Scientists with the CMS experiment at the Large Hadron Collider used collisions of lead nuclei to measure how a very hot, strongly interacting form of matter responds to compression. They report a value for the squared speed of sound of c_s^2 = 0.241 ± 0.002 (stat) ± 0.016 (syst) at an effective temperature T_eff = 219 ± 8 (syst) MeV. This number is in good agreement with results from lattice quantum chromodynamics (lattice QCD), a theoretical tool for the strong force.

The team measured two simple quantities in many collision events: the mean transverse momentum of charged particles, <pT>, and the charged-particle multiplicity, N_ch. In very central lead–lead collisions, the overall collision volume is roughly fixed, while the energy and entropy can fluctuate from event to event. Under these conditions theory gives a relation roughly of the form c_s^2 = d ln <pT> / d ln N_ch, where <pT> is related to an effective temperature and N_ch is related to entropy. In practice the analysis used normalized versions of these observables and a hydrodynamics-motivated conversion T_eff ≈ <pT>/3 to assign the quoted temperature.

The measurement used 2018 PbPb data at a nucleon–nucleon center-of-mass energy of √s_NN = 5.02 TeV, corresponding to an integrated luminosity of 0.607 nb^−1. Key detector systems for the analysis were the silicon tracker (for charged-particle tracks), the hadron-forward calorimeters (for event selection and centrality), and zero-degree calorimeters (to reject pileup). Tracks were measured down to pT = 0.3 GeV in parts of the analysis and selected within |η| < 0.5 for PbPb. Systematic uncertainties are dominated by tracking corrections and extrapolations needed to estimate the full pT range.

The authors also looked at proton–lead (pPb) collisions to see whether similar thermodynamic information can be extracted from smaller systems. They used datasets at √s_NN = 5.02 TeV (0.51 nb^−1) and 8.16 TeV (186 nb^−1). The pPb results can agree with lattice QCD under some assumptions about the system’s dynamical evolution (a boost-invariant picture with T_eff ≈ <pT>/3) but show worse agreement if a three-dimensional, asymmetric evolution is assumed (using T_eff ≈ <pT>/2.45). Model comparisons showed that the TRAJECTUM model is consistent with the PbPb value within uncertainties, while the HIJING model does not describe the high-multiplicity pPb data.