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Thermodynamics of charmed hadrons across chiral crossover from lattice QCD

T0 review · 4 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read Lattice QCD charm fluctuations show charmed baryon partial pressure is about twice the PDG hadron gas value at the chiral crossover, with mesons about 20% larger, and that charmed hadrons melt sequentially.

desk verdict Solid sub-Tpc analysis of charmed partial pressures, but the headline enhancement factors rest on an unpublished continuum extrapolation that makes the absolute numbers uncheckable from this preprint. read the letter →

arxiv 2501.01300 v2 pith:IVVIWXBU submitted 2025-01-02 hep-lat hep-exhep-phhep-th

Sipaz Sharma , Frithjof Karsch , Peter Petreczky This is my paper · ORCID
classification hep-lathep-exhep-phhep-th
keywords latticeQCDcharmfluctuationsgeneralizedsusceptibilitiescharmedhadronshadronresonancegaschiralcrossoverquark-gluonplasmamissingresonances
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper uses lattice QCD calculations of charm fluctuations and their correlations with baryon number, electric charge, and strangeness to isolate partial pressures from charmed mesons, charmed baryons, and charm quark-like excitations. It seeks to establish that experimentally unobserved charmed hadrons predicted by quark models—mostly baryons—contribute substantially to the charm pressure at and below the chiral crossover, and that open-charm hadrons dissolve sequentially rather than all at once. The paper finds that at the crossover temperature $T_{pc}=(156.5\pm 1.5)$ MeV the lattice charmed baryon partial pressure is about 1.95 times the value expected from the experimentally known PDG spectrum, while the charmed meson partial pressure is about 1.22 times larger. Above $T_{pc}$ a charm quark-like contribution emerges and grows, while low-lying $1S$ and $1P$ charmed hadron states persist until roughly 166 MeV, supporting a picture of sequential melting.

What carries the argument

The machinery is the set of generalized charm susceptibilities $\chi^{BQSC}_{klmn}$, which are derivatives of the QCD pressure with respect to baryon, electric-charge, strangeness, and charm chemical potentials, computed with the Highly Improved Staggered Quark (HISQ) action on $N_\tau=8$ lattices. Ratios of these susceptibilities, whose cutoff effects largely cancel, are multiplied by a continuum-extrapolated $\chi^C_4$ to obtain absolute partial pressures. These are combined with a quasi-particle decomposition $P^C = P^C_M + P^C_B + P^C_q$, where the partial pressures are linear combinations of $\chi^C_4$, $\chi^{BC}_{13}$, and $\chi^{BC}_{22}$, and compared with Boltzmann hadron resonance gas formulas using either the PDG spectrum (PDG-HRG) or quark-model augmented spectra (QM-HRG and 1S1P-HRG).

What would settle it

A direct continuum extrapolation of the partial pressures themselves—computing $P_C^B$ and $P_C^M$ at several lattice spacings such as $N_\tau=6$, 8, 10, and 12 and taking the continuum limit, rather than using $N_\tau=8$ ratios multiplied by a continuum-extrapolated $\chi^C_4$—would settle whether the ~1.95 baryon and ~1.22 meson enhancement factors at $T_{pc}$ are real or cutoff artifacts.

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Extended reading notes

Core claim

The central claim is that continuum-extrapolated lattice QCD results for the partial charm pressure can be decomposed, through generalized susceptibilities, into charmed-meson, charmed-baryon, and charm quark-like contributions. Below and at the chiral crossover this decomposition shows that the baryonic sector is almost twice as large as the PDG hadron spectrum alone predicts, while the mesonic sector is about 20% larger, with both matching quark-model augmented hadron resonance gas predictions. At the crossover the hadron resonance gas description breaks down, signaling the onset of charm deconfinement, yet the low-lying $1S$ and $1P$ charmed hadron states survive to about 166 MeV, indicating sequential melting. The emerging quark-like partial pressure is used to extract a temperature-dependent in-medium charm quark mass that starts near the $D$-meson mass and decreases with temperature.

Load-bearing premise

The central numbers stand on the assumption that the $N_\tau=8$ lattice ratios are effectively continuum and that the unpublished continuum extrapolation of $\chi^C_4$ is accurate; if either fails, the enhancement factors and all trends above $T_{pc}$ shift.

Editorial extensions

If this is right

  • The charmed baryon sector of the PDG hadron list is incomplete at the level of roughly a factor of two in partial pressure at $T_{pc}$, so quark-model predicted charmed baryons, not mesons, are the dominant missing contribution.
  • Open-charm hadrons begin to dissolve at the chiral crossover, but the dissociation is sequential: low-lying $1S$ and $1P$ charmed states survive to about 166 MeV while higher excitations melt first.
  • A charm quark-like contribution to the partial pressure appears at $T_{pc}$ and grows, overtaking hadron-like contributions near $T\sim 175$ MeV, so charmed hadron-like excitations can persist well into the quark-gluon plasma regime.
  • The temperature-dependent in-medium mass of the charm quark-like excitation, starting near the $D$-meson mass around 162 MeV and decreasing with temperature, gives a quantitative handle on charm in-medium interactions in the quark-gluon plasma.
  • Charmed hadron masses are not strongly affected by chiral symmetry restoration at $T_{pc}$, since the $1S1P$-HRG prediction does not overshoot the lattice meson pressure above the crossover.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Extending the same decomposition to higher temperatures would predict that above roughly two times $T_{pc}$ the charm partial pressure becomes dominated by quark-like excitations and hadron-like contributions vanish, which can be tested once continuum-extrapolated susceptibilities become available at those temperatures.
  • If the missing charmed baryons are thermodynamically real, heavy-ion yields of charmed baryons should show a corresponding enhancement across collision energies; a direct comparison of these lattice partial pressures with measured $D$-meson and charmed-baryon yields would test this connection.
  • The near-equality of the baryonic enhancement factor (1.95) with the QM-HRG prediction suggests the quark-model spectrum is nearly complete thermodynamically at $T_{pc}$; future data at smaller lattice spacings that reproduce the same ratio would harden the missing-resonance interpretation into a quantitative prediction for spectroscopy.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 4 minor

Summary. The manuscript analyzes (2+1)-flavor HISQ lattice data for generalized charm susceptibilities chi_13^BC, chi_22^BC, and chi_4^C, using N_tau=8 configurations whose ratios are normalized by continuum-extrapolated chi_4^C values. The continuum extrapolation of chi_4^C is deferred to a separate publication. From these inputs, the authors construct partial pressures of charmed baryons, mesons, and quark-like excitations via Eqs. (6)-(8), and compare the hadronic partial pressures with HRG predictions based on PDG-only and quark-model (QM) spectra, as well as a truncated 1S+1P spectrum. The central quantitative findings are enhancement factors E_B=1.948+/-0.234 and E_M=1.215+/-0.098 at T_pc, evidence that the charmed baryonic sector is substantially more incomplete than the mesonic sector, and a quark-like partial pressure that emerges at T_pc and yields a temperature-dependent in-medium charm quark mass. The paper also argues for sequential melting, with 1S/1P states surviving to about 166 MeV.

Significance. If the result holds, this is the first lattice-QCD-based quantitative determination of partial charm pressures across the chiral crossover, offering direct support for the existence of experimentally unobserved charmed hadrons predicted by quark-model calculations and by the SHMc analysis. A particular strength is that the QM-HRG and PDG-HRG comparisons use external hadron spectra rather than fits to the lattice data, so the missing-resonance enhancement is not circular. The paper also makes a falsifiable prediction that 1S/1P states persist up to about 166 MeV, and it uses publicly available lattice and analysis codes. The main caveats are that the absolute normalization relies on an unpublished continuum extrapolation and the high-temperature decomposition is model-dependent; both need to be assessed before the quantitative claims can be considered established.

major comments (4)
  1. [Sec. 2 / Fig. 2] The absolute partial pressures are constructed as (chi_13^BC/chi_4^C)_{N_tau=8} and (1 - chi_13^BC/chi_4^C)_{N_tau=8} multiplied by continuum chi_4^C, but the continuum extrapolation is not shown; the text explicitly defers it to 'a forthcoming publication.' Since the PDG-HRG and QM-HRG partial pressures in the denominator are absolute, any error in chi_4^C(cont) propagates linearly into the enhancement factors: for example, a 20% uncertainty would shift E_B from 1.948 to roughly 1.56 or 2.34 and E_M from 1.215 to roughly 0.97 or 1.46, the latter wiping out the claimed meson enhancement. The manuscript needs to present the extrapolation or cite a publicly available result, and to quote a systematic error for the absolute normalization.
  2. [Sec. 2 (cutoff-effect claim)] The statement that lattice cutoff effects 'cancel to a large extent' in the ratios is asserted and referenced to Bazavov et al. (2024), but no comparison at another lattice spacing (e.g., N_tau=10 or 12) is shown in this manuscript for chi_13^BC/chi_4^C or the related ratios. Because these ratios are the only lattice input to Fig. 2, the claimed cancellation should be demonstrated in the manuscript or accompanied by an explicit estimate of the residual lattice-spacing uncertainty.
  3. [Sec. 5, Eqs. (5)-(8)] The decomposition of the total charm pressure into quark-like, baryon-like, and meson-like partial pressures assumes a specific quasi-particle model inherited from Mukherjee et al. (2016), where each sector has the Boltzmann-form chemical-potential dependence of Eqs. (3)-(4). The resulting P_C^q and m_C^q are not direct lattice observables; they depend on this model and on the assumption that the three sectors jointly saturate the lattice susceptibilities. The text states that prior work passed 'numerous validity tests,' but for the high-temperature claims made here, please provide at least one direct test showing that the model simultaneously describes the three susceptibilities entering Eqs. (6)-(8), or state explicitly which lattice observables the model is not able to reproduce.
  4. [Sec. 4, Fig. 2 (1S1P-HRG comparison)] The claim that for T_pc < T <= 166.1 MeV both P_C^B and P_C^M are described by 1S1P-HRG is based on visual inspection; no quantitative goodness-of-fit or residual analysis is presented. Given that this comparison is the central evidence for sequential melting, please add a statistical measure (e.g., chi^2/dof over the relevant temperature window) or pointwise pulls for both panels. The same visual-only reasoning is used for the statement that PDG-HRG describes P_C^B at the highest two temperatures.
minor comments (4)
  1. [Abstract / Introduction] There are several typographical issues, including 'demonstratethatatthechiralcrossover' with missing spaces and 'rather then' for 'rather than'; these should be corrected.
  2. [Fig. 2 caption] The label 'Lattice[b]' is not defined in the caption; it refers to LCP[b] from Sec. 2, but a reader looking only at the figure cannot tell how it differs from LCP[a].
  3. [Sec. 3.2 vs. Sec. 5] The quantity m_C^q is first called the pole mass of the charm quark in the text below Eq. (4), but later it is reinterpreted as a temperature-dependent in-medium quasi-particle mass. Please use consistent terminology and clarify whether Eq. (4) is intended to define a quasi-particle from the outset.
  4. [References] The Borsanyi et al. reference is incomplete: the entry gives 'QCD Crossover at Finite Chemical Potential from Lattice Simulations 125, 052001' without a journal name or year. Please check that all references have complete bibliographic information.

Circularity Check

1 steps flagged · score 4.0 of 10

Low-temperature enhancement factors are independent external comparisons, but the above-Tpc quark-like pressure and in-medium charm mass rest on a quasi-particle ansatz validated only by self-citation; absolute partial pressures also depend on an unpublished continuum extrapolation.

  1. self citation load bearing [Section 4, Eq. (5); Section 5]
    "To investigate the nature of charm degrees of freedom above Tpc, we extend the simple hadron gas model allowing the presence of partial charm quark pressure based on Ref. Mukherjee, Petreczky and Sharma (2016), P_C(T, mu) = P_C^M + P_C^B + P_C^q. In our recent works Bazavov et al. (2024); Sharma (2024a,b), we show that this model successfully passes numerous validity tests and satisfies various constraints Bazavov et al. (2024)."

    The above-Tpc decomposition into meson, baryon, and quark partial pressures is an ansatz imported from the authors' own prior work. Equations (6)-(8) define P_q^C, P_B^C, and P_M^C algebraically in terms of generalized susceptibilities, so the emergence of a nonzero quark-like pressure at Tpc, the sequential-melting interpretation, and the in-medium mass m_q^C extracted from Eq. (4) are statements about that self-defined model. The only stated validation is the authors' own Bazavov et al. (2024) and Sharma (2024a,b), with no validity tests reproduced in this manuscript. Thus the high-temperature claims reduce to a self-citation chain rather than to an independent lattice-QCD derivation.

full rationale

The paper's low-temperature headline—P_C^B from lattice is roughly 1.95 times the PDG-HRG expectation and P_C^M roughly 1.22 times—is not circular. The PDG-HRG and QM-HRG spectra are external inputs; the lattice partial pressures are built from generalized susceptibilities, and no parameter of those spectra is fitted to the lattice data. The enhancement factors in Fig. 2 are genuine comparisons, not fits. Likewise, using Eq. (4) to convert the quark-like partial pressure into an in-medium mass is an inversion or reparametrization, not a prediction, so it does not by itself constitute circularity. The circularity concern is confined to the above-Tpc interpretation. Eq. (5) is introduced as an extension based on the authors' own Mukherjee-Petreczky-Sharma 2016 model, and its validity is asserted by citing their own Bazavov et al. 2024 work; the validity tests are not reproduced here. Equations (6)-(8) then define P_q^C, P_B^C, and P_M^C, so claims such as 'charm quark-like excitation emerges at Tpc' and the sequential-melting pattern are statements about that self-cited ansatz. This is load-bearing self-citation, but the central low-T enhancement result has independent external content, so the appropriate score is 4 rather than 6 or higher. The additional checkability issue—absolute pressures rest on Ntau=8 ratios from a previous paper and a continuum extrapolation deferred to a forthcoming publication—is a verification gap, not a circular reduction.

Assumptions & free parameters 1 free parameters · 6 assumptions · 1 invented entities

The central sub-Tpc comparison introduces no free fit parameters: the charmed hadron spectra are external inputs from PDG and quark-model calculations. The extracted in-medium quark mass is a re-parameterization of the modeled pressure rather than a prediction. The main assumptions are the Boltzmann approximation, the validity of HRG, the accuracy of the continuum normalization, and the three-sector quasi-particle decomposition.

free parameters (1)
  • Temperature-dependent in-medium charm quasi-particle mass m_C^q(T) = Approximately 1.7 to 1.9 GeV, decreasing with temperature (Fig. 3 Right)
    Obtained by inverting Eq. (4) against the quasi-particle pressure P_q at each temperature. It is a re-parameterization of the modeled pressure rather than an independently predicted quantity.
assumptions (6)
  • standard math Grand canonical partition function derivatives define the generalized susceptibilities used throughout.
    Eq. (2) is the standard lattice QCD definition of conserved charge susceptibilities.
  • domain assumption The Boltzmann approximation is accurate for charmed hadrons and charm quarks at temperatures near Tpc.
    Sec. 3 assumes charmed states are heavy enough that K2(m/T) with exponential suppression describes their partial pressures.
  • domain assumption Charm quarks treated in the quenched approximation on HISQ configurations, with Ntau=8 ratios nearly continuum, give reliable charm susceptibilities.
    Sec. 2 relies on cancellation of cutoff effects in ratios and on continuum-extrapolated chi4^C values not shown in the paper.
  • domain assumption The hadron resonance gas is a valid non-interacting description of charm degrees of freedom below and at the chiral crossover.
    Used in Secs. 3 and 4 to compare lattice partial pressures to PDG-HRG and QM-HRG.
  • domain assumption The charm pressure decomposes into exactly meson-like, baryon-like, and quark-like sectors with fixed quantum number assignments.
    Eqs. (5)-(8) assume B=1/3, Q=2/3 for the quark-like sector and integer charges for hadron-like sectors; this model comes from Mukherjee et al. (2016) and is not derived here.
  • domain assumption The quark-model charmed hadron spectrum of Ebert et al. and Chen et al. reliably represents the missing experimentally unobserved states.
    QM-HRG predictions in Figs. 1 and 2 use that spectrum as an external input, and the interpretation of enhancement depends on its accuracy.
invented entities (1)
  • Charm quark-like excitation in the quark-gluon plasma
    purpose: Accounts for the difference between chi_13^BC and chi_22^BC and yields a temperature-dependent in-medium mass through Eq. (4)
    This quasi-particle degree of freedom is extracted through the assumed decomposition in Eqs. (5)-(8) from the same susceptibility data. No independent observable outside the model is provided, and the temperature-dependent mass is inferred from the same pressure it is meant to explain.

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Cite this review

Pith. "Pith review of Thermodynamics of charmed hadrons across chiral crossover from lattice QCD." pith.science (2026). https://pith.science/paper/IVVIWXBU

@misc{pith2026250101300,
  author       = {Pith},
  title        = {Pith review of: Thermodynamics of charmed hadrons across chiral crossover from lattice QCD},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IVVIWXBU}},
  note         = {Machine review of arXiv:2501.01300}
}
abstract

We use up to fourth-order charm fluctuations and their correlations with net baryon number, electric charge, and strangeness fluctuations, calculated within the framework of lattice QCD, to study the continuum partial pressure contributions of charmed baryons and mesons. We show that, at and below the chiral crossover temperature, these partial pressures receive enhanced contributions from experimentally unobserved charmed hadrons predicted by the Quark Model. Additionally, we demonstrate that at the chiral crossover, the Hadron Resonance Gas description breaks down, signaling the modification of open charm hadrons and thereby implying the onset of charm deconfinement. We present evidence for the survival of low-lying non-radial $1S$ and $1P$ hadron-like excitations above the chiral crossover, which hints at the sequential melting of charmed hadrons. Finally, we investigate the continuum partial pressure contribution of charm quark-like excitation that emerges at the chiral crossover and calculate its temperature-dependent in-medium mass.

Figures

Figures reproduced from arXiv: 2501.01300 by the authors.

Figure 1
Figure 1. Comparison of QM-HRG and PDG-HRG predictions for charmed baryons [Left] and charmed mesons [Right]. Δ = 100|1 − QM-HRG∕PDG-HRG|𝑇𝑝𝑐 . The yellow bands represent 𝑇𝑝𝑐 with its uncertainty. mesonic sector. In recent years, the experimental discovery of various Λ𝐶 and Ω𝐶 resonances, in particular by LHCb and Belle collaborations Kato et al. (2016); Aaij et al. (2017a,b); Chen and Liu (2017) have confirmed this. 3.2. Char… view at source ↗
Figure 2
Figure 2. Shown are partial charmed baryon pressure [Left] and partial charmed meson pressure [Right] along with the respective QM-HRG, PDG-HRG and 1S1P-HRG (see text) predictions. The yellow bands represent 𝑇𝑝𝑐 with its uncertainty. 155 160 165 170 175 T [MeV] 0.0000 0.0002 0.0004 0.0006 0.0008 0.0010 P C q 155 160 165 170 175 T [MeV] 1.675 1.700 1.725 1.750 1.775 1.800 1.825 1.850 1.875 mC q [GeV] [PITH_FULL_IMAGE:figures/… view at source ↗
Figure 3
Figure 3. Shown is the partial pressure contribution of charm quark-like excitation above 𝑇𝑝𝑐 [Left] and the temperature dependent in-medium mass of a charm quark-like excitation above 𝑇𝑝𝑐 [Right]. The yellow bands represent 𝑇𝑝𝑐 with its uncertainty. 175 MeV, the relative partial pressure contributions from hadron and quark-like excitations cross. Based on this trend, it is expected that above 𝑇 ∼ 175 MeV, 𝑃 𝐶 𝑞 will become t… view at source ↗

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