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Hadrons persist in hot QCD matter up to 250 MeV

2026-07-09 19:03 UTC pith:B5Y7PD2K

load-bearing objection Three-parameter EoS fits lattice QCD well, but the headline claim about hadronic persistence to ~250 MeV is model-dependent on an ad hoc switching function the 2 major comments →

arxiv 2607.07140 v1 pith:B5Y7PD2K submitted 2026-07-08 nucl-th hep-ph

Hadronic and partonic composition of QCD matter across the crossover

Artemiy Lysenko , Mark I. Gorenstein , Marek Gazdzicki , Roman Poberezhniuk , Volodymyr Vovchenko This is my paper
classification nucl-th hep-ph PACS 12.38.Mh12.38.Gc25.75.Nq
keywords temperaturehadronicpartoniccrossoverchiralinteractionlatticematter
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper constructs a three-parameter equation of state that interpolates between a hadron resonance gas (with van der Waals interactions among baryons and excluded-volume repulsion among mesons) at low temperatures and an ideal quark-gluon gas corrected by a phenomenological interaction term at high temperatures. The two regimes are joined by a smooth switching function. Fitting the three free parameters to lattice QCD data for the trace anomaly, the authors reproduce lattice results for pressure, entropy density, energy density, and speed of sound from 100 to 500 MeV. The fit yields a meson hard-core radius of about 0.2 fm, a QGP interaction scale of about 600 MeV, and a switching temperature of about 216 MeV. This switching temperature far exceeds the widely cited chiral pseudocritical temperature of 155 MeV, leading the authors to conclude that hadronic degrees of freedom remain a substantial component of strongly interacting matter up to roughly 250 MeV, well above the conventional crossover point. The paper thus argues that the transition from hadronic to partonic matter is far more gradual than the chiral transition temperature alone suggests.

Core claim

The central finding is quantitative: when a hadron gas with meson excluded-volume repulsion is smoothly matched to a quark-gluon gas with a phenomenological interaction term, the temperature at which the partonic component takes over is not the chiral pseudocritical temperature of 155 MeV but rather about 216 MeV, with hadronic matter still contributing roughly 43% of the pressure at 250 MeV. This means the conventional identification of the chiral crossover temperature with the hadron-to-quark transition temperature is misleading for thermodynamic purposes.

What carries the argument

The mechanism carrying the argument is the switching function K(T) = exp[-(T0/T)^4], which smoothly weights the QGP and hadronic pressures. Its temperature derivative generates crossing terms in the entropy density, but these remain below 10% of the total, so the thermodynamics is dominated by the two physical components rather than by the interpolation artifact. The three fitted parameters (meson radius, QGP interaction strength, switching temperature) are overdetermined by the requirement of simultaneously reproducing pressure, trace anomaly, entropy density, energy density, and speed of sound.

Load-bearing premise

The switching function K(T) = exp[-(T0/T)^4] is an ad hoc interpolation formula. A different smooth crossover function could fit the same lattice data equally well while yielding a different switching temperature and a different hadronic weight at a given temperature. The extracted value of T0 = 216 MeV is therefore conditional on this specific functional choice.

What would settle it

If an alternative, equally smooth switching function fitted to the same lattice trace anomaly data produced a switching temperature near 155 MeV with negligible hadronic weight above 200 MeV, the central claim that hadrons persist to 250 MeV would be an artifact of the chosen interpolation rather than a physical result.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • If hadronic degrees of freedom persist to 250 MeV, then thermal photon and dilepton emission from the crossover region may receive substantial hadronic contributions that current QGP-only calculations miss.
  • The meson hard-core radius of 0.2 fm, being negligible below 160 MeV, should not affect chemical freeze-out fits to hadron yields, preserving the consistency of existing thermal-model analyses.
  • The phenomenological interaction parameter A ~ 600 MeV, being of order the QCD scale, supports the picture that nonperturbative confining correlations survive in the QGP well above the crossover, connecting to proposals about chirally symmetric but still confined matter.
  • The result motivates using conserved-charge susceptibilities as an additional constraint, since at finite chemical potential the switching function and QGP interaction term will contribute to baryon-number fluctuations that the current zero-chemical-potential fit cannot constrain.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 5 minor

Summary. This manuscript constructs a phenomenological equation of state (EoS) for QCD matter at zero chemical potentials by interpolating between a quantum van der Waals hadron resonance gas (with meson excluded-volume repulsion) and an ideal quark-gluon gas supplemented by a $-AT^3$ interaction term. The interpolation uses a switching function $K(T) = e^{-(T_0/T)^k}$. Three parameters ($r_M$, $A$, $T_0$) are fitted to the Wuppertal-Budapest lattice QCD trace anomaly, yielding $r_M{=}0.2$ fm, $A{=}600$ MeV, and $T_0{=}216$ MeV. The EoS reproduces lattice data for pressure, entropy density, energy density, and speed of sound over $T=100$–$500$ MeV. The central physical claim is that $T_0$ substantially exceeds the chiral pseudocritical temperature $T_{pc}{=}155$ MeV, implying hadronic degrees of freedom persist up to $T{=}250$ MeV.

Significance. The paper provides a simple, thermodynamically consistent EoS that accurately reproduces lattice QCD thermodynamics across a broad temperature range with only three fitted parameters. The observation that the trace anomaly peak can be reproduced by hadronic interactions alone (Fig. 1b) is a useful and non-trivial point. The finding that $T_0$ exceeds $T_{pc}$ aligns with emerging theoretical pictures (chiralspin symmetry, quarkyonic matter) in which hadronic correlations survive well above the chiral crossover. The model is falsifiable: alternative switching functions or statistical-mixture approaches could yield different $T_0$ values, and the authors acknowledge this. The code base (Thermal-FIST) is publicly available, supporting reproducibility.

major comments (2)
  1. §IV, Eq. (13) and surrounding discussion: The headline claim that hadronic degrees of freedom persist to $T{=}250$ MeV rests on interpreting $1{-}K(T)$ as the physical hadronic fraction, where $K(T){=}e^{-(T_0/T)^4}$ is an ad hoc interpolation formula. The paper itself acknowledges the choice of switching function is an open question. Since the three parameters are fitted to the trace anomaly and the crossing terms in entropy are $<10$% of the total, a different smooth functional form (e.g., Fermi function, tanh, or the statistical-mixture approach of Ref. [40]) could redistribute weight between HRG and QGP components while fitting the same lattice data comparably well, potentially shifting $T_0$ and the hadronic fraction at 250 MeV. The paper should either (a) demonstrate robustness of $T_0$ by refitting with at least one alternative switching function, or (b) more prominently qualify $
  2. §IV, Fig. 1(b) and discussion of $r_M$: The trace anomaly peak near $T{=}200$ MeV is already reproduced by the HRG alone for $r_M{=}0.14$ fm, yet the fit yields $r_M{=}0.2$ fm. This suggests partial degeneracy between $r_M$, $A$, and $T_0$: the QGP component and switching function absorb the difference between the HRG-only peak and the lattice data. The paper should discuss this degeneracy explicitly and explain what drives the fit toward $r_M{=}0.2$ fm rather than $0.14$ fm. Without this, it is unclear whether $r_M$ is independently constrained or merely compensates for the QGP/switching contributions.
minor comments (5)
  1. §IV: The statement that crossing terms are 'below approximately 10% of the total entropy density' should specify the temperature range where this maximum is reached, to clarify whether the bound holds across the entire crossover region or only at specific temperatures.
  2. §IV, Eq. (14): The crossing term $dK/dT (p_Q - p_H)$ could change sign depending on the relative magnitudes of $p_Q$ and $p_H$. A brief comment on its sign and magnitude across the temperature range would help readers interpret Fig. 3(b).
  3. §III, Eq. (11): The relation $A {=} 1.8 Lambda_{MS}$ is quoted using a value from Ref. [44]. The numerical value of $Lambda_{MS}$ used should be stated explicitly to make the comparison self-contained.
  4. §II: The meson excluded-volume prescription (Eqs. 6–7) treats all meson species with a single hard-core radius. A brief comment on whether this simplification is motivated by lack of species-specific data or by a physical argument would contextualize the approach relative to multi-component excluded-volume formulations.
  5. Abstract and §V: The phrase 'hadronic states remaining an important component' could be read as a direct QCD prediction. Adding a qualifier such as 'within this model' or 'as inferred from this EoS parametrization' would prevent misinterpretation.

Circularity Check

1 steps flagged

Mild circularity: 'reproduction' of pressure, entropy, energy density, and speed of sound is a thermodynamic consequence of the trace-anomaly fit, not independent validation.

specific steps
  1. fitted input called prediction [Sec. IV, Eqs. (8), (12), (14); abstract]
    "The three model parameters—the meson hard-core radius, the strength of the partonic interaction term, and the switching temperature—are determined from a fit to lattice QCD results for the trace anomaly. The resulting equation of state reproduces the lattice data on the pressure, entropy density, energy density, and speed of sound in the temperature range T=100–500 MeV. [...] All remaining thermodynamic observables are then obtained without further adjustment."

    The trace anomaly I(T) = (ε−3p)/T⁴ = T·d(p/T⁴)/d(ln T) is the logarithmic derivative of the scaled pressure. Fitting the three model parameters to the trace anomaly determines p(T) up to the boundary condition p→0 as T→0, which the model satisfies by construction (K→0, HRG pressure vanishes). Once p(T) is fixed, Eq. (8) yields s = dp/dT, ε = T·dp/dT − p, and c²ₛ = dp/dε as mathematical identities. The 'reproduction' of these quantities is therefore a consequence of thermodynamic consistency, not an independent test of the model. The paper presents this as validation ('without further adjustment'), but the only genuinely fitted quantity is the trace anomaly; the rest follow by construction. This is mild because (a) the paper is transparent about using Eq. (8), (b) it is standard practice in

full rationale

The paper's central physical claim — T₀ ≃ 216 MeV and the persistence of hadronic degrees of freedom to ~250 MeV — is not circular: T₀ is a genuinely fitted parameter, and its interpretation, while model-dependent (the switching function form is ad hoc and the paper acknowledges this), does not reduce to its inputs by definition. The QvdW-HRG model (Ref. [20], co-authored by Vovchenko and Gorenstein) is a model choice validated against nuclear matter properties, not a self-citation invoked to prove uniqueness. The Thermal-FIST package (Ref. [25]) is a computational tool. No uniqueness theorem is invoked. The only circularity is the mild one above: fitting the trace anomaly and then 'reproducing' p, s, ε, c²ₛ, which are all derived from the same p(T) via standard thermodynamic identities. This is standard practice in EoS modeling and the paper is transparent about it, so the score remains low.

Axiom & Free-Parameter Ledger

5 free parameters · 5 axioms · 2 invented entities

The model has three genuinely free parameters fitted to data, plus two fixed from prior work and one fixed by hand. The two invented entities (r_M and A) are phenomenological parametrizations without independent microscopic derivation. The switching function is the most significant ad hoc element.

free parameters (5)
  • r_M (meson hard-core radius) = 0.2 fm
    Fitted to lattice QCD trace anomaly. Controls excluded-volume repulsion between mesons.
  • A (QGP interaction scale) = 600 MeV
    Fitted to lattice QCD trace anomaly. Controls the phenomenological −AT³ correction to the QGP pressure.
  • T_0 (switching temperature) = 216 MeV
    Fitted to lattice QCD trace anomaly. Controls the crossover point of the switching function K(T).
  • k (switching function exponent) = 4
    Fixed by hand following Ref. [15], not fitted. Controls the width of the crossover.
  • a, b (baryon van der Waals parameters) = a=329 MeV fm³, b=3.42 fm³
    Fixed from nuclear matter saturation properties (Ref. [26]), not fitted in this work.
axioms (5)
  • domain assumption Lattice QCD data from the Wuppertal-Budapest Collaboration (Ref. [13]) are correct and represent physical QCD thermodynamics at zero chemical potential.
    The entire model is fitted to this dataset. Sec. IV.
  • ad hoc to paper The switching function K(T) = exp[−(T₀/T)^k] provides a physically meaningful interpolation between hadronic and partonic phases.
    This functional form is not derived from QCD; it is a phenomenological choice. Sec. IV, Eq. 13.
  • ad hoc to paper The −AT³ correction to the QGP pressure is an adequate phenomenological parametrization of nonperturbative effects in the temperature range 100–500 MeV.
    This power law is not derived from first principles; it is chosen for simplicity and asymptotic behavior. Sec. III, Eq. 11.
  • domain assumption Van der Waals parameters fitted to nuclear matter at T=0 are universal for all baryon species at all temperatures.
    Parameters a and b from Ref. [20] are used without temperature dependence. Sec. II.
  • domain assumption The PDG2020 hadron list is complete enough for thermodynamic calculations in the considered temperature range.
    The HRG model sums over all listed hadrons and resonances. Sec. II.
invented entities (2)
  • Meson hard-core radius r_M no independent evidence
    purpose: Parametrizes short-range repulsive interactions between mesons via excluded volume.
    Treated as a phenomenological parameter; no direct experimental measurement of meson hard-core radius is cited. The fitted value is consistent with some literature estimates but is not independently constrained.
  • QGP interaction scale A no independent evidence
    purpose: Parametrizes nonperturbative interactions in the QGP via a −AT³ pressure correction.
    Phenomenological parameter with no independent derivation. The scale ~Λ_QCD is noted as qualitatively consistent but not quantitatively derived.

pith-pipeline@v1.1.0-glm · 17440 in / 3196 out tokens · 301488 ms · 2026-07-09T19:03:54.623466+00:00 · methodology

0 comments
read the original abstract

We construct a simple equation of state of strongly interacting matter at zero chemical potentials that provides a unified description of lattice QCD thermodynamics in terms of hadronic and partonic degrees of freedom. The hadronic phase is described by the quantum van der Waals hadron resonance gas, extended by excluded-volume repulsion between mesons, while the quark-gluon plasma is modeled as an ideal gas of quarks and gluons supplemented with a phenomenological interaction term proportional to $T^3$. The two regimes are connected by a smooth crossover switching function. The three model parameters - the meson hard-core radius, the strength of the partonic interaction term, and the switching temperature - are determined from a fit to lattice QCD results for the trace anomaly. The resulting equation of state reproduces the lattice data on the pressure, entropy density, energy density, and speed of sound in the temperature range $T=100$-$500$ MeV. The fit yields a meson hard-core radius $r_M \simeq 0.2$ fm, a partonic interaction scale $A \simeq 600$ MeV, and a switching temperature $T_0 \simeq 216$ MeV, substantially exceeding both the pseudocritical temperature of the QCD chiral crossover and the chemical freeze-out temperature. This finding suggests that the transition from hadronic to partonic degrees of freedom is considerably more gradual than indicated by the chiral pseudocritical temperature alone, with hadronic states remaining an important component of strongly interacting matter up to temperatures of about 250 MeV, well above the QCD chiral crossover.

Figures

Figures reproduced from arXiv: 2607.07140 by Artemiy Lysenko, Marek Gazdzicki, Mark I. Gorenstein, Roman Poberezhniuk, Volodymyr Vovchenko.

Figure 1
Figure 1. Figure 1: Temperature dependence of (a) the scaled pressure [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Temperature dependence of (a) the scaled pressure [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Temperature dependence of (a) the switching function [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Temperature dependence of (a) the scaled pressure [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Temperature dependence of (a) the entropy density [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗

discussion (0)

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