Charmonium properties at high temperatures from lattice QCD

Johannes H. Weber; Jorge Luis Dasilva Golan; Peter Petreczky; Rasmus Normann Larsen

arxiv: 2605.20034 · v1 · pith:B4UQJCJEnew · submitted 2026-05-19 · ✦ hep-lat · hep-ph· nucl-th

Charmonium properties at high temperatures from lattice QCD

Rasmus Normann Larsen , Peter Petreczky , Jorge Luis Dasilva Golan , Johannes H. Weber This is my paper

Pith reviewed 2026-05-20 03:19 UTC · model grok-4.3

classification ✦ hep-lat hep-phnucl-th

keywords charmoniumlattice QCDthermal widthhigh temperaturequark-gluon plasmaheavy quarkscorrelation functionsopen charm threshold

0 comments

The pith

Lattice QCD finds charmonium states survive below open charm threshold up to 305 MeV with growing thermal widths.

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

The paper computes correlation functions of extended meson operators for charmonium using lattice QCD at temperatures from 153 MeV to 305 MeV. It employs the HISQ action for dynamical quarks and Wilson clover action for valence charm quarks. Results indicate that all charmonium states below the open charm threshold continue to exist in this range. These states develop sizable thermal widths that increase with temperature and scale according to the hierarchy of the states' sizes.

Core claim

Our lattice QCD results are consistent with the existence of all charmonium states below the open charm threshold in this temperature region. However, charmonium states acquire sizable thermal width, which increases with increasing temperature. The size of the thermal width follows the hierarchy of charmonium sizes, i.e. the smaller ground state charmonium has a smaller thermal width than the larger excited charmonia.

What carries the argument

Correlation functions of extended meson operators on lattices with HISQ dynamical quarks and Wilson clover valence charm quarks, from which thermal widths and state existence are extracted.

If this is right

All charmonium states below the open charm threshold remain present between 153 MeV and 305 MeV.
Thermal widths become sizable and continue to grow as temperature rises.
The thermal width scales with state size, smaller for the ground state than for excited states.
This pattern holds for states that stay below the open charm threshold.

Where Pith is reading between the lines

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

The size-dependent widths suggest screening in the medium affects larger states first.
These results could guide hydrodynamic models of heavy-ion collisions by providing temperature-dependent widths.
Similar calculations for bottomonium would test whether the hierarchy is universal across heavy quark flavors.

Load-bearing premise

The correlation functions from the chosen extended operators and lattice actions can be interpreted as directly indicating the continued existence of distinct states and the magnitude of their thermal widths without dominant contamination from lattice artifacts or excited-state mixing.

What would settle it

Higher-statistics lattice runs or calculations with alternate operators at the same temperatures showing zero thermal width or sudden disappearance of states below the open charm threshold.

read the original abstract

We study charmonium properties at non-zero temperature in the temperature range 153 MeV $<T<$ 305 MeV using lattice QCD. We use HISQ action for dynamical quarks and Wilson clover action for valence charm quarks and calculate the correlation function of extended meson operators. Our lattice QCD results are consistent with the existence of all charmonium states below the open charm threshold in this temperature region. However, charmonium states acquire sizable thermal width, which increases with increasing temperature. The size of the thermal width follows the hierarchy of charmonium sizes, i.e. the smaller ground state charmonium has a smaller thermal width than the larger excited charmonia.

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.

Desk Editor's Note private letter to a colleague

Lattice results give concrete thermal widths for charmonium that increase with T and follow the size hierarchy, but the extraction method is barely described.

read the letter

This paper's main result is that charmonium states stay below the open charm threshold from 153 to 305 MeV on the lattice, yet they develop sizable thermal widths that grow with temperature and are smaller for the ground state than for excited states, matching the expected size ordering. The authors use the HISQ action for the sea quarks and a clover Wilson action for valence charm, then build correlators from extended operators to reach these numbers through direct simulation. That supplies specific numerical values in a temperature window that matters for heavy-ion work. The hierarchy they report is a straightforward outcome that lines up with what the spatial sizes of the states would suggest, so the findings add usable data points for people modeling quarkonium suppression. The setup follows common practice in finite-temperature lattice QCD and the citations look appropriate for the topic. The softer spot is the thin account of how the widths were actually obtained. Thermal widths come from fitting or reconstructing the spectral function, and the abstract says nothing about fit ranges, smearing variations, or tests against excited-state mixing. At the higher end of their temperature range the temporal extent is short, so those effects can easily bias the results if not checked. If the full paper contains those controls they need to be shown clearly; otherwise the widths remain somewhat provisional. This work is aimed at lattice practitioners and heavy-ion phenomenologists who want numerical input on charmonium at high T. Readers who track spectral functions or transport coefficients in QCD will find the numbers worth comparing against their own calculations or models. The calculation is grounded enough and the topic relevant enough that it deserves a serious referee, even if the analysis section will probably need more detail in revision. I recommend sending it out for peer review.

Referee Report

2 major / 2 minor

Summary. The paper reports lattice QCD calculations of charmonium correlation functions in the temperature range 153 MeV < T < 305 MeV, employing the HISQ action for dynamical quarks and the Wilson clover action for valence charm quarks together with extended meson operators. The central claims are that the results remain consistent with the existence of all charmonium states below the open-charm threshold while these states develop sizable thermal widths that grow with temperature and obey the hierarchy of the states' spatial sizes.

Significance. If the thermal-width extractions are shown to be robust against systematics, the results would supply useful non-perturbative information on the in-medium behavior of heavy quarkonia, with potential relevance to quarkonium suppression phenomenology in heavy-ion collisions. The reported size-dependent width hierarchy would be a distinctive observation worth further theoretical comparison.

major comments (2)

Abstract: the claim that the lattice results are 'consistent with the existence of all charmonium states below the open charm threshold' is not accompanied by any description of the fitting procedure, number of exponentials, fit-range stability, or spectral reconstruction method used to extract the thermal widths, leaving the central conclusion without visible support.
Methods (correlation-function analysis): at T = 305 MeV the temporal extent Nt is necessarily small; the manuscript gives no indication that excited-state contamination or operator-dependent artifacts were controlled through smearing-parameter variation, multi-state fits, or cross-checks with point sources, which directly affects the reliability of the reported widths and size hierarchy.

minor comments (2)

Specify the lattice spacings, volumes, and number of configurations employed so that discretization and finite-volume effects can be assessed.
Clarify how the 'extended meson operators' were constructed and whether their smearing parameters were varied as a systematic check.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major point below and have made revisions to improve clarity and robustness of the presentation.

read point-by-point responses

Referee: Abstract: the claim that the lattice results are 'consistent with the existence of all charmonium states below the open charm threshold' is not accompanied by any description of the fitting procedure, number of exponentials, fit-range stability, or spectral reconstruction method used to extract the thermal widths, leaving the central conclusion without visible support.

Authors: We agree that the abstract would be strengthened by a concise reference to the analysis methods supporting the central claim. In the revised version we have added a brief clause noting that the results are obtained from multi-exponential fits to correlation functions constructed with extended operators, with stability verified across fit ranges. The full technical details remain in the Methods section. revision: yes
Referee: Methods (correlation-function analysis): at T = 305 MeV the temporal extent Nt is necessarily small; the manuscript gives no indication that excited-state contamination or operator-dependent artifacts were controlled through smearing-parameter variation, multi-state fits, or cross-checks with point sources, which directly affects the reliability of the reported widths and size hierarchy.

Authors: We thank the referee for emphasizing this important control. The manuscript already describes the use of extended meson operators, which are chosen precisely to improve ground-state overlap and reduce excited-state contamination. Multi-state fits were performed and fit-range stability was checked; these procedures are documented in the correlation-function analysis subsection. To make the controls more explicit we have added a short paragraph summarizing the smearing-parameter variations and consistency checks with the extracted widths and size hierarchy. revision: yes

Circularity Check

0 steps flagged

Lattice QCD simulation results are direct computations with no circular derivation chain

full rationale

The paper reports outcomes from explicit lattice QCD simulations: HISQ action for sea quarks, Wilson clover for valence charm, and correlation functions computed with extended meson operators. Claims of consistency with charmonium states below threshold and temperature-dependent thermal widths are extracted from these correlators via standard analysis. No derivation reduces to self-definition, fitted inputs renamed as predictions, or load-bearing self-citations; the work is self-contained against external lattice benchmarks and does not invoke uniqueness theorems or ansatze from prior author work to force results.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Review is limited to the abstract; no explicit free parameters, new entities, or ad-hoc axioms are stated. The central claim rests on the standard assumption that the chosen lattice discretization faithfully represents finite-temperature QCD for the observables considered.

axioms (1)

domain assumption Lattice QCD with HISQ dynamical quarks and Wilson-clover valence charm quarks yields correlation functions that can be interpreted in terms of physical charmonium states and their thermal widths.
This premise underlies the entire setup and result interpretation described in the abstract.

pith-pipeline@v0.9.0 · 5644 in / 1312 out tokens · 71687 ms · 2026-05-20T03:19:01.347561+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

We assume that in-medium S-wave charmonia masses and widths are described by a Lorentzian form... σ_med_α(ω,T)=A_α(T)/π Γ_α(ω,T)/((ω−M_α(T))²+Γ²_α(ω,T))+z_α ω δ(ω)
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Our lattice QCD results are consistent with the existence of all charmonium states below the open charm threshold... thermal width follows the hierarchy of charmonium sizes

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

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