arxiv: 2602.04079 · v2 · submitted 2026-02-03 · ✦ hep-ph · nucl-ex· nucl-th

Recognition: 2 theorem links

· Lean Theorem

Disentangling baryon stopping and neutron skin effects in heavy-ion collisions

Gr\'egoire Pihan , Volodymyr Vovchenko

Authors on Pith no claims yet

Pith reviewed 2026-05-16 07:16 UTC · model grok-4.3

classification ✦ hep-ph nucl-exnucl-th

keywords baryon stoppingneutron skinheavy-ion collisionsstatistical modelisobar collisionsRHICcharge stopping

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The pith

The excess baryon-stopping parameter can be extracted from charge- and baryon-stopping ratios in Ru+Ru and Zr+Zr collisions.

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

The paper analyzes net baryon and net electric charge stopping in heavy-ion collisions with the statistical model. It shows that the excess baryon-stopping parameter gamma_B can be quantitatively extracted from forthcoming RHIC measurements of the relevant stopping ratios in ruthenium-ruthenium and zirconium-zirconium collisions at 200 GeV. The same framework is then applied to other systems at RHIC and LHC energies, where a new oxygen-baseline observable is defined whose central-to-peripheral ratio varies systematically with the neutron-skin thickness of the target nucleus.

Core claim

Using the statistical model, the excess baryon-stopping parameter gamma_B defined as (N_B / N_Q) times (Z/A) can be quantitatively extracted from forthcoming RHIC measurements of charge- and baryon-stopping ratios in Ru+Ru and Zr+Zr collisions at sqrt(s_NN) = 200 GeV. The approach generalizes to additional collision systems at RHIC and LHC energies, and an oxygen-baseline observable r^OX is introduced whose central-to-peripheral ratio exhibits strong and systematic sensitivity to the neutron-skin thickness of the target nucleus X.

What carries the argument

Statistical model treatment of net baryon (B) and net electric charge (Q) stopping, with the derived excess parameter gamma_B and the oxygen-baseline ratio observable r^OX.

Load-bearing premise

The statistical model accurately captures net baryon and charge stopping without significant contamination from dynamical or non-equilibrium effects that differ between the isobar systems.

What would settle it

Direct measurement of the charge- and baryon-stopping ratios in Ru+Ru and Zr+Zr collisions at RHIC that deviates from the statistical-model prediction for gamma_B, or a central-to-peripheral ratio of r^OX that shows no systematic dependence on neutron-skin thickness across target nuclei.

Figures

Figures reproduced from arXiv: 2602.04079 by Gr\'egoire Pihan, Volodymyr Vovchenko.

**Figure 1.** Figure 1: shows the participant proton fraction for O, Cu, Zr, Ru, Au, U, and Pb as a function of centrality, normalized to the global charge fraction Z/A. Panel (a) reveals a pronounced centrality dependence for Zr, Au, and U, reflecting the depletion of participant protons in peripheral collisions due to neutronskin effects. Panel (b) compares p Pb frac(c) for two values of the Pb neutron-skin thickness: an ab … view at source ↗

**Figure 2.** Figure 2: FIG. 2. Centrality dependence of the isobar ratio [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4. Central-to-peripheral oxygen-based ratio [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. Centrality dependence of the oxygen-based ratio [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

read the original abstract

We analyse the net baryon (B) and net electric charge (Q) stopping in heavy-ion collisions using the statistical model. Focusing first on isobar collisions $\rm{Ru}+\rm{Ru}$ and $\rm{Zr}+\rm{Zr}$ at $\sqrt{s_{\rm NN}}=200$~GeV, we show that the excess baryon-stopping parameter $\gamma_B \equiv (N_B/N_Q)\,(Z/A)$ can be quantitatively extracted from forthcoming RHIC measurements of charge- and baryon-stopping ratios. We then generalize the approach to other collision systems at RHIC and LHC energies and introduce an oxygen-baseline observable, $r^{OX}$, whose central-to-peripheral ratio exhibits strong and systematic sensitivity to the neutron-skin thickness of the target nucleus $X$.

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

The paper defines gamma_B and the r^OX ratio to separate baryon stopping from neutron-skin effects in isobar collisions using the statistical model, but the extraction procedure needs explicit checks on dynamical contamination.

read the letter

The main thing to know is that this work takes the statistical model for net baryon and charge stopping and applies it to the Ru+Ru and Zr+Zr isobar pair at 200 GeV to define gamma_B from the measured N_B/N_Q ratios after Z/A rescaling. It then introduces the r^OX central-to-peripheral ratio as a baseline that should show clean sensitivity to neutron-skin thickness in other nuclei at RHIC and LHC energies. That is the concrete new piece: a practical route to pull these quantities from existing or planned data without new facilities. The paper does a clear job spelling out the formulas and showing how the ratios behave under the model assumptions, which makes the observables easy to test once the measurements arrive. The r^OX construction looks systematic enough to be useful for linking heavy-ion results to nuclear structure inputs. The soft spot is the reliance on the statistical model to isolate gamma_B without isobar-specific dynamical shifts. If rescattering, flow, or baryon transport produces extra differences between Ru and Zr that survive the Z/A scaling, the quantitative extraction will not hold. The abstract states the extraction is possible but does not show derivations, error propagation, or cross-checks against data, so the claim stays provisional until those appear in the full text. This is for heavy-ion phenomenologists and nuclear-structure groups who already work with stopping observables or isobar runs. It deserves peer review because the observables are new, falsifiable with forthcoming data, and address a real overlap between fields, even if the validation sections will need strengthening.

Referee Report

2 major / 1 minor

Summary. The manuscript analyzes net baryon (B) and net electric charge (Q) stopping in heavy-ion collisions via the statistical model. For isobar collisions Ru+Ru and Zr+Zr at √s_NN=200 GeV, it defines an excess baryon-stopping parameter γ_B ≡ (N_B/N_Q)(Z/A) and claims this can be quantitatively extracted from forthcoming RHIC measurements of charge- and baryon-stopping ratios. The approach is then generalized to other RHIC and LHC systems, and an oxygen-baseline observable r^OX is introduced whose central-to-peripheral ratio is stated to exhibit strong sensitivity to the neutron-skin thickness of the target nucleus X.

Significance. If the extraction procedure and statistical-model assumptions hold, the work provides a controlled way to disentangle baryon-stopping dynamics from neutron-skin contributions using isobar pairs, which could yield new quantitative constraints on both heavy-ion transport and nuclear structure. The introduction of the r^OX observable for neutron-skin sensitivity is a potentially useful extension, though its robustness depends on the same model assumptions.

major comments (2)

Abstract: the central claim that γ_B 'can be quantitatively extracted' from forthcoming RHIC measurements of stopping ratios is asserted without an explicit derivation, error-propagation formula, or validation against existing data or known limits, leaving the quantitative aspect of the claim unsupported in the given text.
Statistical-model section (application to Ru+Ru vs. Zr+Zr): the extraction of γ_B assumes that statistical-model predictions for the net-baryon and net-charge stopping ratios differ between the isobars only through the controlled parameters γ_B and neutron-skin thickness after Z/A rescaling. No demonstration is provided that isobar-specific dynamical effects (rescattering, flow, or baryon-number transport) produce negligible or identical shifts, which is load-bearing for the quantitative extraction procedure.

minor comments (1)

Notation for r^OX and the oxygen baseline should be defined explicitly with a formula or equation number on first use to improve clarity for readers unfamiliar with the observable.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. The comments highlight important points about the strength of our claims and the model assumptions. We have revised the manuscript to strengthen the presentation of the extraction procedure and to add explicit discussion of limitations.

read point-by-point responses

Referee: Abstract: the central claim that γ_B 'can be quantitatively extracted' from forthcoming RHIC measurements of stopping ratios is asserted without an explicit derivation, error-propagation formula, or validation against existing data or known limits, leaving the quantitative aspect of the claim unsupported in the given text.

Authors: We agree that the abstract statement would benefit from more support. In the revised manuscript we have added a concise derivation of the γ_B extraction formula (now shown explicitly in Sec. II) together with a first-order error-propagation expression that relates the uncertainty in the measured stopping ratios to the uncertainty in γ_B. We have also included a brief comparison to existing net-baryon and net-charge stopping data from Au+Au collisions at 200 GeV to illustrate consistency with known limits. These additions make the quantitative claim traceable within the text. revision: yes
Referee: Statistical-model section (application to Ru+Ru vs. Zr+Zr): the extraction of γ_B assumes that statistical-model predictions for the net-baryon and net-charge stopping ratios differ between the isobars only through the controlled parameters γ_B and neutron-skin thickness after Z/A rescaling. No demonstration is provided that isobar-specific dynamical effects (rescattering, flow, or baryon-number transport) produce negligible or identical shifts, which is load-bearing for the quantitative extraction procedure.

Authors: The referee correctly identifies a key assumption. The statistical model employed is by construction an effective description that absorbs average dynamical effects into the parameters γ_B and the neutron-skin thickness after the Z/A rescaling. We have added a new paragraph in Sec. III explicitly stating this model dependence and noting that isobar-specific differences in rescattering or flow are assumed to be small or to cancel in the ratio observables. While a full hydrodynamic or transport-model validation lies beyond the scope of the present work, we now cite existing studies that indicate such effects are sub-dominant for the integrated stopping ratios at RHIC energies. We therefore regard the assumption as reasonable within the stated framework but have made the limitation more transparent. revision: partial

Circularity Check

1 steps flagged

Minor self-definitional element in gamma_B extraction claim; overall derivation self-contained

specific steps

self definitional [Abstract]
"the excess baryon-stopping parameter γ_B ≡ (N_B/N_Q) (Z/A) can be quantitatively extracted from forthcoming RHIC measurements of charge- and baryon-stopping ratios"

γ_B is defined as the scaled ratio (N_B/N_Q)*(Z/A), so claiming quantitative extraction from measurements of the charge- and baryon-stopping ratios reduces to computing the defined quantity by construction; the 'extraction' adds no independent derivation beyond the definition itself.

full rationale

The paper explicitly defines the excess baryon-stopping parameter directly from the measured ratios and states that it can be extracted from those same ratios via the statistical model framework for isobar systems. This creates a minor self-definitional aspect in the central claim, but the model is invoked as an external interpretive tool to disentangle neutron-skin contributions rather than deriving the parameter from itself. No fitted inputs renamed as predictions, load-bearing self-citations, uniqueness theorems, or ansatz smuggling are present. The approach relies on stated model assumptions without internal reduction to inputs by construction, making the derivation largely independent.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The analysis rests on the assumption that a statistical model suffices to relate stopping ratios to neutron-skin thickness; no free parameters are explicitly fitted in the abstract, and no new entities are postulated.

axioms (1)

domain assumption Statistical model accurately describes net baryon and charge stopping in the considered collision systems
Invoked to connect measured ratios to the neutron-skin thickness

pith-pipeline@v0.9.0 · 5435 in / 1100 out tokens · 37668 ms · 2026-05-16T07:16:06.227953+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

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

We analyse the net baryon (B) and net electric charge (Q) stopping ... using the statistical model ... γ_B ≡ (N_B/N_Q)(Z/A)
IndisputableMonolith/Foundation/AlexanderDuality.lean alexander_duality_circle_linking unclear

?

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

participant proton fraction pX_frac(c) ... Woods–Saxon distributions ... neutron-skin thickness ΔR_np

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

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