Thermal lattice QCD results from the FASTSUM collaboration

Antonio Smecca; Benjamin J\"ager; Benjamin Page; Chris Allton; Gert Aarts; Jon-Ivar Skullerud; Maria Paola Lombardo; M. Naeem Anwar; Ryan Bignell; Sergio Chaves Garc\'ia-Mascaraque

REVIEW 3 major objections 4 minor 16 references

Thermal lattice QCD results from the FASTSUM collaboration

T0 review · 3 major / 4 minor · reviewed 2026-08-12 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Thermal lattice QCD shows open charm meson masses shifting with temperature, charmed baryon parity partners degenerating above the transition, and bottomonium string tension weakening as the medium heats.

desk verdict A solid proceedings summary of FASTSUM's published thermal hadron results, but the only new piece—the NRQCD bottomonium potential—is too under-described to support its 'clear' string-tension claim. read the letter →

arxiv 2411.15937 v1 pith:QTYPUHSE submitted 2024-11-24 hep-lat

Chris Allton , Gert Aarts , M. Naeem Anwar , Ryan Bignell , Timothy J. Burns , Sergio Chaves García-Mascaraque , Simon Hands , Benjamin Jäger

show 7 more authors

Seyong Kim Maria Paola Lombardo Benjamin Page Sínead Ryan Jon-Ivar Skullerud Antonio Smecca Thomas Spriggs

This is my paper · ORCID

classification hep-lat PACS 11.15.Ha12.38.Gc12.38.Mh

keywords thermallatticeQCDopencharmmesonscharmedbaryonsparitydoublingbottomoniuminterquarkpotentialNRQCDanisotropiclatticesstringtension

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

The paper reviews lattice QCD computations on 2+1 flavour anisotropic lattices that ask whether hadron properties change as the quark–gluon medium heats, and answers yes in three channels. Open charm mesons show a ground-state mass that departs from its low-temperature value for $127\ \mathrm{MeV} \le T \le 190\ \mathrm{MeV}$, below the transition temperature. Charmed baryons show parity partners becoming approximately degenerate above the transition, and the bottomonium interquark potential shows a string tension that weakens with temperature. The shared technical ingredient is the anisotropic lattice, whose much finer temporal spacing makes these thermal effects resolvable in temporal correlation functions. If the results hold, temperature-dependent hadron masses and potentials must enter descriptions of heavy-ion collisions and the early universe.

What carries the argument

The central objects are temporal correlation functions on anisotropic lattices, together with two comparison devices. The first is the model correlator $G_{\mathrm{model}}(\tau; T, T_0)$, a single-ground-state $\cosh$ form with a reference mass $M(T_0)$, and the double ratio $R_{\mathrm{double}}(\tau; T, T_0) = [G(\tau;T)/G_{\mathrm{model}}(\tau;T,T_0)]/[G(\tau;T_0)/G_{\mathrm{model}}(\tau;T_0,T_0)]$, which cancels part of the excited-state contamination and isolates thermal mass variation. The second is the reconstructed correlator $G_{\mathrm{rec}}$, built by combining the spectral function at a reference temperature with fermionic kernels at other temperatures; its ratio to the actual correlator separates physics changes from geometry changes, and it feeds the baryon parity-doubling ratio $R$. The bottomonium potential comes from the hal-qcd method, which reverse-engineers the potential in the Schrödinger equation from Bethe–Salpeter wavefunctions obtained with non-local mesonic operators.

What would settle it

Repeat the double-ratio measurement on an ensemble with a smaller lattice spacing at the same physical temperatures; if $R_{\mathrm{double}}$ returns to unity within errors across $127\ \mathrm{MeV} \le T \le 190\ \mathrm{MeV}$, the claimed open-charm mass shift is a discretization artifact, not a thermal effect.

Watch

Extended reading notes

Core claim

For each channel the paper establishes a thermal modification by comparing finite-temperature lattice data with a reference built from data at the lowest temperature studied. For open charm mesons, the double ratio $R_{\mathrm{double}}$ deviates from unity for $127\ \mathrm{MeV} \le T \le 190\ \mathrm{MeV}$, which the authors interpret as a genuine shift of the ground-state mass with temperature; the fits are confined to $T \lesssim T_{pc}$ because the single-ground-state $\cosh$ model is trusted only there. For charmed baryons, an integrated ratio of positive- and negative-parity correlation functions falls toward zero as $T$ rises and reaches the degenerate limit above the transition, with inflection points that agree with $T_{pc}$ from the chiral condensate. For bottomonium, a preliminary NRQCD interquark potential extracted by reversing the Schrödinger equation shows the string tension decreasing as temperature increases.

Load-bearing premise

The analysis assumes that each meson correlation function is dominated by its ground state with a simple $\cosh$ form, so the model $G_{\mathrm{model}}$ can stand in for the full correlation function; if excited states contaminate the channel below $T_{pc}$, the extracted mass shifts could be artifacts rather than thermal changes in the ground state.

Editorial extensions

If this is right

Heavy-ion phenomenology that assumes vacuum charm meson masses must incorporate temperature-dependent masses across the hadronic phase.
The baryon parity-doubling ratio provides a spectral, baryonic marker of the transition whose inflection points match the chiral condensate estimate of $T_{pc}$.
A temperature-dependent string tension implies that the confining interaction in bottomonium weakens before deconfinement, informing models of quarkonium dissociation.
The paper's mass-shift claim is deliberately limited to $T \lesssim T_{pc}$; above the transition the single-state model is not trusted, so the hadronic-phase result does not extrapolate automatically.

Reading between the lines

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

A sharper test of the open-charm mass shift would be to reanalyse the same correlators with a spectral function that includes excited states and a thermal width; if the shift persists, it is a genuine ground-state movement, and if not, it is an excited-state artifact.
The parity-doubling inflection could be developed into a quark-mass-independent transition thermometer, since the singly-charmed channels already give transition temperatures consistent with the chiral condensate.
One testable extension of the bottomonium result is to check whether the inverse screening length extracted from the potential follows the same temperature dependence as the static heavy-quark free energy.
Because all three signals come from a single set of ensembles, reproducing the double ratios on configurations with different anisotropy or spatial spacing would directly test whether the effects are thermal rather than lattice artifacts.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Quick take: this is a conference proceedings, and it does exactly what a proceedings should: it reviews the FASTSUM thermal hadron spectrum programme and points to the original papers. The open charm and charm baryon sections are summaries of peer-reviewed work [1,2,3-5], and they are honest about their limits. The one genuinely new item is the preliminary bottomonium potential from NRQCD and the hal-qcd 'linear regression' inversion. That section needs to be treated with caution.

What's good: The double-ratio analysis for open charm mesons is presented cleanly, with the reference temperature defined and the T<=T_pc restriction stated explicitly. The reconstructed-correlator method for baryons and the parity-doubling ratio R are standard and well cited. The paper does not oversell the charm results: it says deviations appear for 127<=T<=190 MeV and stops before claiming anything at higher T. Citation practice looks fine; the key results are in the referenced collaboration papers.

Where it is soft: The bottomonium potential in Fig. 3 (right) is the load-bearing new claim. It is plotted for a single time window (12-17 a_tau), with no error bars, and the extraction method is described only by 'in preparation' and 'PhD thesis' refs. The text says the plot shows 'a clear temperature variation with a reduction in the string tension,' but from the figure alone a reader cannot tell whether the differences between T=141 and T=281 MeV exceed the uncertainties, or whether a different time window would change the slopes. That is a real gap, and the stress-test note is right. I would not describe this as established until the method and systematic checks are written up. Also, the paper frames the open-charm M(T) fit as if it might be circular; it is not circular, just model-dependent, and the limitation is acknowledged. Single-state dominance below T_pc is a legitimate concern, but the paper confines itself to that regime.

Bottom line: For someone wanting a quick map of FASTSUM's thermal hadron results and entry points to the literature, this is useful. The charm sections are worth a skim; the bottomonium section should not be cited for the string-tension result until the full paper appears. As a proceedings it is acceptable, but the new result needs peer review in the full paper, not here.

Referee Report

3 major / 4 minor

Summary. This proceedings paper summarizes the FASTSUM collaboration's thermal lattice QCD results using 2+1 flavour anisotropic ensembles with a_s = 0.11208(31) fm and a_s/a_tau = 3.453(6). The paper presents three physics topics: (i) open-charm meson correlation functions, analyzed through a double ratio against a single-state cosh model and through fits of temperature-dependent ground-state masses for T ≲ T_pc; (ii) charmed-baryon parity partners, studied via an integrated ratio R that approaches the degenerate limit at high temperature; and (iii) a preliminary NRQCD bottomonium interquark potential extracted with the HAL QCD method, which is claimed to show a temperature-dependent string tension. The first two topics are presented as summaries of published work, while the bottomonium potential is new to this proceedings.

Significance. If established, the open-charm and charmed-baryon results provide useful evidence for in-medium modification of hadron properties and for approximate parity doubling across the chiral transition, and they connect to heavy-ion phenomenology. A strength of the paper is that the charm sections rely on peer-reviewed publications [1–5], and the authors explicitly acknowledge the limitation of the single-state model for T larger than T_pc. The bottomonium string-tension result, if validated, would be a genuinely new quantitative result, but at present it is the least secure part of the manuscript and needs substantially more evidence before it can support the central claim made about it.

major comments (3)

[Section 5, Fig. 3 (right)] The central new result of this proceedings, described as 'a clear temperature variation with a reduction in the string tension', is not supported by the evidence shown. The potential is extracted with the unpublished 'linear regression' method of Refs. [15,16], using a single time window (12–17 a_tau), and the plotted V_C(r) curves carry no statistical or systematic uncertainties. To make the claim checkable, the authors should validate the Schrödinger-equation inversion for NRQCD correlators at these temperatures, demonstrate stability under variation of the fit window, and provide error bands or at least uncertainties that show the slope differences are significant. Unless those conditions are met, the string-tension reduction should be explicitly labelled preliminary rather than presented as an established result.
[Section 3, Eq. (1) and Figs. 1–2] The interpretation of deviations of R_double from unity as changes in the ground-state mass relies on the single-state model G_model, which contains only a ground-state cosh with mass M(T0). The paper itself restricts the fits of M(T) to T ≲ T_pc because of lack of confidence in G_model at larger temperatures, but the summary statement 'for intermediate temperatures, 127 MeV ≤ T ≤ 190 MeV, there are signs of a deviation ... implying that the ground state mass differs from M(T0)' includes the 190 MeV ensemble, which lies above T_pc = 167(3) MeV. At those temperatures the deviation could be produced by excited-state contamination or finite-width effects rather than a ground-state mass change. The claim should either be restricted to the range where fits are actually performed or explicitly presented as a model-dependent indicator only.
[Section 3, Fig. 2 and Section 4, Fig. 3 (left)] Two of the paper's central plots are presented without visible uncertainties, although they support quantitative claims of thermal variation. In Fig. 2 the temperature-dependent masses are claimed to show 'clear thermal variations', and in Fig. 3 (left) the approach of R toward the degenerate limit is used to infer parity doubling above T_pc. For the R values, the highest-temperature singly-charmed points appear to lie around 0.2–0.3 rather than near zero, so the phrase 'approximate parity partner degeneracy' needs a quantitative criterion or a citation to the detailed analysis in Refs. [2–5] demonstrating that the residual values are consistent with degeneracy within errors. Without error bars, the statistical significance of the mass variations and of the residual non-degeneracy cannot be assessed from the manuscript alone.

minor comments (4)

[Section 3, last paragraph] The notation G_model(τ;T,T) is unclear; presumably it denotes the same single-state model with a temperature-dependent mass M(T) in place of M(T0). Please define this notation explicitly.
[Section 4, Eq. (2)] The text and the caption of Fig. 3 refer to a sum over τ starting from n0, but Eq. (2) does not indicate the lower limit of the summation. Please make the summation range explicit in the equation.
[Section 5] The acronym 'hal-qcd' is usually written 'HAL QCD'; harmonize the spelling with Ref. [13] for consistency.
[Figure 1 caption] The caption contains an unrendered LaTeX artifact, 'Rdouble(/uni03C4;T;T0)', which should be typeset as proper mathematics.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the open-charm double ratio and charm-baryon reconstructed correlator are data-versus-model comparisons, and the bottomonium caveat is a reproducibility limitation, not a circular reduction.

full rationale

The derivation chain is not circular. In the open-charm analysis, the paper defines G_model with M(T0) fitted at the reference temperature T0 = 47 MeV and then forms the double ratio R_double = [G(T)/G_model(T,T0)] / [G(T0)/G_model(T0,T0)]; the denominator is a fit-quality normalisation rather than the claim, and deviations for T > T0 are data-versus-model comparisons. The temperature-dependent masses M(T) are subsequently obtained by independent fits to G_model(τ;T,T), not by renaming the original M(T0) fit, and the paper explicitly restricts those fits to T ≲ T_pc where it trusts the single-state ansatz. The charm-baryon reconstructed-correlator ratio G_rec/G follows from an exact kernel identity and compares data at Nτ with the spectral content at N0, so it does not assume parity degeneracy; the R→0 limit is a definition of the observable, not an input that forces the conclusion. The bottomonium potential is obtained by inverting Bethe-Salpeter wavefunctions via the hal-qcd method, and the string-tension reduction is read from the potential gradient, not defined in terms of the method's outputs. Although Section 5 relies on an in-preparation self-citation [15,16] and a single time window without error bars, that is a robustness and reproducibility limitation, not a circularity: no equation in the paper reduces the string-tension claim to the linear-regression method's assumptions, and the claim is not forced by construction.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The paper introduces no new free parameters beyond standard analysis choices (such as the reference mass and the fit time window) and relies on established lattice QCD methods and domain assumptions. There are no invented physical entities.

free parameters (2)

Reference-temperature ground-state mass M(T0) = Not given in this paper
Used in Eq. (1) to define G_model and the double ratio; fitted to lattice correlation data at the reference temperature T0 = 47 MeV (Section 3).
Time window for the potential fit = 12-17 [a_tau]
The bottomonium potential is extracted using 'one particular time window for the fits' (Figure 3, right panel), with no justification or systematic scan reported in this text.

assumptions (5)

domain assumption Lattice QCD with 2+1 flavors of Wilson quarks on anisotropic lattices provides a valid discretization of thermal QCD.
The ensembles in Table 1 are standard in the field and details are referenced to [1,6].
domain assumption NRQCD reliably approximates bottom quarks at the lattice spacings used here.
Used for the bottomonium potential extraction (Section 5), a standard approach for heavy quarks.
domain assumption The correlation function is dominated by the ground state in the temperature range used for the fits, so G_model with a single mass is applicable.
Explicitly limited: the paper restricts to T <= T_pc because 'we do not have confidence in the applicability of G_model(τ;T,T) for larger temperatures' (Section 3).
domain assumption The HAL QCD method yields the interquark potential from Bethe-Salpeter wavefunctions.
The method is referenced to [13,14] (Section 5), and is used without derivation here.
domain assumption The reconstructed correlator method, expressing the fermionic kernel as a sum over kernels at other temperatures, is valid.
Used in Section 4 and referenced to [11].

how reviews work

0 comments

Cite this review

Pith. "Pith review of Thermal lattice QCD results from the FASTSUM collaboration." pith.science (2026). https://pith.science/paper/QTYPUHSE

@misc{pith2026241115937,
  author       = {Pith},
  title        = {Pith review of: Thermal lattice QCD results from the FASTSUM collaboration},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QTYPUHSE}},
  note         = {Machine review of arXiv:2411.15937}
}

read the original abstract

The FASTSUM Collaboration has developed a comprehensive research programme in thermal lattice QCD using 2+1 flavour ensembles. We review our recent hadron spectrum analyses of open charm mesons and charm baryons at non-zero temperature. We also detail our determination of the interquark potential in the bottomonium system using NRQCD quarks. All of our work uses anisotropic lattices where the temporal lattice spacing is considerably finer than the spatial one allowing better resolution of temporal correlation functions.

Figures

Figures reproduced from arXiv: 2411.15937 by the authors.

**Figure 1.** Double Ratio plots for the 𝐷−meson family at low (left) and intermediate (right) temperatures, clearly showing a thermal effect for𝑇 ≳ 127 MeV, see Eq.(1). The reference temperature is set to𝑇0 = 47 MeV. 0 30 60 90 120 150 180 T [MeV] 1700 1750 1800 1850 1900 1950 2000 2050 2100 M [MeV] 0 30 60 90 120 150 180 T [MeV] 1700 1750 1800 1850 1900 1950 2000 2050 2100 M [MeV] D * (vector) D (pseudoscalar) 0 30 60 90 120 15… view at source ↗

**Figure 2.** The ground state mass of the 𝐷−meson family for 𝑇 ≲ 𝑇𝑝𝑐 showing clear thermal variations. 𝑇𝑝𝑐 = 167(3) MeV is shown by the vertical band. To quantify this, we study the double ratio, 𝑅double (𝜏;𝑇, 𝑇0) = 𝑅model(𝜏;𝑇, 𝑇0) 𝑅model(𝜏;𝑇0, 𝑇0) where 𝑅model(𝜏;𝑇, 𝑇0) = 𝐺(𝜏;𝑇) 𝐺model(𝜏;𝑇, 𝑇0) . (1) 𝐺(𝜏;𝑇) is the correlation function data obtained from the lattice simulation. This double ratio is a means of partially cancelling… view at source ↗

**Figure 3.** (Left) The integrated ratio, 𝑅 for charm baryons showing the approach towards parity degeneracy as 𝑇 increases. 𝑅 is defined in Eq.(2) and the sum over 𝜏 starts from 𝑛0. The vertical lines show the points of inflection near 𝑇𝑝𝑐 for the singly-charmed channels (doubly-charmed channels have no points of inflection). (Right) Preliminary results for the interquark potential in (NRQCD) bottomonium mesons for a variety of… view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

16 extracted references · 4 canonical work pages

[1]

Aarts, C

G. Aarts, C. Allton, R. Bignell, T.J. Burns, S.C. García-Mascaraque et al.,Open charm mesons at nonzero temperature: results in the hadronic phase from lattice QCD, 2209.14681

arXiv
[2]

Aarts, C

G. Aarts, C. Allton, M.N. Anwar, R. Bignell, T.J. Burns et al.,Non-zero temperature study of spin 1/2 charmed baryons using lattice gauge theory, Eur. Phys. J. A60(2024) 59 [2308.12207]

arXiv 2024
[3]

Aarts, C

G. Aarts, C. Allton, S. Hands, B. Jäger, C. Praki et al.,Nucleons and parity doubling across the deconfinement transition,Phys. Rev. D92(2015) 014503 [1502.03603]

arXiv 2015
[4]

Aarts, C

G. Aarts, C. Allton, D. De Boni, S. Hands, B. Jäger et al.,Light baryons below and above the deconfinement transition: medium effects and parity doubling,JHEP 06 (2017) 034 [1703.09246]

arXiv 2017
[5]

Aarts, C

G. Aarts, C. Allton, D. De Boni and B. Jäger,Hyperons in thermal QCD: A lattice view, Phys. Rev. D99(2019) 074503 [1812.07393]

arXiv 2019
[6]

Aarts et al.,Properties of the QCD thermal transition with Nf=2+1 flavors of Wilson quark, Phys

G. Aarts et al.,Properties of the QCD thermal transition with Nf=2+1 flavors of Wilson quark, Phys. Rev. D105 (2022) 034504 [2007.04188]

arXiv 2022
[7]

Aarts, C

G. Aarts, C. Allton, T. Harris, S. Kim, M.P. Lombardo et al.,The bottomonium spectrum at finite temperature from N𝑓 = 2 + 1 lattice QCD,JHEP 07 (2014) 097 [1402.6210]

arXiv 2014
[8]

Aarts, C

G. Aarts, C. Allton, A. Amato, P. Giudice, S. Hands et al.,Electrical conductivity and charge diffusion in thermal QCD from the lattice, JHEP 02(2015) 186 [1412.6411]

arXiv 2015

Show all 16 references

[9]

Nikolaev, G

A. Nikolaev, G. Aarts, C. Allton, D. De Boni, J. Glesaaen et al.,Mesonic correlators at non-zero baryon chemical potential,PoS LATTICE2019(2020) 077 [2001.04415]

2020 arXiv
[10]

Wilson, R.A

D.J. Wilson, R.A. Briceno, J.J. Dudek, R.G. Edwards and C.E. Thomas,The quark-mass dependence of elastic𝜋𝐾 scattering from QCD,Phys. Rev. Lett.123 (2019) 042002 [1904.03188]

2019 arXiv
[11]

H.T. Ding, A. Francis, O. Kaczmarek, F. Karsch, H. Satz et al.,Charmonium properties in hot quenched lattice QCD, Phys. Rev. D86(2012) 014509 [1204.4945]

2012 arXiv
[12]

Datta, S

S. Datta, S. Gupta, M. Padmanath, J. Maiti and N. Mathur,Nucleons near the QCD deconfinement transition,JHEP 02 (2013) 145 [1212.2927]

2013 arXiv
[13]

Ishii, S

N. Ishii, S. Aoki and T. Hatsuda,The Nuclear Force from Lattice QCD, Phys. Rev. Lett.99 (2007) 022001 [nucl-th/0611096]

2007 arXiv
[14]

Evans, C.R

P.W.M. Evans, C.R. Allton and J.I. Skullerud,Ab initio calculation of finite-temperature charmonium potentials, Phys. Rev. D89(2014) 071502 [1303.5331]

2014 arXiv
[15]

Spriggs, C

T. Spriggs, C. Allton, T.J. Burns and S. Kim, in preparation
[16]

Spriggs, PhD Thesis, Swansea University

T. Spriggs, PhD Thesis, Swansea University. 6

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.

[1] [1]

Aarts, C

G. Aarts, C. Allton, R. Bignell, T.J. Burns, S.C. García-Mascaraque et al.,Open charm mesons at nonzero temperature: results in the hadronic phase from lattice QCD, 2209.14681

arXiv

[2] [2]

Aarts, C

G. Aarts, C. Allton, M.N. Anwar, R. Bignell, T.J. Burns et al.,Non-zero temperature study of spin 1/2 charmed baryons using lattice gauge theory, Eur. Phys. J. A60(2024) 59 [2308.12207]

arXiv 2024

[3] [3]

Aarts, C

G. Aarts, C. Allton, S. Hands, B. Jäger, C. Praki et al.,Nucleons and parity doubling across the deconfinement transition,Phys. Rev. D92(2015) 014503 [1502.03603]

arXiv 2015

[4] [4]

Aarts, C

G. Aarts, C. Allton, D. De Boni, S. Hands, B. Jäger et al.,Light baryons below and above the deconfinement transition: medium effects and parity doubling,JHEP 06 (2017) 034 [1703.09246]

arXiv 2017

[5] [5]

Aarts, C

G. Aarts, C. Allton, D. De Boni and B. Jäger,Hyperons in thermal QCD: A lattice view, Phys. Rev. D99(2019) 074503 [1812.07393]

arXiv 2019

[6] [6]

Aarts et al.,Properties of the QCD thermal transition with Nf=2+1 flavors of Wilson quark, Phys

G. Aarts et al.,Properties of the QCD thermal transition with Nf=2+1 flavors of Wilson quark, Phys. Rev. D105 (2022) 034504 [2007.04188]

arXiv 2022

[7] [7]

Aarts, C

G. Aarts, C. Allton, T. Harris, S. Kim, M.P. Lombardo et al.,The bottomonium spectrum at finite temperature from N𝑓 = 2 + 1 lattice QCD,JHEP 07 (2014) 097 [1402.6210]

arXiv 2014

[8] [8]

Aarts, C

G. Aarts, C. Allton, A. Amato, P. Giudice, S. Hands et al.,Electrical conductivity and charge diffusion in thermal QCD from the lattice, JHEP 02(2015) 186 [1412.6411]

arXiv 2015