CMS-HIN-23-003

CMS-HIN-23-003 ; CERN-EP-2023-292
Extracting the speed of sound in the strongly interacting matter created in ultrarelativistic lead-lead collisions at the LHC
CMS Collaboration
12 January 2024
Submitted to Reports on Progress in Physics
Abstract: Ultrarelativistic nuclear collisions create a strongly interacting state of hot and dense quark-gluon matter that exhibits a remarkable collective flow behavior with minimal viscous dissipation. To gain deeper insights into its intrinsic nature and fundamental degrees of freedom, we extracted the speed of sound in this medium created using lead-lead (PbPb) collisions at a center-of-mass energy per nucleon pair of 5.02 TeV. The data were recorded by the CMS experiment at the CERN LHC and correspond to an integrated luminosity of 0.607 nb$^{-1}$. The measurement is performed by studying the multiplicity dependence of the average transverse momentum of charged particles emitted in head-on PbPb collisions. Our findings reveal that the speed of sound in this matter is nearly half the speed of light, with a squared value of 0.241 $ \pm $ 0.002 (stat) $ \pm $ 0.016 (syst) in natural units. The effective medium temperature, estimated using the mean transverse momentum, is 219 $ \pm $ 8 (syst) MeV. The measured squared speed of sound at this temperature aligns precisely with predictions from lattice quantum chromodynamic (QCD) calculations. This result provides a stringent constraint on the equation of state of the created medium and direct evidence for a deconfined QCD phase being attained in relativistic nuclear collisions.
Links: e-print arXiv:2401.06896 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; Physics Briefing ; CADI line (restricted) ;

Figures	Summary	References	CMS Publications

Figures
png pdf	Figure 1: Conceptual representation of temperature vs. entropy density from mid-central to ultra-central heavy ion collisions.
png pdf	Figure 2: The event fraction distribution as a function of the charged-particle multiplicity, $ N_{\text{ch}} $, within the kinematic range of $ \|\eta\| < $ 0.5 and extrapolated to the full $ p_{\mathrm{T}} $ range, in PbPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}}= $ 5.02 TeV. The $ N_{\text{ch}} $ value is normalized by its value in the 0-5% centrality class ($ N_{\text{ch}}^{0} $). The curve represents a fit to the data using the S. Das et al. model [37].
png pdf	Figure 3: The average transverse momentum of charged particles, $ \langle {p_{\mathrm{T}}} \rangle $, as a function of the charged-particle multiplicity, $ N_{\text{ch}} $, within the kinematic range of $ \|\eta\| < $ 0.5 and extrapolated to the full $ p_{\mathrm{T}} $ range in PbPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}}= $ 5.02 TeV. Both $ \langle {p_{\mathrm{T}}} \rangle $ and $ N_{\text{ch}} $ are normalized by their values in the 0-5% centrality class ($ \langle {p_{\mathrm{T}}} \rangle^{0} $ and $ N_{\text{ch}}^{0} $). Bars and the red band correspond to statistical and systematic uncertainties, respectively. Hydrodynamic simulations from the TRAJECTUM model [18] and the model by Gardim et al. [16] are also shown for comparison. The dashed line is a fit to the data using Eq. (2) in the range of $ N_{\text{ch}}/N_{\text{ch}}^{0} > $ 1.14.
png pdf	Figure 4: The speed of sound, $ c^2_{\mathrm{s}} $, as a function of the effective temperature, $ T_{\text{eff}} $, with the CMS data point obtained from ultra-central PbPb collision data at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}}= $ 5.02 TeV. The size of the red box indicates systematic uncertainties of $ c^2_{\mathrm{s}} $ and $ T_{\text{eff}} $, while statistical uncertainties are smaller than the marker size. Values extracted from the TRAJECTUM simulation [18] following the same fitting procedure as the data and from the earlier work [15] are presented as the other colored boxes. The curve shows the prediction from lattice QCD calculations [6]. The dashed line at the value of 1/3 corresponds to the upper limit for noninteracting, massless gas (``ideal gas'') systems [40].

Summary

In summary, this study presents a measurement with a new hydrodynamic probe that results in the most precise determination to date of the speed of sound in the medium created through ultrarelativistic nuclear collisions. By determining the dependence of the average transverse momentum on the total multiplicity for charged particles in nearly head-on lead-lead collisions at a center-of-mass energy per nucleon pair of 5.02 TeV, a squared speed of sound of 0.241 $ \pm $ 0.002 (stat) $ \pm $ 0.016 (syst) in natural units is determined. The effective medium temperature, estimated using the mean transverse momentum, is 219 $ \pm $ 8 (syst) MeV. The excellent agreement of lattice quantum chromodynamics predictions with the experimental results provides strong evidence for the existence of a deconfined phase of matter at extremely high temperatures.

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