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arxiv: 2606.10049 · v1 · pith:VPTPRZHRnew · submitted 2026-06-08 · ✦ hep-lat · hep-ph· nucl-ex· nucl-th

Momentum Dependence of Heavy Quark Diffusion in a Thermal Gluonic Plasma on the Lattice

Harshit Pandey , Sayantan Sharma This is my paper

Pith reviewed 2026-06-27 13:55 UTC · model grok-4.3

classification ✦ hep-lat hep-phnucl-exnucl-th
keywords heavy quarksdrag coefficientdiffusion coefficientlattice QCDthermal plasmagluonsmomentum dependence
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The pith

A lattice method extracts momentum dependence of heavy quark drag and diffusion in a gluonic plasma

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

This paper proposes a numerical strategy to simulate the real-time dynamics of a heavy quark with different initial momenta in a three-dimensional lattice discretization of an effective theory for high-temperature QCD. The plasma consists of non-perturbatively interacting soft gluons. The approach makes it possible to determine how the drag and diffusion coefficients vary with the heavy quark's momentum. Previously such quantities were only available at zero momentum or in perturbative approximations. Knowing the momentum dependence matters for understanding how heavy quarks lose energy while traversing the quark-gluon plasma created in heavy-ion collisions.

Core claim

The authors demonstrate a numerical strategy that simulates the real-time dynamics of a heavy quark with varying initial momenta in an effective three-dimensional lattice theory of thermal gluons, thereby determining the momentum dependence of the associated drag and diffusion coefficients for the first time in a non-perturbative setting.

What carries the argument

The numerical strategy for evolving the heavy quark in the lattice-discretized effective theory of thermal gluons while measuring its momentum loss.

If this is right

  • Drag and diffusion coefficients are obtained as functions of momentum.
  • The extraction is performed in a fully non-perturbative interacting plasma.
  • The method works in a non-Abelian gauge theory without Abelian approximations.
  • It provides input for transport models of heavy quarks in hot QCD matter.

Where Pith is reading between the lines

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

  • If the coefficients decrease at higher momenta, it would imply reduced energy loss for fast heavy quarks.
  • The technique might be adapted to study light quark or gluon transport on similar lattices.
  • Finite volume effects could be quantified by changing the lattice size in future runs.

Load-bearing premise

The lattice simulation accurately captures the heavy quark's momentum evolution without introducing large uncontrolled errors from discretization or the effective theory truncation.

What would settle it

If the computed drag coefficient at large momentum deviates significantly from the known perturbative result without matching the expected approach to that limit, the numerical extraction would be called into question.

Figures

Figures reproduced from arXiv: 2606.10049 by Harshit Pandey, Sayantan Sharma.

Figure 1
Figure 1. Figure 1: Variance of the momentum distribution (⟨p 2 x ⟩ − ⟨px⟩ 2 )/T 2 for a heavy quark with a zero and finite initial momenta |p|/T = 0.54 in a typical thermal configuration consisting of non-perturbatively interacting soft SU(3) gluons at T ∼ 480 MeV. We calculate the variance of the momentum distribution along the x-direction for a heavy quark with a zero initial mo￾mentum by solving the Dirac equation, but by… view at source ↗
Figure 2
Figure 2. Figure 2: The κ/ϵ3/4 for zero initial momentum of a heavy quark, obtained in an effective theory of soft (green points) SU(2) and (orange points) SU(3) gluons, shown as a function of temperature. For a comparison, we show the values of the same ratio in QCD without dynamical quarks as a function of temperature, where the parametric dependence of κ was taken from Ref. [18] and ϵ is simply the Stefan-Boltzmann value o… view at source ↗
Figure 3
Figure 3. Figure 3: The ratio of drag and diffusion coefficients ηD/T κL/T 3 × 2  M T  as a function of initial fermion momenta |p|/T, for a high temperature effective theory of soft (green) SU(2) and (orange) SU(3) gluons at T = 1.6 Tc. At T = 1.6 Tc, we calculate the MMOD for heavy quarks that have an initial momentum, both along and transverse to their direction. This allows us to extract the drag and diffusion coefficie… view at source ↗
Figure 5
Figure 5. Figure 5: The κT (p)/ϵ3/4 of a heavy quark as a function of its initial momenta |p|/T for different temperatures in a (top panel) SU(2) and (bottom panel) SU(3) plasma consisting of soft gluons. 5. Implications of our findings & Outlook In this work, we have developed a framework based on first￾principles lattice gauge theory to calculate the momentum de￾pendence of the motion of a heavy quark inside a non-Abelian p… view at source ↗
read the original abstract

We study the dynamics of a heavy quark in a thermal plasma consisting of non-perturbatively interacting soft momentum gluons at high temperatures, described in terms of an effective theory of QCD discretized on a three-dimensional lattice. We propose a numerical strategy that allows us to simulate the dynamics of a heavy quark for different values of initial momenta in this thermalized plasma. This allows, for the first time, to extract the momentum dependence of the heavy quark drag and diffusion coefficients in a non-perturbatively interacting thermal, non-Abelian plasma.

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.

Referee Report

1 major / 0 minor

Summary. The manuscript proposes a numerical strategy to simulate the dynamics of a heavy quark with varying initial momenta in a thermal plasma of non-perturbatively interacting soft gluons, described via an effective theory of QCD discretized on a three-dimensional lattice. This is claimed to enable, for the first time, extraction of the momentum dependence of the heavy quark drag and diffusion coefficients in a non-perturbative, non-Abelian thermal plasma.

Significance. If the proposed strategy is validated without uncontrolled systematics, the work would provide the first non-perturbative lattice results on momentum-dependent heavy-quark transport coefficients in a thermal gluonic plasma. This is relevant for heavy-flavor phenomenology in the quark-gluon plasma, where momentum dependence enters energy-loss and flow calculations. The lattice discretization of the effective theory is a methodological strength for accessing non-perturbative effects beyond weak-coupling expansions.

major comments (1)
  1. [Numerical strategy description] The manuscript presents the numerical strategy but does not report explicit validation against known limits (e.g., perturbative drag coefficient or free-theory diffusion) or quantitative error estimation for the extracted coefficients. This is load-bearing for the central claim that the approach enables reliable extraction of momentum dependence.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their positive evaluation of the potential impact of our work and for the constructive comment. We respond to the major comment below.

read point-by-point responses

  1. Referee: [Numerical strategy description] The manuscript presents the numerical strategy but does not report explicit validation against known limits (e.g., perturbative drag coefficient or free-theory diffusion) or quantitative error estimation for the extracted coefficients. This is load-bearing for the central claim that the approach enables reliable extraction of momentum dependence.

    Authors: We agree that explicit validation against known limits and quantitative error estimation are essential to substantiate the reliability of the extracted coefficients. The current manuscript is a proposal of the numerical strategy and focuses on its description, without performing the full set of simulations or reporting numerical extractions. In a revised version we will add a dedicated section outlining validation procedures (including comparisons to the perturbative drag coefficient at high momentum and to free-theory diffusion) together with a discussion of how systematic uncertainties can be quantified. This directly addresses the load-bearing aspect of the central claim. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper proposes a numerical strategy for simulating heavy quark dynamics on a 3D lattice effective theory to extract momentum-dependent drag and diffusion coefficients for the first time. No load-bearing derivation steps, self-definitions, fitted inputs renamed as predictions, or self-citation chains are identifiable in the abstract or described approach. The central claim is a methodological proposal that remains independent of its own outputs and does not reduce to any input by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Review based on abstract; full details on parameters and assumptions not accessible.

axioms (1)
  • domain assumption The effective three-dimensional theory captures the relevant dynamics of heavy quarks in high-temperature QCD.
    Extracted from abstract description of the setup.

pith-pipeline@v0.9.1-grok · 5616 in / 1017 out tokens · 21578 ms · 2026-06-27T13:55:20.904612+00:00 · methodology

discussion (0)

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