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| CMS-HIN-23-003 ; CERN-EP-2023-292 | ||
| Extracting the speed of sound in quark-gluon plasma with ultrarelativistic lead-lead collisions at the LHC | ||
| CMS Collaboration | ||
| 12 January 2024 | ||
| Rep. Prog. Phys. 87 (2024) 077801 | ||
| 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 determine the speed of sound in an extended volume of quark-gluon plasma 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 | Additional Figures | References | CMS Publications |
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| Figures | |
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Figure 1:
Conceptual representation of temperature vs. entropy density from mid-central to ultra-central heavy ion collisions. |
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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 [39]. |
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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 [19] and the model by Gardim et al. [17] 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. |
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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 [19] following the same fitting procedure as the data and from the earlier work [16] are presented as the other colored boxes. The curve shows the prediction of $ c^2_{\mathrm{s}} $ as a function of $ T $ 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 [42]. |
| Summary |
| In summary, this study presents a measurement with a new hydrodynamic probe in ultrarelativistic nuclear collisions that results in the most precise determination to date of the speed of sound in an extended volume of quark-gluon plasma matter. 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. |
| Additional Figures | |
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Additional Figure 1:
Charged particle transverse momentum $ p_{\mathrm{T}} $, measured within pseudorapidity $ |\eta| < $ 0.5 and for $ p_{\mathrm{T}} > $ 0.3 GeV, as a function of total HF transverse energy sum $ E_{\mathrm{T, sum}}^{\mathrm{HF}} $ in PbPb collisions (0-10% centrality class) at a nucleon-nucleon center-of-mass energy of 5.02 TeV. |
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Additional Figure 2:
The transverse momentum $ p_{\mathrm{T}} $ spectrum generated by the HYDJET event generator, with a curve superimposed on it representing the Hageborn function [38] fitted in the range $ p_{\mathrm{T}} > $ 0.4 GeV, and extrapolated to $ p_{\mathrm{T}} < $ 0.4 GeV in PbPb collisions (0-5% centrality class) at a nucleon-nucleon center-of-mass energy of 5.02 TeV. The mean $ p_{\mathrm{T}} $ value from the HYDJET event generator is $ \langle p_\mathrm{T} \rangle= $ 0.700 GeV, while the extrapolated one is $ \langle p_\mathrm{T} \rangle= $ 0.703 GeV. |
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Additional Figure 3:
The measured transverse momentum $ p_{\mathrm{T}} $ spectrum (solid markers) fitted by the Hagedorn function [38] in the range $ p_{\mathrm{T}} > $ 4.0 GeV and extrapolated to $ p_{\mathrm{T}} < $ 0.4 GeV (open circles) in PbPb collisions (0-5% centrality class) at a nucleon-nucleon center-of-mass energy of 5.02 TeV. |
png pdf |
Additional Figure 4:
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 pseudorapidity $ |\eta| < $ 0.5 and $ p_{\mathrm{T}} > $ 0.3 GeV, in PbPb collisions at a nucleon-nucleon center-of-mass energy of 5.02 TeV. 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 [19] and model by Gardim et. al. [17] are also shown for comparison. |
png pdf |
Additional Figure 5:
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 pseudorapidity $ |\eta| < $ 0.5 and $ p_{\mathrm{T}} > $ 0.3 GeV, in PbPb collisions at a nucleon-nucleon center-of-mass energy of 5.02 TeV. Results are obtained with different centrality estimators based on the total HF transverse energy sum with 3 $ < |\eta| < $ 5 (red circles) and charged track multiplicity with 1 $ < |\eta| < $ 2.4 and $ p_{\mathrm{T}} > $ 0.3 GeV (blue squares). 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. |
png pdf |
Additional Figure 6:
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 pseudorapidity $ |\eta| < $ 0.5 and $ p_{\mathrm{T}} > $ 0.3 GeV, in PbPb collisions at a nucleon-nucleon center-of-mass energy of 5.02 TeV. Results are obtained with different centrality estimators based on the total HF transverse energy sum with 3 $ < |\eta| < $ 5 (red circles) and charged track multiplicity with 1 $ < |\eta| < $ 2.4 and $ p_{\mathrm{T}} > $ 0.3 GeV (blue squares). 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. |
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