Constraining the chiral magnetic effect using spectator and participant planes across Au+Au and isobar collisions at $\sqrt{s_{_{\rm NN}}} = 200$ GeV

Bang-Xiang Chen; Guo-Liang Ma; Xin-Li Zhao

REVIEW 4 major objections 5 minor 80 references

Constraining the chiral magnetic effect using spectator and participant planes across Au+Au and isobar collisions at $\sqrt{s_{_{\rm NN}}} = 200$ GeV

T0 review · 4 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read The paper claims that the two-plane CME extraction is more reliable in Au+Au than in isobar collisions, with $b/a = 0.88 \pm 0.08$, and that Au+Au shows a stronger CME signal when the spectator plane is used.

desk verdict The b/a=0.88 result for Au+Au is a credible model output, but the paper's central claim of a stronger CME in Au+Au rests on a chi-square analysis that is internally inconsistent across the two planes and statistically fragile. read the letter →

arxiv 2501.02794 v1 pith:VNBNDRIF submitted 2025-01-06 nucl-th hep-phnucl-ex

Bang-Xiang Chen , Xin-Li Zhao , Guo-Liang Ma This is my paper · ORCID

classification nucl-thhep-phnucl-ex

keywords chiralmagneticeffecttwo-planemethodspectatorplaneparticipantcharge-dependentazimuthalcorrelationsAMPTmodelisobarcollisionsAu+Au

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 tries to establish where the chiral magnetic effect (CME) shows up most cleanly in relativistic heavy-ion collisions at 200 GeV, by comparing Au+Au collisions with the isobar systems Ru+Ru and Zr+Zr. It uses the two-plane method: the charge-separation observable $\Delta\gamma$ is measured relative to the participant plane (the overlap zone of the collision) and to the spectator plane (non-interacting nucleons, which track the magnetic field better). The central quantitative result is that the CME signal-to-background ratio between the two planes, $b/a$, is $0.88 \pm 0.08$ for Au+Au, much closer to unity than the isobar value $0.65 \pm 0.18$; because the standard extraction formula assumes $b/a=1$, a value closer to 1 means the method is less biased. A chi-square fit of the transport model to STAR data then indicates that Au+Au carries a stronger CME signal than Ru+Ru or Zr+Zr, especially when the spectator plane is used. If correct, future CME searches should favor Au+Au over isobar systems and treat the spectator-plane $\Delta\gamma$ as the more sensitive observable.

What carries the argument

The machinery is the two-plane decomposition of the charge-dependent azimuthal correlator $\Delta\gamma\{\psi\} = \Delta\gamma_{\rm Bkg}\{\psi\} + \Delta\gamma_{\rm CME}\{\psi\}$, where $\psi$ is either the spectator plane $\psi_{\rm SP}$ or the participant plane $\psi_{\rm PP}$. The ratios $a = v_2\{SP\}/v_2\{PP\}$ and $A = \Delta\gamma\{SP\}/\Delta\gamma\{PP\}$ enter the standard extraction formula $f_{\rm CME} = (A/a - 1)/(1/a^2 - 1)$, which assumes the CME signal ratio is the same as the flow ratio; the paper replaces this with $b = \Delta\gamma_{\rm CME}\{PP\}/\Delta\gamma_{\rm CME}\{SP\}$, obtained from Eq. (13) as the difference between CME-on and CME-off AMPT simulations. The key mechanism is that final-state rescattering rotates and damps the CME current, decorrelating it from the participant plane while the spectator plane keeps tracking the magnetic field direction; this decorrelation is weaker in Au+Au than in Ru+Ru, which is why $b/a$ stays closer to 1 in Au+Au.

What would settle it

In STAR data for 20–50% centrality, the spectator-plane double ratio $(\Delta\gamma/v_2)\,dN_{\rm ch}/d\eta$ should order Au+Au > Ru+Ru > Zr+Zr if the paper's chi-square conclusion is right; a measurement with small enough errors that breaks this ordering would falsify the claim of a stronger CME in Au+Au.

Watch

Extended reading notes

Core claim

The paper's central claim is that the ratio $b = \Delta\gamma_{\rm CME}\{PP\}/\Delta\gamma_{\rm CME}\{SP\}$, computed in the AMPT model by subtracting the no-CME ($p=0$) simulation from the CME-on ($p>0$) simulation via Eq. (13), is not equal to $a = v_2\{SP\}/v_2\{PP\}$, and that the discrepancy is smaller in Au+Au than in isobar collisions. In 20–50% centrality Au+Au collisions the paper finds $b/a = 0.88 \pm 0.08$, whereas its earlier isobar study found $0.65 \pm 0.18$. Because the modified two-plane formula $f_{\rm CME} = (A/a - 1)/(1/ab - 1)$ reduces to the standard formula only when $b=a$, the Au+Au value shows the correction is mild there. Stage-by-stage evolution in the AMPT model shows $b$ falling as final-state interactions decorrelate the CME current from the participant plane, but less steeply in Au+Au than in Ru+Ru. A simultaneous chi-square fit to STAR data for the three systems prefers a CME strength near 2% when the participant plane is used, but 7.5–10% for Au+Au (5–7.5% for isobars) when the spectator plane is used, which the authors read as a stronger CME signature in Au+Au.

Load-bearing premise

The central conclusion depends on the AMPT model correctly capturing how final-state rescattering rotates and damps the chiral-magnetic-effect current relative to the participant plane; if that decorrelation is unrealistic, the $b/a = 0.88$ value and the Au+Au advantage would not transfer to experiment.

Editorial extensions

If this is right

Two-plane extractions of the CME fraction should quote $f_{\rm CME}\{b\}$ using a transport-model value of $b$, rather than assuming $b=a$; in Au+Au the correction is mild, so the standard formula is a better approximation there than in isobars.
The spectator-plane $\Delta\gamma$ is the observable to focus on: the model fits require a CME strength of 7.5–10% in Au+Au versus about 2% for the participant plane, so a positive CME signal of that size should be visible in STAR data.
The stage-by-stage decrease of $b/a$ in the AMPT model means the two-plane method's reliability is system-size dependent, not a fixed property of the observable.
If Au+Au indeed has a stronger CME signature than Ru+Ru and Zr+Zr, then the isobar upper limits do not directly constrain the CME in Au+Au.
The double-ratio $\Delta\gamma/v_2 \, dN_{\rm ch}/d\eta$ with respect to the spectator plane is the discriminator that separates Au+Au from the isobar systems in the chi-square analysis.

Reading between the lines

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

If the trend $b/a \to 1$ with increasing system size is real, then the two-plane method should be even more reliable in larger collision systems such as U+U or Pb+Pb, and less reliable in smaller systems; this extrapolation is not made in the paper.
The gap between the participant-plane fit ($p \approx 2\%$) and the spectator-plane fit ($p \approx 7.5$–$10\%$) suggests the CME signal may be partly hidden in the participant-plane view; a measurement constraining both planes with better non-flow control would decide which plane carries the truth.
A natural independent test would be to compute $b$ in a different framework, such as anomalous hydrodynamics with a time-dependent magnetic field; agreement with $b/a=0.88$ for Au+Au and $0.65$ for isobars would confirm that the AMPT decorrelation mechanism is the right physics.
Because the paper uses the initial-state spectator plane as a proxy for the magnetic field direction, a direct reconstruction of the field direction (or a calculation with a fully dynamical field) could either strengthen or weaken the claimed spectator-plane advantage.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

The new thing here is an AMPT-based estimate of b/a for Au+Au collisions, 0.88 ± 0.08, using the same two-plane framework as the authors' earlier isobar study, plus a first attempt at a simultaneous three-system comparison against STAR data. The derivation of the corrected fCME{b} formula is clean, and the stage-evolution plots—showing b decreasing through the parton cascade and hadronic rescatterings—are physically sensible and useful. That part is worth reading.

The soft spot is the headline conclusion. The chi-square fits in Fig. 17 put all three systems near p≈2% when using the participant plane, but put Au+Au at 7.5–10% and the isobars at 5–7.5% when using the spectator plane. The paper interprets this as the SP being more sensitive, but that reading is not logically available: if the PP observable is insensitive to CME, then the PP fit cannot constrain p and cannot be cited as evidence for small CME; if it is sensitive, then the two planes give contradictory CME strengths for the same system. Either way, the data do not establish a stronger CME in Au+Au. The statistical basis is also thin: Eq. (14) uses only the model error, omitting experimental uncertainties, and the p grid (0, 2, 5, 7.5, 10%) is too coarse to resolve differences like 7.5% vs 5%.

The b/a difference between Au+Au and isobar is about 1.2σ when errors are combined (0.88 ± 0.08 vs 0.65 ± 0.18), so the phrase "reduced difference" is overstated. And b itself is computed from the same AMPT model that provides the simulated CME signal, with no external validation and no code or data release. That doesn't invalidate the model study, but it means the central claim is a model-dependent translation, not an independent finding.

My take: the b/a=0.88 result and the stage-evolution mechanism are worth publishing, but the "stronger CME in Au+Au" conclusion should be removed or reworked. The paper deserves peer review because a good referee can push for a combined fit with proper error propagation and a clearer statement of what the PP fits can and cannot constrain. I would not cite the central claim in its current form, but I might cite the b/a value as a model prediction.

Recommendation: send it to review, but expect the conclusion to be substantially softened in revision.

Referee Report

4 major / 5 minor

Summary. The manuscript extends the authors' previous AMPT-based two-plane study of the chiral magnetic effect (CME) from isobar collisions to Au+Au collisions at sqrt(s_NN)=200 GeV. It implements a CME-like charge separation with tunable strength p, reconstructs spectator and participant planes, and computes the ratio b = Delta-gamma_CME{PP}/Delta-gamma_CME{SP} through Eq. (13). The authors report b/a = 0.88 +/- 0.08 for Au+Au, compare it with their earlier isobar value 0.65 +/- 0.18, and perform a chi-square scan over p for Au+Au, Ru+Ru, and Zr+Zr using the double ratio Delta-gamma/(v2 dNch/deta). On this basis they claim that the two-plane method is less biased in Au+Au collisions and that Au+Au exhibits a stronger CME signal, especially with respect to the spectator plane.

Significance. The algebraic derivation of fCME{b} in Eq. (12) is correct, and the systematic use of AMPT to track a and b through the evolution stages is informative; the paper offers a falsifiable, quantitative framework for interpreting two-plane measurements. If the claimed b/a contrast and the chi-square hierarchy were statistically robust, the result would be valuable for planning Au+Au measurements. However, the central cross-system conclusion currently rests on a marginally significant b/a difference and on chi-square fits that use only model errors and a coarse p grid; the internal inconsistency between participant-plane and spectator-plane fits prevents the data from establishing the stronger-CME claim. The paper is a useful model study, but its headline conclusion is not yet supported at the claimed level.

major comments (4)

[Sec. III, Fig. 11 and Sec. IV] The headline comparison b/a(Au+Au) = 0.88 +/- 0.08 versus b/a(isobar) = 0.65 +/- 0.18 is not statistically significant: the difference is roughly 0.23 while the quadrature-summed uncertainty is about 0.20, corresponding to about 1.2 sigma. Statements in the abstract and in Sec. IV that Au+Au shows a 'reduced difference' and 'enhances the experimental reliability' therefore go beyond what the two model outputs establish. Please provide a proper propagation of the two determinations, or soften the claim to a suggestive trend.
[Sec. III, Eqs. (14)-(15) and Fig. 17] The chi-square definition in Eq. (14) uses only the model error w_o in the denominator and omits the experimental uncertainties on E_i, and the p grid is coarse (0, 2, 5, 7.5, 10%) with no confidence intervals or Delta-chi^2 thresholds. The reported differences between best-fit p values, for example Au+Au at 7.5% versus Ru+Ru at 5% and Au+Au at 10% versus Zr+Zr at 7.5%, are therefore not shown to be significant. A combined fit that includes experimental errors and reports Delta-chi^2 contours is needed before these values can support the claim of stronger CME in Au+Au.
[Sec. III, Fig. 17 panels (a)-(d)] The participant-plane fits select p about 2% for all three systems, while the spectator-plane fits select p = 7.5-10% for Au+Au and p = 5-7.5% for the isobars. The text interprets this as greater SP sensitivity, but no combined fit is performed. If the PP observable is insensitive to the CME, the PP fit cannot constrain p and cannot be used to argue that the CME is small; if it is sensitive, the two planes give mutually inconsistent CME strengths for the same systems. Either way, the present analysis does not establish that Au+Au has a stronger CME signal.
[Sec. II C, Eqs. (12)-(13) and Figs. 9-11] The value b/a = 0.88 +/- 0.08 is an internal AMPT output, computed from the same model used to generate the CME signal, and the extraction procedure is underspecified: the text does not state which p values, centrality bins, and error treatment enter the constant-fit value, and the p = 2% point is excluded 'due to its large statistical uncertainties' without a documented criterion. Because the claimed Au+Au advantage is driven by the stage-dependent decrease of b/a in Figs. 15-16, the model uncertainty on b/a (for example, from parton cross-section or string-melting parameters) should be quantified for the conclusion to be robust.

minor comments (5)

[Eq. (14)] The sum is written as 'nX k=0' and the indices k and n are inconsistent; please define all indices and clarify what 'normalized chi-square' means.
[Fig. 14] The quantity fCME{p} is plotted but never defined in the text; please add its definition or cite the precise equation from Ref. [64].
[Eqs. (2)-(5)] The notation <...> is used both for event averages in Eqs. (2)-(3) and in the double-average notation of Eqs. (4)-(5); please define the averaging convention explicitly.
[Introduction and Fig. 6 caption] There are several typographical issues, including the stray Chinese comma after 'AMPT model ，' in the introduction and inconsistent comma usage in the Fig. 6 caption.
[References] Ref. [57] is an arXiv preprint from 2024; please update it if a published version now exists.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the b correction is a model output and the Au+Au conclusion is a fit interpretation, not a circular reduction; the isobar baseline is self-cited but anchored to published STAR comparisons.

full rationale

After walking the derivation chain, I find no circular step that satisfies the hard evidence test. The quantity b is not fitted to the STAR observables it later corrects: Eq. (13) defines b as the ratio of AMPT Δγ differences between CME-on and CME-off (p≠0 vs p=0) runs, and the b/a=0.88 value is a constant fit to those model outputs, not to the experimental Δγ ratios. The p values in the Sec. III chi-square analysis (Eq. (14), Fig. 17) are tunable model inputs; the abstract's 'stronger CME in Au+Au' is a restatement of which grid point (Au+Au p=7.5-10% vs isobar p=5-7.5% in the SP panels) minimizes χ². This is a parameter constraint, not an independent prediction, so it may be statistically fragile but it is not circular. The isobar comparison is admittedly imported from the same authors' previous work ('all the calculations about Ru+Ru and Zr+Zr collisions are taken from Ref. [64]'), and the b/a=0.65 baseline is load-bearing; however, Ref. [64] is a published, externally STAR-data-anchored calculation rather than an unverified uniqueness theorem, so this self-citation does not make the derivation circular. I therefore assign score 2.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central claim depends on three fitted CME strength parameters per system and on the model assumption that AMPT correctly captures the CME signal's plane decorrelation. No new physical entities are introduced.

free parameters (3)

p_Au (CME strength in Au+Au) = PP fit: ~2%; SP fit: 7.5-10%
Percentage of initial partons given a CME-like charge separation; fitted via chi-square to STAR double ratios (Eq. 15).
p_Ru (CME strength in Ru+Ru) = PP fit: ~2%; SP fit: ~5%
Same definition; fitted to STAR data for the isobar system.
p_Zr (CME strength in Zr+Zr) = PP fit: ~2%; SP fit: ~7.5%
Same definition; fitted to STAR data.

assumptions (4)

domain assumption Background Δγ is dominated by elliptic flow and scales as v2 relative to each plane.
Used in Eqs. (6)-(12) to decompose Δγ into background and CME components; standard in the two-plane method literature.
domain assumption The CME signal component satisfies ΔγCME{PP} = b ΔγCME{SP} with b independent of centrality within 20-50%.
Eq. (10) and the constant fit b/a=0.88±0.08 in Sec. III; the form is assumed and then computed in the model.
domain assumption AMPT's initial CME implementation from Ref. [75] adequately represents the real CME current and its decorrelation during evolution.
The entire calculation of b and the chi-square fits rely on this model assumption; not independently validated.
standard math The ratio a equals <cos 2(ψPP - ψSP)>.
Standard relation from event-plane correlations, verified in Fig. 5.

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Cite this review

Pith. "Pith review of Constraining the chiral magnetic effect using spectator and participant planes across Au+Au and isobar collisions at $\sqrt{s_{_{\rm NN}}} = 200$ GeV." pith.science (2026). https://pith.science/paper/VNBNDRIF

@misc{pith2026250102794,
  author       = {Pith},
  title        = {Pith review of: Constraining the chiral magnetic effect using spectator and participant planes across Au+Au and isobar collisions at $\sqrts__\rm NN = 200$ GeV},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VNBNDRIF}},
  note         = {Machine review of arXiv:2501.02794}
}

abstract

We investigate the chiral magnetic effect (CME) in relativistic heavy-ion collisions through an improved two-plane method analysis of the $\Delta\gamma$ observable, probing $\mathcal{CP}$-symmetry breaking in strong interactions and topological properties of the QCD vacuum. Using a multiphase transport model with tunable CME strengths, we systematically compare Au+Au and isobar collisions at $\sqrt{s_{_{\rm NN}}} = 200$ GeV. We observe a reduced difference in the CME signal-to-background ratio between the spectator and participant planes for Au+Au collisions compared to isobar collisions. A comprehensive chi-square analysis across all three collision systems reveals stronger CME signatures in Au+Au collisions relative to isobar collisions, particularly when measured with respect to the spectator plane. Our findings demonstrate an enhanced experimental reliability of the two-plane method for the CME detection in Au+Au collisions.

Figures

Figures reproduced from arXiv: 2501.02794 by the authors.

**Figure 2.** FIG. 2: (Color online) The centrality dependence of elliptic flow [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** FIG. 3: (Color online) The centrality dependence of ∆ [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

Figures from the paper (14 more)

**Figure 4.** Figure 4: FIG. 4: (Color online) The centrality dependence of ∆ [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]

**Figure 5.** Figure 5: FIG. 5: (Color online) The centrality dependence of [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]

**Figure 6.** Figure 6: FIG. 6: (Color online) The centrality dependence of [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]

**Figure 7.** Figure 7: FIG. 7: (Color online) The centrality dependence of [PITH_FULL_IMAGE:figures/full_fig_p007_7.png]

**Figure 8.** Figure 8: FIG. 8: (Color online) The centrality dependence of [PITH_FULL_IMAGE:figures/full_fig_p008_8.png]

**Figure 9.** Figure 9: FIG. 9: (Color online) AMPT results on centrality dependence of [PITH_FULL_IMAGE:figures/full_fig_p008_9.png]

**Figure 10.** Figure 10: FIG. 10: (Color online) AMPT results on centrality dependence of the [PITH_FULL_IMAGE:figures/full_fig_p009_10.png]

**Figure 11.** Figure 11: FIG. 11: (Color online) The centrality dependence of [PITH_FULL_IMAGE:figures/full_fig_p009_11.png]

**Figure 12.** Figure 12: FIG. 12: (Color online) The centrality dependence of the [PITH_FULL_IMAGE:figures/full_fig_p010_12.png]

**Figure 13.** Figure 13: FIG. 13: (Color online) Upper panel: The centrality dependence of [PITH_FULL_IMAGE:figures/full_fig_p010_13.png]

**Figure 14.** Figure 14: FIG. 14: (Color online) The [PITH_FULL_IMAGE:figures/full_fig_p011_14.png]

**Figure 15.** Figure 15: FIG. 15: (Color online) Upper panel: The centrality dependence of [PITH_FULL_IMAGE:figures/full_fig_p012_15.png]

**Figure 16.** Figure 16: FIG. 16: (Color online) The centrality dependence of the ratio of [PITH_FULL_IMAGE:figures/full_fig_p012_16.png]

**Figure 17.** Figure 17: FIG. 17: (Color online) The two-dimensional normalized chi-square distribution with respect to the different CME signal [PITH_FULL_IMAGE:figures/full_fig_p013_17.png]

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