arxiv: 2604.10889 · v1 · submitted 2026-04-13 · ✦ hep-ph

Recognition: unknown

Heavy-quark transport across the QCD crossover driven by a lattice-constrained in-medium potential

Wu Wang , Yuqi Luo , Fei Sun , Sa Wang , Jungang Deng , Wei Xie , Shuang Li , Kejun Wu

Authors on Pith no claims yet

Pith reviewed 2026-05-10 16:41 UTC · model grok-4.3

classification ✦ hep-ph

keywords heavy-quark transportQCD crossoverquark-gluon plasmain-medium potentialspatial diffusion coefficientlattice QCDheavy flavor

0 comments

The pith

Lattice-constrained potential yields heavy-quark diffusion coefficient of 2π T D_s ≈ 0.5-1.7 across QCD crossover

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

The paper develops a framework for heavy quark transport in the quark-gluon plasma that uses a single in-medium potential constrained by lattice QCD data on static quark-antiquark properties. This potential combines perturbative Yukawa screening with a non-perturbative confining string term and is applied consistently to dynamic transport without splitting momentum scales. The approach shows that the string contribution is crucial for high opacity near the critical temperature, leading to a diffusion coefficient that matches recent lattice results. This provides a unified way to model heavy flavor dynamics through the QCD phase transition.

Core claim

By employing an in-medium effective potential that incorporates both short-range Yukawa screening and long-range string tension, both fitted to lattice QCD data, the authors compute the heavy-quark spatial diffusion coefficient across the crossover region. Their calculation yields 2π T D_s between 0.5 and 1.7, in agreement with lattice extractions, and demonstrates that the confining term is essential near T_c.

What carries the argument

The lattice-constrained in-medium effective potential, combining Yukawa and confining string contributions, used as the interaction kernel for transport.

If this is right

The non-perturbative string tension is required to reproduce the strong coupling near T_c.
The spatial diffusion coefficient remains small throughout the crossover, indicating persistent strong interactions.
This framework eliminates the need for arbitrary soft-hard separation scales in transport calculations.
Results offer a dynamical explanation for heavy-quark behavior in hot QCD matter.

Where Pith is reading between the lines

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

This method could be extended to calculate other transport coefficients like drag or momentum diffusion for heavy quarks.
Phenomenological models of heavy-ion collisions might benefit from incorporating this temperature-dependent potential directly.
Similar lattice-constrained potentials could be tested for light quark or gluon transport properties.

Load-bearing premise

The static in-medium potential extracted from lattice QCD can be directly inserted into the dynamic transport equations without accounting for additional medium effects or scale-dependent adjustments.

What would settle it

A lattice QCD calculation of the heavy-quark spatial diffusion coefficient near the crossover temperature that falls significantly outside the range 0.5 to 1.7 for 2π T D_s would contradict the model's predictions.

Figures

Figures reproduced from arXiv: 2604.10889 by Fei Sun, Jungang Deng, Kejun Wu, Sa Wang, Shuang Li, Wei Xie, Wu Wang, Yuqi Luo.

**Figure 3.** Figure 3: FIG. 3. (Color online) The dimensionless transport coefficient [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

**Figure 2.** Figure 2: FIG. 2. (Color online) Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4. The dimensionless heavy-quark momentum diffusion [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5. The dimensionless spatial diffusion coefficient 2 [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗

read the original abstract

We present a self-consistent framework for heavy-quark transport in the quark-gluon plasma across the QCD crossover region. By synthesizing perturbative and non-perturbative interactions into a unified interaction kernel, we circumvent the traditional reliance on arbitrary soft-hard momentum separation scales. The interaction is governed by an in-medium effective potential, incorporating short-range Yukawa screening and long-range confining string contributions, both rigorously constrained by the latest lattice QCD data. Our results reveal that the non-perturbative string tension is indispensable for capturing the extreme opacity of the medium near the critical temperature $T_c$. Specifically, our model predicts a spatial diffusion coefficient of $2\pi T D_s \approx 0.5 \sim 1.7$, demonstrating a striking quantitative agreement with the recent lattice QCD extractions. Ultimately, our results provide a robust dynamical interpretation of the strong heavy-quark coupling near the QCD crossover and offer a unified framework for describing heavy-flavor transport in hot and dense QCD matter.

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

They feed a lattice-fixed potential with both Yukawa and string pieces into a transport model and get a diffusion coefficient that overlaps recent lattice numbers, but the static-to-dynamic step lacks supporting checks.

read the letter

The main thing here is that the authors take an in-medium potential constrained by lattice QCD static correlators, keep both the short-range screened term and the long-range string tension, and use that single kernel in a heavy-quark transport calculation across the crossover. The string tension dominates the opacity near Tc and the resulting 2π T D_s range of roughly 0.5 to 1.7 sits inside the lattice extractions they cite. No extra momentum cutoffs are inserted by hand, which is cleaner than the usual patchwork approach. That is the concrete piece of work they have done. The parameter count stays low because the Yukawa mass and string tension are both tied to the same lattice data set. The output is a definite number that can be compared directly to other extractions. The soft spot is the direct transfer of the static potential into the dynamic transport kernel. Near the crossover the medium is strongly coupled, so it is not automatic that the same V(r,T) governs scattering for moving quarks without velocity or retardation corrections. The abstract gives no auxiliary calculation, such as finite-velocity Wilson loops or real-time correlators, to test whether the quasi-static identification holds. If that step needs adjustment, the quantitative match becomes less robust. This paper is for people who model heavy-flavor suppression and flow in heavy-ion collisions and want one framework that covers the transition region without switching regimes. It is worth sending to referees who know both lattice statics and transport methods, because the calculation is explicit and the claim is falsifiable. I would recommend peer review, with the main question being whether the static potential remains accurate once the quarks are moving.

Referee Report

1 major / 2 minor

Summary. The manuscript presents a self-consistent framework for heavy-quark transport in the QGP across the QCD crossover. It employs an in-medium effective potential with short-range Yukawa screening and long-range confining string tension, both constrained solely by lattice QCD static correlators, to construct a unified interaction kernel without arbitrary soft-hard momentum separation scales. The resulting spatial diffusion coefficient is reported as 2π T D_s ≈ 0.5–1.7, claimed to agree quantitatively with recent lattice extractions, with the non-perturbative string term identified as essential for the medium opacity near T_c.

Significance. If the central mapping from static lattice data to dynamical transport holds, the result would be significant: it supplies a parameter-light, unified description that bridges perturbative and non-perturbative regimes, demonstrates the necessity of the string contribution near the crossover, and furnishes a dynamical interpretation of strong heavy-quark coupling consistent with lattice diffusion coefficients. Such a framework could reduce reliance on ad-hoc scales in heavy-flavor phenomenology.

major comments (1)

[Interaction kernel and transport equation] The transport calculation inserts the static lattice-constrained potential V(r,T) directly into the interaction kernel of the dynamical transport equation. No auxiliary calculation (finite-velocity Wilson loops, real-time correlators, or velocity-dependent checks) is presented to verify that this quasi-static identification remains accurate for moving heavy quarks near T_c, where the string tension is stated to dominate the opacity. This assumption is load-bearing for the quantitative agreement claim with lattice D_s values.

minor comments (2)

[Model implementation] Clarify the precise numerical implementation of the string tension term in the transport kernel and its temperature dependence across the crossover; a dedicated equation or table would improve reproducibility.
[Results] The abstract and results section use the range 0.5 ∼ 1.7; ensure the exact bounds are consistently defined and referenced to specific temperature intervals or parameter choices.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the detailed and constructive report. We address the single major comment below regarding the quasi-static use of the lattice potential.

read point-by-point responses

Referee: [Interaction kernel and transport equation] The transport calculation inserts the static lattice-constrained potential V(r,T) directly into the interaction kernel of the dynamical transport equation. No auxiliary calculation (finite-velocity Wilson loops, real-time correlators, or velocity-dependent checks) is presented to verify that this quasi-static identification remains accurate for moving heavy quarks near T_c, where the string tension is stated to dominate the opacity. This assumption is load-bearing for the quantitative agreement claim with lattice D_s values.

Authors: We agree that the framework directly inserts the static lattice-constrained V(r,T) into the interaction kernel without presenting finite-velocity Wilson loops, real-time correlators, or explicit velocity-dependent checks. This quasi-static identification is a standard approximation in heavy-quark transport models, justified by the large heavy-quark mass that keeps velocities non-relativistic and suppresses leading velocity corrections. The potential, including the string term, is Fourier-transformed to obtain the momentum-space kernel for scattering rates in the Born approximation. While no dedicated auxiliary calculations are included, the resulting 2πT Ds values show quantitative agreement with independent lattice extractions, and the necessity of the string contribution is demonstrated by explicit on/off comparisons. We view this as sufficient for the present scope and do not plan changes to the manuscript. revision: no

Circularity Check

0 steps flagged

No significant circularity: static lattice constraints on potential are independent of computed diffusion coefficient.

full rationale

The derivation constrains an in-medium potential V(r,T) solely from lattice QCD static quark-antiquark correlators (Yukawa screening plus string tension), then inserts this fixed V(r,T) into the interaction kernel of a transport equation to obtain the spatial diffusion coefficient 2π T D_s. The reported range 0.5–1.7 is presented as a prediction and compared to separate lattice extractions of D_s. Because the input lattice data (static correlators) and the target observable (dynamic diffusion) are distinct, and no parameter is adjusted to the D_s data itself, the agreement does not reduce to a tautology or fitted-input prediction. No self-citation chain, uniqueness theorem, or ansatz smuggling is invoked to force the central result. The framework therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The model depends on lattice QCD inputs for the potential parameters and assumes a specific functional form for the interaction.

free parameters (2)

Yukawa screening mass
Determined from lattice QCD data
string tension
Non-perturbative contribution constrained by lattice

axioms (2)

domain assumption The effective interaction kernel is the sum of perturbative Yukawa and non-perturbative string terms
Used to model the in-medium potential
ad hoc to paper No arbitrary soft-hard momentum separation is needed in the unified framework
Claimed to circumvent traditional approaches

pith-pipeline@v0.9.0 · 5486 in / 1463 out tokens · 76642 ms · 2026-05-10T16:41:11.796496+00:00 · methodology

discussion (0)

Reference graph

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