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arxiv: 2605.21052 · v1 · pith:DMS3O77Tnew · submitted 2026-05-20 · ⚛️ nucl-ex · hep-ex

Study of the thermodynamic properties of hot QCD matter with the CMS experiment

Cesar A. Bernardes This is my paper

Pith reviewed 2026-05-21 01:43 UTC · model grok-4.3

classification ⚛️ nucl-ex hep-ex
keywords speed of soundQCD matterquark-gluon plasmaPbPb collisionstransverse momentumlattice QCDCMS experimentthermodynamic properties
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The pith

CMS measurements in ultra-central PbPb collisions extract a squared speed of sound of 0.241 for strongly interacting matter at 219 MeV.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper presents an analysis that uses the way the average transverse momentum of particles changes with collision multiplicity in the most central lead-lead collisions to determine the speed of sound squared in hot QCD matter. This approach yields a value of 0.241 with small uncertainties at an effective temperature of 219 MeV. The result matches predictions from lattice QCD calculations. Complementary data from proton-lead collisions are examined to look for signs of quark-gluon plasma in smaller systems. A sympathetic reader would care because confirming this thermodynamic property helps validate models of the early universe and high-energy nuclear matter.

Core claim

The analysis of the multiplicity dependence of the mean transverse momentum in ultra-central PbPb collisions at sqrt(s_NN) = 5.02 TeV yields c_s^2 = 0.241 ± 0.002 (stat) ± 0.016 (syst) at an effective temperature of T_eff = 219 ± 8 (syst) MeV, in good agreement with lattice-QCD calculations.

What carries the argument

The multiplicity dependence of the mean transverse momentum in ultra-central collisions, which encodes the squared speed of sound through a thermodynamic relation.

If this is right

  • The extracted value supports the use of hydrodynamic models for describing the expansion of the quark-gluon plasma.
  • Agreement with lattice QCD indicates that the equation of state at these temperatures is well constrained.
  • Studies in pPb collisions may reveal if similar thermodynamic properties appear in smaller collision systems.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • This measurement could help refine temperature profiles in hydrodynamic simulations of heavy-ion collisions.
  • Extending the method to other collision energies might map the speed of sound across a wider range of temperatures.

Load-bearing premise

The multiplicity dependence of the mean transverse momentum in ultra-central PbPb collisions directly encodes the squared speed of sound of the strongly interacting matter via the hydrodynamic or thermodynamic relation.

What would settle it

A measured c_s^2 value that significantly deviates from lattice QCD predictions at the same effective temperature would indicate that the encoding relation does not hold as assumed.

Figures

Figures reproduced from arXiv: 2605.21052 by Cesar A. Bernardes.

Figure 1
Figure 1. Figure 1: The normalized mean transverse momentum of charged particles as [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The speed of sound squared as a function of the effective temperature. [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: The quantity d ln⟨pT⟩/d ln Nch is shown as a function of the effective temperature, Teff = ⟨pT⟩/X, where X = 3 (upper) is used for boost-invariant calculations and X = 2.45 (lower) for calculations that account for system asymmetries. Comparisons with lattice-QCD calculations and with HIJING and TRAJECTUM simulations are also shown [10]. 4 Summary and outlook The CMS experiment has performed precise measur… view at source ↗
Figure 4
Figure 4. Figure 4: The mean transverse momentum as a function of charged-particle [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
read the original abstract

These proceedings summarize recent CMS measurements at the LHC that extract the squared speed of sound, $c_s^2$, of strongly interacting matter at extreme temperatures from the multiplicity dependence of the mean transverse momentum in ultra-central lead-lead (PbPb) collisions at $\sqrt{s_{\mathrm{NN}}} = 5.02\ \mathrm{TeV}$. The analysis yields $c_s^2 = 0.241 \pm 0.002\, (\mathrm{stat}) \pm 0.016\, (\mathrm{syst})$ at an effective temperature of $T_{\mathrm{eff}} = 219 \pm 8\, (\mathrm{syst})\,\mathrm{MeV}$, in good agreement with lattice-QCD calculations. Complementary studies in proton-lead (pPb) collisions are also presented to investigate possible quark-gluon plasma signatures in smaller systems.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. This manuscript summarizes CMS measurements at the LHC extracting the squared speed of sound c_s² of strongly interacting matter from the multiplicity dependence of mean transverse momentum in ultra-central PbPb collisions at √s_NN = 5.02 TeV. The analysis reports c_s² = 0.241 ± 0.002 (stat) ± 0.016 (syst) at T_eff = 219 ± 8 (syst) MeV, in agreement with lattice QCD. Complementary pPb studies are presented to investigate QGP signatures in smaller systems.

Significance. If the mapping from observed d<p_T>/dN to the thermodynamic derivative holds, the result supplies a valuable experimental anchor for the equation of state of hot QCD matter near 200 MeV, complementing lattice calculations. The ultra-central selection is a reasonable attempt to reduce geometric uncertainties, and the quoted agreement with lattice QCD is a positive consistency check, though it does not independently validate the extraction assumptions.

major comments (2)
  1. [Results section (central extraction)] The precise functional form relating the multiplicity dependence of <p_T> to c_s² (e.g., via c_s² = dp/dε or a hydrodynamic approximation) is not specified. Without this relation and the temperature extraction procedure, the numerical value 0.241 cannot be independently verified from the reported slope.
  2. [Centrality selection and fluctuation analysis] In the 0–1% ultra-central class, multiplicity variations arise predominantly from initial-state participant-number and color-charge fluctuations (Glauber/CGC). The manuscript must demonstrate that the <p_T> response follows the equilibrium thermodynamic volume change assumed in the derivation rather than initial-state dynamics; otherwise the extracted c_s² is biased. Lattice agreement alone does not test this mapping.
minor comments (2)
  1. [Abstract] The abstract quotes T_eff with only a systematic uncertainty; state whether a statistical uncertainty was evaluated and found negligible.
  2. [Experimental setup] Clarify the exact centrality definition and event selection criteria used for the ultra-central sample to allow reproduction.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive review of our manuscript. We address each major comment below and indicate the revisions we will make to improve clarity and address the concerns raised.

read point-by-point responses

  1. Referee: The precise functional form relating the multiplicity dependence of <p_T> to c_s² (e.g., via c_s² = dp/dε or a hydrodynamic approximation) is not specified. Without this relation and the temperature extraction procedure, the numerical value 0.241 cannot be independently verified from the reported slope.

    Authors: We agree that the explicit functional form and temperature extraction details should be provided for reproducibility. The extraction uses the thermodynamic relation c_s² = dp/dε applied to the observed slope of <p_T> versus multiplicity in the ultra-central regime, combined with a hydrodynamic approximation for the system response. The effective temperature is determined from the <p_T> spectra in the selected events. In the revised manuscript we will add a dedicated paragraph in the Results section stating the precise relation and the full temperature extraction procedure, allowing independent verification of the quoted value. revision: yes

  2. Referee: In the 0–1% ultra-central class, multiplicity variations arise predominantly from initial-state participant-number and color-charge fluctuations (Glauber/CGC). The manuscript must demonstrate that the <p_T> response follows the equilibrium thermodynamic volume change assumed in the derivation rather than initial-state dynamics; otherwise the extracted c_s² is biased. Lattice agreement alone does not test this mapping.

    Authors: This is a substantive point concerning the interpretation of multiplicity variations. Our ultra-central selection is intended to minimize geometric fluctuations, with the remaining multiplicity spread used to probe the thermodynamic response. We will expand the discussion to include a quantitative comparison with Glauber and CGC model predictions for initial-state fluctuations and show that the observed <p_T> trend is inconsistent with a purely initial-state origin. While lattice-QCD agreement remains a valuable consistency check, we will explicitly note that it does not constitute an independent validation of the thermodynamic mapping and will highlight the underlying assumptions more clearly. revision: partial

Circularity Check

0 steps flagged

No circularity: experimental extraction compared to independent lattice QCD

full rationale

The paper reports an experimental measurement of c_s² extracted from the multiplicity dependence of mean transverse momentum in ultra-central PbPb collisions at 5.02 TeV, using a hydrodynamic/thermodynamic relation to map the observed slope to the speed of sound at an effective temperature. This value is then compared to external lattice-QCD calculations. No load-bearing step reduces by construction to a fitted parameter, self-definition, or self-citation chain; the central result is presented as data-driven and tested against an independent theoretical benchmark. The mapping assumption itself is an interpretive step but does not create circularity within the derivation.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review provides no explicit list of free parameters, background assumptions, or invented entities; the extraction implicitly assumes a relation between observed mean-pT multiplicity slope and thermodynamic speed of sound that is not detailed here.

pith-pipeline@v0.9.0 · 5668 in / 1179 out tokens · 38423 ms · 2026-05-21T01:43:09.963879+00:00 · methodology

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