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REVIEW 4 major objections 4 minor 46 references

Neutron Skin from Conserved Charge Measurements at Collider Experiments

T0 review · 4 major / 4 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read A double ratio of charge yields in p+Pb collisions can measure the neutron skin of 208Pb.

desk verdict A genuinely new observable for the lead neutron skin, with a clean simulation-based sensitivity study whose main vulnerability is the neglected charge diffusion, explicitly acknowledged in footnote 2. read the letter →

arxiv 2509.21644 v3 pith:263MTEDF submitted 2025-09-25 nucl-th

Grégoire Pihan , Akihiko Monnai , Björn Schenke , Chun Shen This is my paper · ORCID
classification nucl-th PACS 25.75.-q21.10.Gv24.10.Nz
keywords neutronskinlead-208proton-leadcollisionsnetelectricchargebaryonnumberrelativistichydrodynamicsLHCbsymmetryenergy
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 proposes that the neutron skin of a heavy nucleus—the excess of neutrons at the nuclear surface—can be measured at colliders through conserved charge yields in proton–lead collisions, without parity-violating electron scattering. The central observable is a double ratio: the net-electric-charge-to-net-baryon ratio in peripheral (80–100%) events divided by the same ratio in central (0–20%) events, evaluated in a forward rapidity window on the lead-going side. Using event-by-event (3+1)-dimensional relativistic hydrodynamics, the authors show this double ratio decreases approximately linearly with the neutron skin thickness of 208Pb, and that the net-charge-to-proton version in the 4.5 < y < 5.5 window at LHC collider mode is ready for near-term experimental test. Such a measurement would give a new, independent constraint on the density dependence of the nuclear symmetry energy and could help adjudicate the tension between the PREX-II result and ab initio calculations.

What carries the argument

The load-bearing object is the double ratio $R_{c_1,c_2}^{X,Y} = [N_X(c_1)/N_Y(c_1)] \div [N_X(c_2)/N_Y(c_2)]$, with $c_1 = 80\text{--}100\%$ and $c_2 = 0\text{--}20\%$. It isolates centrality-dependent changes in the ratio of net electric charge ($X=Q$) to net baryon number ($Y=B$) or to net protons ($Y=p$), so that the geometry-driven effect of the neutron-rich surface survives while overall normalization cancels. The supporting machinery is the initial-state sampling with isospin-dependent Woods–Saxon profiles whose neutron diffuseness is varied to dial $\Delta R_{np}$, followed by (3+1)-dimensional viscous hydrodynamic evolution with conserved charge currents and a charge-dependent lattice-QCD equation of state.

What would settle it

Compute the same double ratio with nonzero baryon and electric-charge diffusion coefficients in the hydrodynamic currents; if the centrality-differential shift in the 4.5 < ylab < 5.5 window at √sNN = 5.02 TeV is as large as the change produced by varying ΔRnp by 0.11 fm, the claimed sensitivity is not robust. Experimentally, an LHCb measurement of the net-charge-to-proton double ratio in that window that shows a flat or opposite centrality dependence would falsify the prediction.

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Extended reading notes

Core claim

The paper's central claim is that the centrality-dependent double ratio of net electric charge to net baryon number in p+208Pb collisions is a sensitive and robust probe of the lead neutron skin. Low-multiplicity (peripheral) events preferentially sample the nuclear surface, so they involve more proton–neutron interactions than high-multiplicity (central) events; the net electric charge per baryon is therefore suppressed in peripheral relative to central events, and this suppression grows with the neutron skin thickness. The authors compute this double ratio with a (3+1)-dimensional viscous hydrodynamic model initialized with isospin-dependent Woods–Saxon densities and baryon-junction stopping, and report an approximately linear fall of the double ratio with ΔRnp. They provide predictions at √sNN = 5.02 TeV and 72 GeV, and show that replacing net baryons by net protons, the experimentally accessible proxy, gives nearly identical results.

Load-bearing premise

The prediction assumes that dissipative diffusion of conserved charges, which is omitted from the hydrodynamic currents, affects peripheral and central events in the same way; if baryon or electric-charge diffusion differs between event classes at forward rapidity, the calibration of the double ratio to the neutron skin thickness could shift substantially.

Editorial extensions

If this is right

  • LHCb can test the collider-mode prediction by measuring the net-charge-to-proton double ratio in the 4.5 < ylab < 5.5 window for 0–20% and 80–100% centrality classes.
  • A confirmed signal would provide an independent cross-check of the PREX-II extraction of the 208Pb neutron skin.
  • Because the double ratio reacts almost linearly to ΔRnp, a single measurement would calibrate the skin thickness once the relation is fixed by the simulation.
  • The same methodology extends to other neutron-rich nuclei, such as 48Ca, and to the fixed-target 208Pb-on-hydrogen setup at SMOG2.
  • Measurements in the deeper fragmentation region 5.5 < ylab < 7.5 are predicted to be even cleaner but require detector coverage beyond current LHCb acceptance.

Reading between the lines

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

  • The calibration curve could shift if dissipative charge diffusion does not affect peripheral and central events equally; rerunning the simulation with finite baryon and electric-charge diffusion coefficients would test this directly.
  • Combining this collider-based extraction with PREX-II and the Bayesian heavy-ion extraction cited in the paper could yield a tighter joint posterior on the symmetry-energy slope L than any single method alone.
  • Because the observable is built from event-class ratios rather than absolute yields, part of the detector acceptance error may cancel; a realistic LHCb acceptance study would clarify whether the 4.5 < y < 5.5 window is indeed feasible in the near term.
  • The linear dependence on ΔRnp suggests that even an upper bound from a first measurement would already narrow the range of allowed symmetry-energy slopes, an implication the paper does not explicitly draw.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 4 minor

Summary. This paper proposes a new observable for constraining the neutron skin thickness of 208Pb in p+208Pb collisions: the double ratio of net electric charge to net baryon number (or net proton number) in forward rapidity windows, taken for peripheral (80-100%) events and divided by the same ratio for central (0-20%) events. The authors compute this observable with the iEBE-MUSIC (3+1)D viscous hydrodynamic framework, using 3D-Glauber initial conditions with baryon junctions, charge-dependent neos-4D equation of state, and a hadronic afterburner. Results are presented for LHC collider mode at 5.02 TeV and for the LHCb SMOG2 fixed-target configuration at 72 GeV. The paper finds that the double ratio decreases monotonically with increasing neutron skin thickness, with particularly clean sensitivity in collider mode, and recommends experimental measurement by LHCb.

Significance. If the central prediction is correct, this is a genuinely new and experimentally accessible avenue for neutron-skin measurements that is complementary to parity-violating electron scattering and to Bayesian analyses of flow observables. The paper has notable strengths: the observable is a forward output of a multi-stage model with no parameter fitted to the double-ratio target; the work uses a modern (3+1)D hydrodynamic description with multiple conserved charges and a lattice-QCD-based equation of state; initial-state and final-state results are compared; and the data are stated to be openly available. The proposed observable could help resolve the tension between the PREX-II result and ab initio calculations of the 208Pb neutron skin. However, several load-bearing transport assumptions are not quantitatively supported, and the predictions are presented without uncertainty quantification, so the sensitivity claim is not yet fully established.

major comments (4)
  1. [Eq. (2) and footnote 2] The neglect of dissipative diffusion in the conserved charge currents is load-bearing for the central claim, because the double ratio directly compares the longitudinal transport of electric charge and baryon number between two centrality classes. The text asserts that diffusion effects are 'similar' in the two centralities, but no quantitative estimate is provided. More seriously, footnote 2 states that including baryon diffusion can make the net electric charge vanish at midrapidity, making the ratio impractical there. If the zero crossing moves with centrality, the forward window 4.5<y<5.5 used for the main prediction could receive a centrality-dependent shift in Q/B. I ask for a quantitative test: include a baryon and charge diffusion term in Eq. (2) (even with a simple diffusion coefficient), and show that the double-ratio sensitivity to the neutron skin in the chosen rapidity window is preserved, or quantify how much the inferred skin changes when diffusion is included.
  2. [Model description, baryon stopping assumption] The assumption that baryon stopping is energy independent is a strong simplification for predictions at two very different collision energies, 72 GeV and 5.02 TeV. The text mentions that a more rigorous treatment would account for energy dependence, and later claims the observable is 'robust to variations in stopping', but no stopping parameter scan is shown. Please provide a systematic variation of the baryon-junction stopping parameters and show the resulting spread in the double ratio. Without this, the quantitative curves in Figs. 1 and 2 may be tied to one specific stopping model, which is particularly relevant because the fixed-target forward window already deviates from unity by about 20% at zero neutron skin.
  3. [Figs. 1-3 and uncertainty quantification] The predicted double-ratio curves are presented as single lines with no statistical error bars and no systematic envelope from the model inputs (Woods-Saxon radii, diffuseness parameters, shear and bulk viscosities, particlization energy density, and equation of state). Since the proposed experimental test must distinguish different values of ΔRnp, the reader needs to know the expected statistical precision of the quoted rapidity windows and the model-induced systematic uncertainty. Without this information, the statement that the probe is 'sensitive and robust' cannot be evaluated quantitatively. I recommend adding error bars from event statistics and a band from plausible variations of at least the diffuseness and viscosity parameters around their default values.
  4. [Footnote 1 and centrality selection] The entire method relies on the correlation between event activity (multiplicity) and impact parameter in p+A collisions, but footnote 1 only states that the correlation is 'sizable enough' without a quantitative measure. Because p+A collisions have weaker multiplicity-impact-parameter correlations than A+A collisions, it is important to show the impact-parameter distribution and average number of participants in the 0-20% and 80-100% classes for the specific centrality definitions used. I ask for this diagnostic, and also for a demonstration that the centrality selection itself does not introduce a bias that mimics or obscures the neutron-skin signal.
minor comments (4)
  1. [Fig. 1 caption] The caption contains a duplicated word: 'triangle and and star markers' should read 'triangle and star markers'.
  2. [Centrality definition, Section 3] The centrality classes are defined by multiplicity in rapidity intervals 1.25<y_lab<3 (collider) and 0.6<y_lab<2.6 (fixed target), but the text does not specify whether these are pseudo-rapidity or rapidity intervals. Please clarify the exact observable used for the event-activity selection.
  3. [Fig. 2 and Fig. 3 discussion] In the fixed-target forward window the double ratio deviates from unity by about 20% even at zero neutron skin; the manuscript mentions this but does not quantify the impact of this baseline on the extraction precision. A few sentences with the expected signal-to-baseline ratio would help the reader judge the practical sensitivity.
  4. [Data availability statement] The statement 'The data that support the findings of this article are openly available [41], embargo periods may apply' is vague. Please specify the repository or DOI and the embargo status, since reproducibility is a strength of this work.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the double-ratio sensitivity is a forward model output, not a fitted target or a definitional identity.

full rationale

No circular step is present. The double ratio R^{X,Y}_{c1,c2} is an event-level observable computed by forward (3+1)D hydrodynamic simulation; the neutron skin thickness ΔRnp is an input parameter varied through the Woods-Saxon neutron diffuseness Δa_np, not a parameter fitted to reproduce the double ratio. The near-unity value at ΔRnp = 0 is an explicit consistency check, and the paper identifies final-state mechanisms (thermal smearing and baryon junction stopping) that can push the ratio away from unity, showing the output is not algebraically equal to the input. The neglect of charge diffusion in Eq. (2) is a physics assumption affecting robustness of the extraction, not a definitional identity; footnote 2's caveat about midrapidity reinforces that the observable is not tautologically constructed. Self-citations provide model infrastructure (iEBE-MUSIC, 3D-Glauber, neos-4D), but the central sensitivity claim is computed, not imported from those references.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The central claim pulls its predictive power from a chain of model components: Woods-Saxon geometry, 3D-Glauber initial state with baryon junctions, charge diffusion neglect, viscosity and EoS inputs, and particlization. Most are standard or prior-calibrated, but the charge-diffusion neglect and energy-independent baryon stopping are assumptions specific to this study. No new physical entity is introduced.

free parameters (5)
  • Neutron diffuseness difference Δa_np = a_n - a_p = Varied to produce ΔRnp = 0.0, 0.11, 0.22, 0.28, 0.63 fm
    Chosen by hand as the control parameter that generates different neutron skin thicknesses; the central sensitivity claim is a function of this scan.
  • Base Woods-Saxon radii R_p^WS and R_n^WS = 6.68 fm and 6.69 fm
    Taken from Refs [13,15] representing a halo-type neutron skin; not fitted here, but the baseline geometry enters the observable.
  • Proton diffuseness a_p = 0.448 fm
    Fixed from Refs [23,24] and used to define the proton density distribution.
  • Shear and bulk viscosity parameters = η0=0.08, b=2, μB0=0.6 GeV, a=0.7, ζ0=0.1, Tpeak=0.17 GeV-0.15 GeV^-1 μB^2, widths 0.01/0.08 GeV
    Calibrated in prior works; the hydrodynamic response of charges depends on them, but they are not refit to the double ratio.
  • Hydrodynamic initial time and particlization energy density = τ_hydro = 0.5 fm/c, ε_sw = 0.2 GeV/fm^3
    Standard choices in the iEBE-MUSIC framework; they affect the longitudinal evolution and final charge distributions.
assumptions (5)
  • domain assumption Conserved charge diffusion is neglected in hydrodynamics.
    Invoked in Eq. (2) and the following paragraph; the longitudinal evolution of Q and B, which determines the double ratio, is modeled without dissipative charge currents. The authors assert centrality-similar effects without a quantitative test, and footnote 2 notes baryon diffusion can make the net charge vanish at midrapidity.
  • domain assumption Baryon stopping via baryon junctions is the same at both collision energies.
    Stated in the 3D-Glauber description; charge transport in rapidity depends on this, and the double-ratio predictions are sensitive to stopping assumptions.
  • domain assumption Event activity is sufficiently correlated with impact parameter in p+Pb to define centrality classes.
    The peripheral-versus-central comparison assumes that 80-100% multiplicity events sample the nuclear periphery and thus the neutron-rich surface layer.
  • domain assumption The lead nucleus is spherically symmetric with Woods-Saxon density profiles.
    Used in Eq. (1); nuclear deformation and detailed surface fluctuations are ignored.
  • domain assumption The neos-4D lattice-QCD-based equation of state correctly describes charge-dependent thermodynamics.
    Used for hydrodynamic evolution; extracted from prior lattice QCD work, not independently verified in this paper.

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Cite this review

Pith. "Pith review of Neutron Skin from Conserved Charge Measurements at Collider Experiments." pith.science (2026). https://pith.science/paper/263MTEDF

@misc{pith2026250921644,
  author       = {Pith},
  title        = {Pith review of: Neutron Skin from Conserved Charge Measurements at Collider Experiments},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/263MTEDF}},
  note         = {Machine review of arXiv:2509.21644}
}
abstract

We propose a novel method for measuring the neutron skin of heavy nuclei using collider experiments. Specifically, we demonstrate that the neutron skin thickness of the lead nucleus can be extracted in $p$+$^{208}$Pb collisions by analyzing a double ratio: The ratio of net electric charge to net baryon number measured near the lead-going rapidity, taken for high-multiplicity events and divided by the same ratio for low-multiplicity events. We compute the expected sensitivity of the double ratio to the neutron skin within a comprehensive (3+1)D relativistic hydrodynamic framework that incorporates multiple conserved charge currents and a charge-dependent lattice-QCD-based equation of state. We provide predictions for both $p$+$^{208}$Pb collisions at ${\sqrt{s_{\mathrm{NN}}}=72}$~GeV and $\sqrt{s_{\mathrm{NN}}}=5.02$~TeV, corresponding to the center of mass energies realized in the SMOG2 fixed-target setup at LHCb and the LHC collider mode, respectively.

Figures

Figures reproduced from arXiv: 2509.21644 by the authors.

Figure 1
Figure 1. FIG. 1. The double ratio as a function of the neutron skin [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Similar double ratios as in Fig. [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. The differential [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

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Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.