Energy loss of heavy-flavor quarks in color string medium

Daria Prokhorova; Evgeny Andronov; Shuzhe Shi

REVIEW 1 major objections 2 minor 111 references

Energy loss of heavy-flavor quarks in color string medium

T0 review · 1 major / 2 minor · reviewed 2026-05-18 · grok-4.3

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

Pith's one-line read Heavy-flavor quarks lose less transverse momentum in a fluctuating color-string medium than in hydrodynamic descriptions of small systems.

desk verdict The paper finds lower heavy-flavor quark energy loss in a fluctuating color-string medium than in EPOS4HQ hydrodynamics, but the mapping from string energy density to scattering rate lacks a clear derivation. read the letter →

arxiv 2509.24316 v1 pith:I2Y6XJF3 submitted 2025-09-29 hep-ph

Daria Prokhorova , Shuzhe Shi , Evgeny Andronov This is my paper · ORCID

classification hep-ph

keywords heavy-flavorquarksenergylosscolorstringsproton-protoncollisionselasticscatteringfluctuatingmediumquark-gluonplasmasmallsystems

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 calculates the energy loss of charm quarks produced in hard scatterings as they move through the medium created in proton-proton collisions at LHC energies. It models that medium as a set of color strings whose longitudinal oscillations and varying overlaps generate fluctuations in color field energy density. Those fluctuations set the rate at which the quarks scatter elastically with gluons. The resulting loss is substantially smaller than the loss obtained when the same collisions are described with an expanding hydrodynamic medium. A reader would care because the difference bears directly on whether tiny collision systems form an equilibrated quark-gluon plasma or retain string-like, non-equilibrated dynamics.

What carries the argument

The varying overlaps of longitudinally oscillating color strings, which produce fluctuations in color field energy density that directly govern the elastic scattering rate of heavy-flavor quarks with gluons inside the string volume.

What would settle it

A measurement of charm-quark transverse-momentum loss in high-multiplicity proton-proton events that matches the higher values predicted by hydrodynamic models rather than the lower values from the string model would falsify the central result.

Watch

Extended reading notes

Core claim

The central claim is that charm quarks traversing the non-equilibrated medium formed by fluctuating color strings from multi-pomeron exchanges in minimum-bias proton-proton collisions experience significantly lower momentum loss than they do in an expanding hydrodynamic scenario, with the loss computed event by event via a hybrid simulation that accounts for the dynamic initialization of the medium at each time step.

Load-bearing premise

The premise that energy-density fluctuations arising from string overlaps set the elastic scattering rates of heavy quarks with gluons without requiring additional equilibration of the medium.

Editorial extensions

If this is right

The transverse-momentum dependence of momentum loss for charm quarks follows from event-by-event propagation through the fluctuating string environment.
The lower energy loss stems from the non-equilibrated, dynamically initialized medium rather than a smooth hydrodynamic expansion.
String-overlap fluctuations create a different scattering environment that reduces the average interaction rate compared with equilibrated descriptions.
The result bears on whether signals of heavy-quark suppression in small systems indicate full quark-gluon plasma formation or string-like dynamics.

Reading between the lines

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

If the string description holds, heavy-flavor observables in proton-proton data could serve as a baseline that distinguishes string dynamics from hydrodynamic flow without assuming equilibrium.
The same fluctuating-medium setup could be used to predict other observables such as azimuthal anisotropies in small systems while remaining outside the hydrodynamic regime.
Testing the model against measured heavy-meson spectra at the LHC would directly probe whether string overlaps capture the dominant energy-loss mechanism in tiny collision volumes.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

This paper reports that heavy-flavor quarks lose noticeably less transverse momentum when they traverse a medium built from overlapping color strings than they do in the expanding hydrodynamic picture of EPOS4HQ, at least in minimum-bias p+p collisions at LHC energies. The result is presented as a preliminary estimate aimed at the debate over whether small systems produce a quark-gluon plasma droplet. The authors generate the medium from a fluctuating number of strings that arise from multi-pomeron exchanges, then let longitudinal oscillations update the local color-field energy density at each time step. Overlaps between strings create spatial and temporal fluctuations that are said to control the elastic scattering rate of charm quarks off gluons inside the string volume. A hybrid event-by-event simulation tracks the quarks from their initial hard production through this environment and computes the momentum loss. The comparison to EPOS4HQ is direct and relevant because both frameworks are applied to the same class of events. The string-based construction is a legitimate extension of existing models rather than a simple reuse, and the dynamic initialization step adds a concrete way to generate fluctuations without assuming full equilibration. The central weakness is the step that turns the fluctuating color-field energy density into a gluon scattering rate. The abstract states that the density governs the rate, yet supplies no explicit functional form, no perturbative matching, and no calibration procedure. If that relation is chosen by hand or normalized only internally, the size of the reported difference can shift without changing the underlying string dynamics. No error bands or checks against limiting cases are mentioned either. Readers already working on heavy-flavor observables in small systems or on extensions of string models will find the setup useful to examine. Anyone looking for a firm quantitative result on energy loss will need the missing technical steps before relying on the numbers. I would send the paper to referees so they can check the rate calculation and the numerical stability of the hybrid approach.

Referee Report

1 major / 2 minor

Summary. The manuscript presents preliminary estimates of heavy-flavor quark energy loss in a non-equilibrated medium formed by fluctuating color strings in minimum-bias pp collisions at LHC energies. Longitudinal string oscillations dynamically initialize the medium at each time step, with overlaps producing fluctuations in color-field energy density that govern the elastic scattering rate of HF quarks with gluons. Using an event-by-event hybrid simulation, the transverse-momentum dependence of momentum loss for charm quarks is computed and compared to the expanding hydrodynamic scenario of the EPOS4HQ model, with the central claim being significantly lower energy loss in the string medium.

Significance. If the energy-density-to-scattering-rate mapping can be placed on a firm footing, the result would be relevant to debates on QGP formation in small systems by indicating that non-equilibrated string dynamics with fluctuations yield less suppression than hydrodynamics. The event-by-event treatment of string overlaps is a methodological strength that captures realistic medium fluctuations.

major comments (1)

[hybrid approach description] The functional dependence of the elastic scattering rate on the fluctuating color-field energy density is not derived, perturbatively matched, or calibrated (see the model description following the statement that 'Their varying overlaps create fluctuations in the color field energy density that governs the elastic scattering rate'). This mapping is load-bearing for the headline quantitative claim of significantly lower energy loss relative to EPOS4HQ; different choices of the functional form (e.g., rate ∝ ε or rate ∝ ε²) could shift the reported difference by an amount comparable to the claimed effect without changing the underlying string dynamics.

minor comments (2)

[Results] The abstract refers to 'preliminary estimates' but the results section should explicitly state the number of events, statistical uncertainties, and any systematic variations in the string parameters to allow assessment of the robustness of the 'significantly lower' conclusion.
Clarify whether the charm-quark production points and initial p_T spectra are taken from the same hard-scattering generator used in the EPOS4HQ comparison or from an independent source.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and for the constructive feedback on the hybrid model description. We appreciate the positive assessment of the event-by-event string overlap treatment and its relevance to small-system QGP debates. We address the major comment below and outline planned revisions.

read point-by-point responses

Referee: The functional dependence of the elastic scattering rate on the fluctuating color-field energy density is not derived, perturbatively matched, or calibrated (see the model description following the statement that 'Their varying overlaps create fluctuations in the color field energy density that governs the elastic scattering rate'). This mapping is load-bearing for the headline quantitative claim of significantly lower energy loss relative to EPOS4HQ; different choices of the functional form (e.g., rate ∝ ε or rate ∝ ε²) could shift the reported difference by an amount comparable to the claimed effect without changing the underlying string dynamics.

Authors: We agree that the mapping from color-field energy density to elastic scattering rate is a central modeling assumption whose justification merits explicit discussion. In the current implementation the rate is taken proportional to the local energy density ε, reflecting the expectation that higher energy density within overlapping strings corresponds to a greater number of gluons available for scattering with the heavy-flavor quark. This linear ansatz is chosen for the preliminary study as a minimal, physically motivated link between the string dynamics and the interaction rate; it is not claimed to be perturbatively derived from first principles. We acknowledge that alternative forms (e.g., quadratic) could alter the quantitative difference relative to EPOS4HQ. In the revised manuscript we will (i) state the proportionality explicitly in the model section, (ii) add a short paragraph motivating the choice from the color-string picture, and (iii) include a brief discussion of the sensitivity to the functional form, noting that a full perturbative matching or calibration lies beyond the scope of this exploratory work but is planned for follow-up studies. These additions will make the assumption transparent without changing the underlying string dynamics or the reported qualitative result of lower energy loss. revision: partial

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; derivation self-contained against external benchmark

full rationale

The paper models HF quark propagation through a fluctuating color-string medium initialized by longitudinal oscillations and overlaps, with elastic scattering rates governed by the resulting color-field energy density on an event-by-event basis. The headline quantitative result is a direct comparison of computed momentum loss to the independent expanding hydrodynamic scenario of the external EPOS4HQ model. No load-bearing step reduces by construction to a fitted parameter, self-citation chain, or internal redefinition of the target observable; the simulation inputs (string dynamics, overlaps) are distinct from the external hydrodynamic reference, satisfying the criterion for a self-contained derivation against external benchmarks.

Assumptions & free parameters 0 free parameters · 1 assumptions · 0 invented entities

The model rests on standard high-energy QCD assumptions about color strings and multi-pomeron exchanges; the hybrid simulation and dynamic initialization constitute the main additions. No new particles or forces are introduced.

assumptions (1)

domain assumption Color strings originate from multi-pomeron exchanges in minimum-bias p+p collisions.
This is invoked to model the fluctuating medium in which HF quarks propagate.

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Cite this review

Pith. "Pith review of Energy loss of heavy-flavor quarks in color string medium." pith.science (2026). https://pith.science/paper/I2Y6XJF3

@misc{pith2026250924316,
  author       = {Pith},
  title        = {Pith review of: Energy loss of heavy-flavor quarks in color string medium},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/I2Y6XJF3}},
  note         = {Machine review of arXiv:2509.24316}
}

read the original abstract

The paper presents preliminary estimates of heavy-flavor (HF) quark energy loss during its propagation through the non-equilibrated medium formed in minimum bias proton-proton (p+p) collisions at LHC energies. The study is inspired by the ongoing hot debates on whether tiny droplets of Quark-Gluon Plasma can be created in collisions of small systems. In this work, we model a p+p event with a fluctuating number of color strings originated from multi-pomeron exchanges. Considered longitudinal oscillations of strings dynamically initialize medium at each time step. Their varying overlaps create fluctuations in the color field energy density that governs the elastic scattering rate of HF quarks with the gluons present within the string volume. We calculate the transverse momentum dependence of the momentum loss for charm (anti-)quarks that are produced in initial hard scatterings and traverse the described environment. The simulation is performed using a developed hybrid approach on an event-by-event basis. Our results show significantly lower HF quarks energy loss compared to that obtained in the expanding hydrodynamic scenario of the new EPOS4HQ model.

Figures

Figures reproduced from arXiv: 2509.24316 by the authors.

**Figure 2.** Transverse momentum loss of a charm quark as a function of its initial transverse momen [PITH_FULL_IMAGE:figures/full_fig_p013_2.png] view at source ↗

**Figure 3.** Transverse momentum loss of a charm quark as a function of its initial transverse momen [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗

Figures from the paper (1 more)

**Figure 4.** Figure 4: Transverse momentum loss of a charm quark as a function of its initial transverse momen [PITH_FULL_IMAGE:figures/full_fig_p014_4.png]

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ε_cell = σ √k_cell / ΔS_str ... T_eff_cell = (30 ε_cell / (16 π²))^{1/4} ... dp/dt integrals with Bose ρ(k)

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