CMS-PAS-HIN-23-003

CMS-PAS-HIN-23-003
Extracting the speed of sound in the strongly interacting matter created in ultrarelativistic nuclear collisions
CMS Collaboration
12 September 2023

Abstract: Ultrarelativistic nuclear collisions yield 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, we extracted the speed of sound in this medium utilizing data from 0.607 nb $^{-1}$ of lead-lead collisions at $\sqrt{\smash[b]{s_{_{\mathrm{NN}}}}}=$ 5.02 TeV, recorded by the CMS experiment in 2018 at the CERN-LHC. This is the most accurate measurement of this intrinsic characteristic to date and is performed using a new hydrodynamic probe in collisions with large overlap of the two lead nuclei. Our findings reveal that the squared speed of sound in this matter is 0.241 $\pm$ 0.002 (stat) $\pm$ 0.016 (syst) times the squared speed of light at an effective medium temperature of 219 $\pm$ 8 (syst) MeV, precisely aligning with predictions from lattice quantum chromodynamic calculations. This result provides the most stringent and direct constraints on the deconfined QCD phase attained by the hot and dense matter created in these collisions.
Links: CDS record (PDF) ; CADI line (restricted) ; These preliminary results are superseded in this paper, Submitted to ROPP. The superseded preliminary plots can be found here.

Figures	Summary	References	CMS Publications

Figures
png pdf	Figure 1: The normalized event count as a function of the charged particle multiplicity, $N_{\mathrm{ch}}$ , within the kinematic range of $\|\eta\| <$ 0.5 and extrapolated to $p_{\mathrm{T}}\approx$ 0 GeV, in PbPb collisions for most central events. The $N_{\mathrm{ch}}$ is normalized by its value in the 0-5% centrality class. The curve represents the fit by the S. Das et. al. model in Ref. [29].
png pdf	Figure 2: The average transverse momentum of charged particles, $\langle p_\mathrm{T} \rangle$ , as a function of the charged particle multiplicity, $N_{\mathrm{ch}}$ , within the kinematic range of $\|\eta\| <$ 0.5 and extrapolated to $p_{\mathrm{T}}\approx$ 0 GeV. Both $\langle p_\mathrm{T} \rangle$ and $N_{\mathrm{ch}}$ are normalized by their values in the 0-5% centrality class. Bars and red bands correspond to statistical and systematic uncertainties, respectively. Hydrodynamic simulations from the Trajectum model [12] and model by Gardim et. al. [10] are also shown for comparison. The dash line is a fit to data by Eq. (1) in the range of $N_{\mathrm{ch}}^{\mathrm{norm}} >$ 1.14.
png pdf	Figure 3: The speed of sound, $c^2_{\mathrm{s}}$ , as a function of the effective temperature, $T_{\mathrm{eff}}$ , with one point extracted utilizing CMS ultra-central collisions PbPb 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 $T_{\mathrm{eff}}$ . Values extracted from the Trajectum simulation [12] following the same fitting procedure as the data and from the earlier work [9] are presented as the other colored boxes. The curve shows the prediction from lattice quantum chromodynamics [1]. The dashed line at the value of 1/3 corresponds to the upper limit for non-interacting, massless (``ideal gas'') systems [30].

Summary

In summary, this study presents a measurement of a new hydrodynamic probe for the most precise extraction to date of the speed of sound in ultrarelativistic heavy ion collisions. By leveraging the dependence of charged multiplicity on average particle transverse momentum in nearly head-on PbPb collisions, we determine the squared speed of sound to be 0.241

$\pm$ 0.002 (stat)

$\pm$ 0.016 (syst) at an effective temperature of approximately 219

$\pm$ 8 (syst) MeV. These findings demonstrate an excellent agreement with lattice quantum chromodynamic predictions, providing robust evidence for the existence of a deconfined phase of matter at extremely high temperatures.

References
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