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arxiv: 2605.21222 · v2 · pith:52SJDOYOnew · submitted 2026-05-20 · ✦ hep-ph · hep-th

System-size dependence of the D⁰--D_s^+ flow splitting from early D_s^+ formation at sqrt{s_(NN)} = 5.36~TeV

Hui Du , Xiao-Wei Hao , Wei Dai , Jiaxing Zhao , Ben-Wei Zhang , Enke Wang This is my paper

Pith reviewed 2026-05-21 04:01 UTC · model grok-4.3

classification ✦ hep-ph hep-th
keywords elliptic flowD0 mesonDs+ mesonsequential hadronizationquark-gluon plasmaheavy-ion collisionshadronization chronometeroxygen-oxygen collisions
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The pith

Sequential hadronization assigns different formation temperatures to D0 and Ds+ mesons, producing a measurable elliptic-flow splitting that scales linearly with partonic flow in the 1.2 Tc to Tc window.

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

The paper investigates the elliptic-flow splitting between prompt D0 and Ds+ mesons in a heavy-quark transport model that incorporates sequential hadronization. Ds+ is taken to form at 1.2 Tc while D0 forms at Tc, which reproduces the observed ordering v2(D0) greater than v2(Ds+) and yields an enhanced Ds+/D0 ratio at low pT. The splitting in oxygen-oxygen collisions is smaller than in lead-lead collisions because the shorter 1.2 Tc to Tc evolution window competes with the initial geometric eccentricity. Across nine collision configurations the hadronic splitting shows a universal linear relation to the partonic flow increment accumulated in that temperature interval, so the splitting functions as a chronometer for when different mesons emerge from the quark-gluon plasma.

Core claim

In the sequential hadronization framework, Ds+ forms at 1.2 Tc and D0 at Tc. This produces v2(D0) greater than v2(Ds+), matching preliminary ALICE data, and an enhanced Ds+/D0 yield ratio at low pT. The hadronic splitting scales linearly with the partonic flow increment accumulated during the 1.2 Tc to Tc evolution window, establishing the D0-Ds+ flow splitting as a hadronization chronometer of the quark-gluon plasma.

What carries the argument

Sequential hadronization with Ds+ forming at 1.2 Tc and D0 forming at Tc, so that the observed hadronic elliptic-flow splitting directly tracks the partonic flow built up in the intervening temperature window.

If this is right

  • The splitting in O-O 0-20% collisions at 5.36 TeV is substantially smaller than in Pb-Pb 30-50% collisions.
  • The sequential scenario produces an enhanced Ds+/D0 yield ratio at low pT.
  • A universal linear scaling exists between the hadronic splitting and the partonic flow increment in the 1.2 Tc to Tc window.
  • The sequential scenario reproduces the v2(D0) greater than v2(Ds+) ordering reported in preliminary data.

Where Pith is reading between the lines

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

  • The linear scaling could be checked in additional small systems to map how the duration of the 1.2 Tc to Tc window changes with collision size.
  • Precision data on the splitting size might help narrow the allowed range for the formation temperatures of other heavy mesons.
  • The same chronometer idea might apply to flow differences among other pairs of heavy-flavor hadrons that form at different temperatures.

Load-bearing premise

That Ds+ forms at 1.2 Tc while D0 forms at Tc, introduced to reproduce the v2(D0) greater than v2(Ds+) ordering.

What would settle it

A measurement in O-O collisions showing v2(D0) less than or equal to v2(Ds+), or the absence of linear scaling between the splitting and the partonic flow increment across multiple collision systems.

Figures

Figures reproduced from arXiv: 2605.21222 by Ben-Wei Zhang, Enke Wang, Hui Du, Jiaxing Zhao, Wei Dai, Xiao-Wei Hao.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 5
Figure 5. Figure 5: illustrates the transverse-momentum (pT ) de￾pendence of the hadronization time difference, ∆τhad ≡ ⟨τhad(D0 )⟩ − ⟨τhad(D+ s )⟩, evaluated across nine distinct configurations encompassing various centrality classes in 0 2 4 6 8 10 12 (GeV/c) T p 0 1 2 3 4 5 ) 6 c (fm/ τ ∆ Pb-Pb 0-10% Pb-Pb 10-30% Pb-Pb 30-50% Pb-Pb 50-70% O-O 0-20% O-O 0-10% O-O 10-30% O-O 30-50% O-O 50-70% Sequential hadronization FIG. 5.… view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
read the original abstract

We investigate the elliptic-flow splitting between prompt $D^0$ and $D_s^+$ mesons within a heavy-quark transport framework with sequential hadronization, in which $D_s^+$ forms at $1.2\,T_c$ and $D^0$ at $T_c$. We present predictions for the $p_T$-differential $v_2$ and $D_s^+/D^0$ yield ratio in O--O $0$--$20\%$ collisions at $\sqrt{s_{NN}} = 5.36$~TeV, where preliminary ALICE data are available. The sequential scenario reproduces the observed $v_2(D^0) > v_2(D_s^+)$ ordering and predicts an enhanced $D_s^+/D^0$ ratio at low $p_T$, whereas a simultaneous baseline yields the opposite ordering. Decomposing the hadronic splitting into its partonic components, we show that the $v_2$ ordering is driven by the late-stage flow accumulated by $D^0$-parent charm quarks during the $1.2\,T_c \to T_c$ interval, with hadronic rescattering essential to preserve the signal in small systems. A systematic scan across nine collision configurations spanning O--O and Pb--Pb centralities reveals a universal linear scaling between the hadronic splitting and the partonic flow increment accumulated during this window. This establishes the $D^0$--$D_s^+$ flow splitting as a hadronization chronometer of the QGP at $\sqrt{s_{NN}} = 5.36$~TeV.

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

2 major / 0 minor

Summary. The manuscript investigates the elliptic-flow splitting between prompt D^0 and D_s^+ mesons in O-O and Pb-Pb collisions within a heavy-quark transport framework that incorporates sequential hadronization, with D_s^+ forming at 1.2 T_c and D^0 at T_c. It presents predictions for the p_T-differential v_2 and the D_s^+/D^0 yield ratio in 0-20% O-O collisions at 5.36 TeV, reproduces the v_2(D^0) > v_2(D_s^+) ordering from preliminary ALICE data, contrasts this with a simultaneous hadronization baseline, and reports a universal linear scaling between the hadronic splitting and the partonic flow increment accumulated in the 1.2 T_c to T_c window across nine collision configurations, thereby proposing the splitting as a QGP hadronization chronometer.

Significance. If the sequential formation temperatures receive independent justification, the reported linear scaling could establish a useful new chronometer for the duration of the hadronization phase. The systematic scan across multiple collision systems and the explicit comparison to simultaneous hadronization constitute strengths that enhance the potential impact of the observable for future heavy-ion experiments.

major comments (2)
  1. The formation temperatures (D_s^+ at 1.2 T_c and D^0 at T_c) are introduced explicitly to reproduce the v_2(D^0) > v_2(D_s^+) ordering observed in preliminary ALICE data. This choice is load-bearing for the sequential hadronization scenario and for the extraction of the claimed universal linear scaling; without independent support from lattice calculations or potential models, the chronometer interpretation risks circular dependence on the same data it aims to explain.
  2. The universality of the linear scaling is obtained from a scan across collision configurations that all share the identical fixed temperature thresholds. It remains to be shown whether the linearity and the sign of the splitting survive if the formation temperatures are varied or replaced by a simultaneous baseline, which could alter the central claim.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thorough review and valuable feedback on our manuscript. We address each of the major comments in detail below and outline the revisions we will make to strengthen the presentation and robustness of our results.

read point-by-point responses

  1. Referee: The formation temperatures (D_s^+ at 1.2 T_c and D^0 at T_c) are introduced explicitly to reproduce the v_2(D^0) > v_2(D_s^+) ordering observed in preliminary ALICE data. This choice is load-bearing for the sequential hadronization scenario and for the extraction of the claimed universal linear scaling; without independent support from lattice calculations or potential models, the chronometer interpretation risks circular dependence on the same data it aims to explain.

    Authors: We acknowledge the referee's concern regarding the motivation for the specific formation temperatures. While the temperatures are chosen such that the model reproduces the observed ordering, this is not the sole basis; the sequential scenario is motivated by the physical expectation that the Ds+ meson, containing a strange quark, hadronizes at a higher temperature than the D0 due to differences in binding energies and coupling to the medium, as suggested by various potential models. In the revised version, we will expand the discussion in the introduction and methodology sections to include citations to relevant lattice QCD studies and potential model calculations that support earlier formation for strange hadrons. This will help mitigate any appearance of circularity by grounding the choice in independent theoretical input, while the data serves as a validation. revision: yes

  2. Referee: The universality of the linear scaling is obtained from a scan across collision configurations that all share the identical fixed temperature thresholds. It remains to be shown whether the linearity and the sign of the splitting survive if the formation temperatures are varied or replaced by a simultaneous baseline, which could alter the central claim.

    Authors: We appreciate this point, which highlights the need to demonstrate robustness. The manuscript does include a simultaneous hadronization baseline where both species form at Tc, leading to a reversal of the v2 ordering and no splitting in the manner described. This effectively tests the case with zero temperature window. For variations in the formation temperatures, we agree that additional checks would be beneficial. In the revised manuscript, we will include a new figure or subsection showing the scaling for a slightly varied Ds+ formation temperature in selected systems (e.g., O-O and one Pb-Pb centrality), confirming that the linear relation holds with a slope proportional to the accumulated flow in the adjusted interval. This will support the claim that the splitting acts as a chronometer sensitive to the duration of the hadronization phase. revision: yes

Circularity Check

1 steps flagged

Sequential hadronization temperatures (1.2 Tc for Ds+, Tc for D0) chosen to reproduce observed v2 ordering, making chronometer claim dependent on tuned ansatz

specific steps
  1. fitted input called prediction [Abstract]
    "within a heavy-quark transport framework with sequential hadronization, in which D_s^+ forms at 1.2 T_c and D^0 at T_c. ... The sequential scenario reproduces the v_2(D^0) > v_2(D_s^+) ordering observed in preliminary ALICE data ... A systematic scan across nine collision configurations reveals a universal linear scaling between the hadronic splitting and the partonic flow increment accumulated during this window, establishing the D^0--D_s^+ flow splitting as a hadronization chronometer of the quark-gluon plasma."

    The temperatures 1.2 Tc (Ds+) and Tc (D0) are introduced specifically so that the model reproduces the observed v2 ordering; the linear scaling and chronometer interpretation are then obtained from scans that all employ these same fixed thresholds. The claimed universality therefore measures flow accumulation inside a window whose boundaries were tuned to the data rather than fixed independently.

full rationale

The derivation begins by adopting a sequential hadronization framework with fixed formation temperatures selected to match the ALICE v2(D0) > v2(Ds+) ordering. A systematic scan across collision systems then extracts a linear scaling between hadronic splitting and partonic flow in the 1.2 Tc–Tc window, which is presented as establishing a universal chronometer. Because the temperature thresholds are not derived from lattice QCD, potential models, or coalescence calculations but are instead introduced to reproduce the data sign, the scaling and chronometer interpretation are extracted inside a framework whose key input already encodes the target splitting behavior. This constitutes a fitted-input-called-prediction pattern with moderate circularity; the O–O predictions remain new but the central interpretive claim reduces to the modeling choice.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The framework depends on two tuned formation temperatures and the assumption that the transport model correctly evolves charm quarks through the QGP; no new particles or forces are postulated.

free parameters (2)
  • Ds+ formation temperature = 1.2 Tc
    Set to 1.2 Tc to implement sequential hadronization and reproduce the v2 ordering seen in data.
  • D0 formation temperature = Tc
    Set to Tc as the standard critical temperature for light-hadron formation.
axioms (1)
  • domain assumption Heavy-quark transport accurately captures charm-quark diffusion and flow development in the QGP.
    Core assumption of the model used to generate all predictions.

pith-pipeline@v0.9.0 · 5838 in / 1442 out tokens · 58642 ms · 2026-05-21T04:01:35.273475+00:00 · methodology

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