicity $N$ in ultracentral relativistic heavy-ion collisions: $⟨p_T⟩\propto N^{b_{\mathrm{UC}}}$. It has been put forward that this exponent $b_{\mathrm{UC}}$ is the speed of sound of quark-gluon plasma measured at a temperature determined from $⟨p_T⟩$. We study step by step the connection between (i) the energy and entropy of hydrodynamic simulations and (ii) experimentally measurable observables. We show that an argument based on energy and entropy should yield an exponent equal to the pressure over energy density $P/\epsilon$, rather than the speed of sound $c_s^2$; however, we also observe that $⟨p_T⟩$ and $N$ are not sufficiently accurate proxies for the energy and entropy to make this possible in practice. From simulations, we find that the exponent $b_{\mathrm{UC}}$ is significantly different whether the ''effective volume'' is strictly constant or not, a condition that cannot be enforced experimentally. Additional tests using a modified equation of state find that the exponent $b_{\mathrm{UC}}$ exhibits a variable degree of correlations with the speed of sound and with $P/\epsilon$, but is not an accurate measurement of either quantity in general.

8 pages, 4 figures -- v4: version accepted for publication

References in corpus (12)

• The equation of state in (2+1)-flavor QCD
• The QCD equation of state with dynamical quarks
• Equation of state and QCD transition at finite temperature
• The QCD Equation of State to $\mathcal{O}({\mu }_B^6)$ from Lattice QCD
• Constraining the Eq. of State of Super-Hadronic Matter from Heavy-Ion Collisions
• Lattice QCD equation of state at finite chemical potential from an alternative expansion scheme
• Thermodynamics of hot strong-interaction matter from ultrarelativistic nuclear collisions
• The mean transverse momentum of ultracentral heavy-ion collisions: A new probe of hydrodynamics
• Extracting the speed of sound in quark-gluon plasma with ultrarelativistic lead-lead collisions at the LHC
• Disentangling sources of momentum fluctuations in Xe+Xe and Pb+Pb collisions with the ATLAS detector
• Accessing the speed of sound in relativistic ultracentral nucleus-nucleus collisions using the mean transverse momentum
• Analytical insights into the interplay of momentum, multiplicity and the speed of sound in heavy-ion collisions

Cited by in corpus (2)

• The size of the quark-gluon plasma in ultracentral collisions: impact of initial density fluctuations on the average transverse momentum
• Extracting the speed of sound of QCD from transverse momentum fluctuations