{"id":"5c7d157a-77ba-4067-8884-f1297805392a","arxiv_id":"2505.05046","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"In Ru+Ru and Zr+Zr collisions at 200 GeV, STAR finds Lambda polarization growing toward peripheral collisions, a first 2.4-sigma hint of in-plane-enhanced polarization, and a 2.9-sigma positive Xi polarization.","lead":"The STAR collaboration measured how often hyperons produced in Ru+Ru and Zr+Zr collisions at RHIC spin along the rotation direction of the collision fireball. The new results include a first hint that Lambda hyperons emitted in-plane are more polarized, and a positive Xi hyperon polarization.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Missing Res(Ψ2) correction in Eqs. (5)-(12) makes the Py,c2 extraction non-reproducible and could shift the 2.4σ in-plane polarization claim.","rationale":"The reader's weakest assumption correctly identifies the missing second-order event-plane resolution treatment as the most load-bearing concern. The first extraction of Py,c2 is a headline new result, and the equations presented in Sec. 3.4 do not show any Res(Ψ2) factor, while the systematic section's claim of a sub-0.1% resolution effect is difficult to reconcile with a resolution of about 0.6 unless the correction is applied elsewhere. The same ambiguity affects Res(Ψ1) in Eq. (5), yet the paper reports consistency between Py,c0 and PH, implying the resolution is somehow handled. This internal tension makes it impossible for a reader to reproduce the central claim from the manuscript. With Res(Ψ2) ~ 0.6, an uncorrected extraction could shift Py,c2 by tens of percent, materially affecting the 2.4σ significance. The Ξ polarization discrepancy (two methods differing by ~2σ) is acknowledged by the paper and is secondary to this issue, as the resolution problem directly undermines the headline azimuthal result. The reader's CONDITIONAL verdict remains appropriate; our concern does not move it, only reinforces it. An honest, concrete check — re-deriving the equations with explicit resolution factors and recomputing the coefficient — would settle whether the published value is correct or whether the manuscript needs a correction.","tokens_in":16119,"tokens_out":9880,"duration_ms":95167,"concrete_test":"Independently re-derive Eq. (6) from the event-plane formalism of Ref. [36] with the measured Ψ2 as a proxy for the reaction plane, tracking whether a factor Res(Ψ2) must multiply the right side. Then recompute Py,c2 in 20-50% centrality using the reported raw moment divided by Res(Ψ2) (and also check Eq. (5) for Res(Ψ1)); if the value moves by more than the quoted total uncertainty, the paper must state the resolution-correction procedure explicitly or amend the equations.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central new result, Py,c2 > 0 at 2.4σ in 20-50% centrality, is extracted from Eqs. (5)-(12) using the measured second-order event plane Ψ2 from TPC tracks as a proxy for the reaction plane. The text states (Sec. 3.4) that Ψ2 is used as a proxy and that Λ/anti-Λ tracks are excluded to avoid self-correlation, but neither the equations nor the systematic accounting display a resolution correction factor analogous to the explicit Res(Ψ1) in Eq. (1). The observed moment ⟨sin(Ψ1−ϕ*B) cos[2(ϕH−Ψ2)]⟩ is attenuated by the finite Ψ2 resolution; with Res(Ψ2) ≈ 0.60 in 20-50% (Fig. 2), omitting this correction would bias Py,c2 by roughly 40% (factor 1/0.6), changing the size and significance of the in-plane polarization claim. The situation is confusing rather than clearly wrong: Eq. (5) faces the same issue for Res(Ψ1), yet Fig. 7 shows Py,c0 from solving Eqs. (5)-(8) agrees with PH from Eq. (1), which explicitly divides by Res(Ψ1). This agreement is only possible if the left-side moments are already resolution-corrected in the analysis, or if the resolution factors are absorbed into A0/A2, neither of which is stated. Sec. 3.5 says the systematic uncertainty from event-plane resolution is below 0.1%, which is hard to reconcile with a 40% uncorrected effect. Either the correction is applied and the equations omit it—making the analysis non-reproducible—or it is not applied and the quoted Py,c2 is biased. A reader cannot tell which from the manuscript.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper reports measurements of the global polarization of Λ, ¯Λ, Ξ−, and ¯Ξ+ hyperons in Ru+Ru and Zr+Zr collisions at √sNN = 200 GeV using STAR data. The analysis uses standard invariant-mass and event-plane methods, with signal extraction cross-checked by three techniques, and reports statistical and systematic uncertainties. The main results are: a Λ+¯Λ polarization of about 0.31% in 20–50% centrality that rises toward peripheral collisions and is consistent with Au+Au results; no significant Λ–¯Λ splitting; no significant pT or η dependence; a first extraction of the second-order azimuthal coefficient of the polarization, Py,c2 = 0.138 ± 0.038 (stat) ± 0.058 (syst) in 20–50% centrality, interpreted as enhanced in-plane polarization at the 2.4σ level; and a positive Ξ−+¯Ξ+ polarization of 0.61 ± 0.21 (stat) ± 0.04 (syst) in 20–50% centrality from the polarization-transfer method. The manuscript concludes that the data are qualitatively consistent with hydrodynamic calculations including shear-induced polarization and show no obvious system-size dependence relative to Au+Au.","tokens_in":16446,"tokens_out":5579,"duration_ms":53172,"significance":"If the central results hold, this is the first measurement of the second-order azimuthal modulation of the global polarization in isobar collisions, providing a new observable that can discriminate between thermal-vorticity and shear-induced contributions in spin-hydrodynamic models. The data set is large (1.8–2.0 billion events per system), the analysis uses well-established methods, and the paper includes useful cross-checks: three signal-extraction techniques, an explicit comparison with Au+Au results, and comparisons with AMPT+MUSIC calculations under two spin-relaxation scenarios. The paper also reports feed-down caveats and does not overstate the Λ–¯Λ splitting. However, the headline claims rest on modest significances (2.4σ and 2.9σ), and there are unresolved internal tensions, most notably the missing documentation of the second-order event-plane resolution correction and a ~2σ discrepancy between the two Ξ polarization methods. These issues must be addressed before the results can be considered quantitatively reliable.","major_comments":[{"comment":"The equations for extracting Py,c0 and Py,c2 do not display a resolution correction for the second-order event plane. Eq. (1) explicitly divides by Res(Ψ1), but Eqs. (5)–(12) use Ψ2 as a proxy for ΨRP with no analogous factor. Since Res(Ψ2) ≈ 0.60 in 20–50% centrality (Fig. 2), the moment ⟨sin(Ψ1−ϕ*_B) cos[2(ϕ_H−Ψ2)]⟩ is attenuated by the Ψ2 resolution; omitting this factor changes the extracted Py,c2 by roughly 40%, directly affecting the size and significance of the in-plane polarization claim. The statement in Section 3.5 that the event-plane-resolution systematic is below 0.1% is hard to reconcile with this unless the moments are already resolution-corrected and the equations simply omit the factor, which would make the analysis non-reproducible as written. Please state explicitly whether the left-hand sides of Eqs. (5)–(12) are corrected for Res(Ψ1) and/or Res(Ψ2), show the correction factors used, and explain the 0.1% systematic estimate in light of a ∼40% uncorrected effect.","section":"Section 3.4, Eqs. (5)–(12) and Section 3.5"},{"comment":"The quoted 2.4σ significance for Py,c2 = 0.138 ± 0.038 (stat) ± 0.058 (syst) does not follow from the stated uncertainties. Combining the two uncertainties in quadrature gives sqrt(0.038² + 0.058²) ≈ 0.069, so the significance is approximately 2.0σ; the value 0.138/0.058 ≈ 2.4 corresponds to the systematic uncertainty alone. Please specify how the significance level was computed and quote the combined-statistical-plus-systematic significance, since the current presentation appears to overstate the result.","section":"Section 4.2, Fig. 8"},{"comment":"The two methods used to measure Ξ polarization give results that differ by about 2σ in the 20–50% centrality bin: PΞ = 0.61 ± 0.21 (stat) ± 0.04 (syst) via polarization transfer versus PΞ = −0.32 ± 0.39 (stat) ± 0.08 (syst) via direct measurement of the daughter Λ distribution. Because both methods are expected to measure the same physical quantity, presenting the polarization-transfer result as a 2.9σ positive observation without resolving this discrepancy is problematic. The authors should either provide a combined estimate, investigate possible sources of the difference (e.g., background treatment or feed-down), or temper the claim accordingly.","section":"Section 4.3, Fig. 9"}],"minor_comments":[{"comment":"There are numerous typographical and formatting issues, including inconsistent spacing in \"Ru +Ru\", \"Zr+Zr\", \"di fference\", and occasionally missing √ before sNN in the text and figure captions. These should be corrected.","section":"Throughout"},{"comment":"The notation Py,c(2n) is not defined; the reader must infer that it refers to the coefficient of cos[2n(ϕH−ΨRP)]. Please define it explicitly.","section":"Section 3.4, Eq. (3)"},{"comment":"The text states that A0 and A2 are extracted directly from the data, but it does not describe how the acceptance function A(pH, p*) is estimated. A brief description of this extraction would improve reproducibility.","section":"Section 3.4, Eqs. (7)–(8)"},{"comment":"The definition of Res(Ψn) = ⟨cos[n(Ψobs_n − Ψn)]⟩ uses the true event-plane angle Ψn, but this quantity is not directly accessible in data; the sentence could clarify that it is estimated using the two-sub-event method.","section":"Section 3.3"},{"comment":"Reference [62] cites a private communication; if the calculation details are not publicly available, the authors should ensure that the quoted model predictions can be verified by interested readers.","section":"References"}],"recommendation":"major_revision","confidential_remarks":"The manuscript presents an interesting and potentially important measurement, but the missing documentation of the second-order event-plane resolution correction directly affects the main new observable, and the quoted significance for Py,c2 appears inconsistent with the stated uncertainties. The Ξ polarization discrepancy between the two methods also needs to be confronted before the positive Ξ claim can be accepted. These issues seem fixable within the scope of a revision, assuming the resolution correction was actually applied and can be documented; if it was not applied, the central result would need to be re-derived. I therefore recommend major revision rather than rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things to know. This is the first global-polarization result in isobar Ru+Ru/Zr+Zr collisions, and the first extraction of Py,c2 — the azimuthal modulation of Lambda polarization relative to the second-order event plane. Both headline numbers are modest (2.4σ in-plane-enhanced Py,c2 in 20-50%; 2.9σ Xi polarization from the polarization-transfer method), but they are genuinely new and feed directly into the shear-vs-thermal-vorticity debate. The second thing to know: the equations behind Py,c2 do not display the event-plane resolution correction, and nobody should use that number as a benchmark until the treatment is written out.\n\nThe paper does solid, standard work. Invariant-mass plus event-plane extraction with three cross-check methods, honest per-bin statistical and systematic uncertainties, and a clear in-text acknowledgment that the two Xi methods disagree at about 2σ. Lambda and anti-Lambda agree with each other, the results sit on top of Au+Au at 200 GeV with no obvious system-size dependence, and the MUSIC+AMPT comparison is qualitative rather than overclaimed. The null Lambda/anti-Lambda splitting and the Ru-vs-Zr difference bound the magnetic-field story at current precision. Citation practice is normal for a collaboration paper.\n\nThe soft spot is the one the stress-test flags, and it is real but probably not fatal. Eqs. (5)-(12) write moments against Psi2 with no division by Res(Psi2), even though Eq. (1) explicitly divides by Res(Psi1), and Sec. 3.5's claim that resolution systematics are below 0.1% does not tell you which quantities were corrected. With Res(Psi2) around 0.6 in 20-50%, that is a large attenuation factor. But Fig. 7 is the key internal check: Py,c0 from the coupled equations agrees with the azimuthally-integrated PH from Eq. (1), which only works if the moments were already resolution-corrected in the analysis. So the likely story is under-documentation rather than a biased headline, but the paper is non-reproducible as written, and the quoted Py,c2 and its 2.4σ could shift once the correction is made explicit. A referee should demand the corrected equations and the numerical impact.\n\nMinor points: the 2σ method spread for Xi means the positive claim rests on one method; the paper says so, and the significance is honestly hedged. Also ref. [65] looks unrelated to the vorticity discussion it sits in — probably a reference-list glitch, but worth a check.\n\nBottom line: this is for the spin-polarization heavy-ion community, and it deserves a serious referee. Send it to review, with the request that the resolution treatment and its effect on Py,c2 be stated explicitly before acceptance.","headline":"First isobar-collision hyperon polarization and first Py,c2 extraction, both at modest significance — worth refereeing once Eqs. (5)-(12) show the event-plane resolution treatment.","tokens_in":16971,"tokens_out":9151,"would_cite":true,"duration_ms":87900,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["25.75.-q","25.75.Ld","24.70.+s"],"model":"deepseek-v4-flash","headline":"This paper extracts the first second-order azimuthal coefficient of Lambda global polarization in isobar Ru+Ru and Zr+Zr collisions, finding in-plane enhanced polarization at 2.4 sigma, and reports a positive Xi polarization at 2.9 sigma.","keywords":["global polarization","hyperon polarization","vorticity","Lambda hyperon","Xi hyperon","isobar collisions","event plane","shear-induced polarization"],"falsifier":"Recompute $P_{y,c2}$ after applying the second-order event-plane resolution correction $1/\\mathrm{Res}(\\Psi_2)$ or a scalar-product estimator; if the corrected value moves by more than the quoted 0.058 percent systematic uncertainty or its significance falls below roughly 2$\\sigma$, the in-plane enhancement claim fails. A second decisive check is to repeat the extraction using $\\Psi_2$ from each sub-event separately and compare the two results.","tokens_in":15894,"feed_emoji":"🌀","tokens_out":13719,"duration_ms":119188,"temperature":0.7,"pith_summary":"The paper reports precision hyperon spin measurements from 1.8 billion Ru+Ru and 2.0 billion Zr+Zr collisions at 200 GeV, and its new results concern how that spin tracks the collision geometry. Its headline finding is a first extraction of the second-order azimuthal coefficient of Lambda polarization, $P_{y,c2}=0.138\\pm0.038\\,(\\mathrm{stat})\\pm0.058\\,(\\mathrm{syst})$ percent for 20-50% centrality, meaning hyperons emitted in the reaction plane are more polarized than out-of-plane ones at 2.4$\\sigma$. It also reports a positive Xi plus anti-Xi polarization, $P_{\\Xi^-+\\bar{\\Xi}^+}=0.61\\pm0.21\\,(\\mathrm{stat})\\pm0.04\\,(\\mathrm{syst})$ percent at 2.9$\\sigma$, obtained through the polarization-transfer method. These measurements matter because the azimuthal modulation is predicted to differ between purely vortical and shear-influenced hydrodynamics, so they offer a new way to identify the mechanism that polarizes quarks in the quark-gluon plasma. The broader pattern is consistent with earlier gold-gold data: polarization rises toward peripheral collisions, shows no particle-antiparticle splitting, and no obvious system-size dependence.","feed_headline":"Isobar collisions reveal in-plane Lambda polarization at 2.4 sigma","feed_subtitle":"First angle-resolved Lambda polarization plus positive Xi signal trace vorticity at 200 GeV.","key_machinery":"The carrying object is the hyperon decay asymmetry: because $\\Lambda \\to p \\pi^-$ violates parity, the mean of $\\sin(\\Psi_1-\\phi^*_B)$ in the hyperon rest frame measures polarization along the system angular momentum, with the first-order event plane $\\Psi_1$ from spectator-neutron deflection fixing the reaction-plane direction. To reach the azimuthal dependence, the paper expands $P_H(\\phi_H-\\Psi_{\\rm RP})$ as a cosine series, keeps the first two terms, and solves a pair of coupled equations that fold in the Lambda elliptic flow $v_2$ and acceptance integrals $A_0,A_2$ (or their tilted variants $\\tilde{A}_0,\\tilde{A}_2$), using the main tracking detector's second-order event plane as a proxy for the reaction plane. For the Xi, the cascade decay allows polarization transfer from $\\Xi$ to the daughter $\\Lambda$ with coefficient $C_{\\Xi\\Lambda}=+0.944$, a more sensitive extraction than the direct $\\alpha_{\\Xi}$ method.","core_discovery":"On the paper's own terms, the discovery is that hyperon spin polarization is not only a global average but carries a measurable second-order pattern tied to the elliptic geometry of the fireball. Decomposing the Lambda polarization as $P_H(\\phi_H-\\Psi_{\\rm RP}) = P_{y,c0} + 2P_{y,c2}\\cos[2(\\phi_H-\\Psi_{\\rm RP})]$ and solving with the measured elliptic flow and data-derived acceptance factors, the paper finds $P_{y,c2}=0.138\\pm0.038\\,(\\mathrm{stat})\\pm0.058\\,(\\mathrm{syst})$ percent in 20-50% centrality, a positive in-plane enhancement at 2.4$\\sigma$. In the same data, the polarization-transfer analysis of the cascade decay $\\Xi \\to \\Lambda \\pi$ yields $P_{\\Xi^-+\\bar{\\Xi}^+}=0.61\\pm0.21\\,(\\mathrm{stat})\\pm0.04\\,(\\mathrm{syst})$ percent at 2.9$\\sigma$, a hint of a strange-baryon hierarchy $P_{\\Xi}>P_{\\Lambda}$. The azimuthally integrated Lambda polarization is $0.310\\pm0.048\\pm0.036$ percent for $\\Lambda$ and $0.270\\pm0.053\\pm0.030$ percent for $\\bar{\\Lambda}$, consistent with no spin-magnetic coupling contribution within the current precision.","pith_inferences":["Beyond the paper: a resolution-corrected reanalysis of $P_{y,c2}$, applying $1/\\mathrm{Res}(\\Psi_2)$ or a scalar-product estimator, is the sharpest single check; the paper's equations do not display such a correction, so the systematic uncertainty on the 2.4$\\sigma$ signal deserves re-examination.","Beyond the paper: the roughly 2$\\sigma$ gap between the direct Xi polarization ($-0.32\\pm0.39\\pm0.08$ percent) and the polarization-transfer value ($0.61\\pm0.21\\pm0.04$ percent) is a natural target for a blinded re-measurement with tighter background and feed-down modeling.","Beyond the paper: comparing $P_{y,c2}$ across collision energies and system sizes in existing data sets would test whether the in-plane enhancement grows with elliptic flow or with vorticity gradients, a separation this single-energy measurement cannot make.","Beyond the paper: combining this isobar sample with higher-statistics future data could push the Lambda-anti-Lambda splitting difference between Ru+Ru and Zr+Zr below the current $\\pm0.14$ percent precision, testing magnetic-field effects at the few-percent level."],"forward_implications":["A positive $P_{y,c2}$ means in-plane-emitted Lambdas carry more spin than out-of-plane ones; at full significance it would discriminate between models that include thermal shear and models that include only thermal vorticity.","The positive Xi polarization at 2.9$\\sigma$ strengthens the picture that multi-strange baryons inherit polarization from an earlier, more vortical stage, with a possible hierarchy $P_{\\Xi}>P_{\\Lambda}$ consistent with feed-down expectations.","Consistency between Lambda and anti-Lambda polarization in both isobar species constrains a late-stage magnetic-field contribution to spin, despite the roughly 15% larger squared magnetic field expected in Ru+Ru than in Zr+Zr.","The similarity to Au+Au at the same energy implies no obvious system-size dependence in global polarization, and the apparent scaling with participant number $\\langle N_{\\rm part}\\rangle$ supports vorticity as the common driver.","No significant $p_T$ or pseudorapidity dependence within $|\\eta|<1$ leaves the rapidity-dependent vorticity predictions untested in the forward region."],"supporting_citations":[{"why":"Supplies the Au+Au Lambda polarization results at the same energy that the paper compares against to conclude there is no system-size dependence.","marker":"[10]"},{"why":"Provides the previous Xi and Omega polarization measurement and the polarization-transfer coefficient used to extract Xi polarization.","marker":"[8]"},{"why":"Supplies the Fourier decomposition of the polarization and the coupled equations used to extract $P_{y,c0}$ and $P_{y,c2}$.","marker":"[36]"},{"why":"Gives the (3+1)D hydrodynamic model with shear-induced polarization whose equilibrium and s-quark-memory scenarios are compared to the data.","marker":"[62]"},{"why":"Shows the sensitivity of the azimuthal polarization dependence to initial conditions and bulk viscosity, motivating the new $P_{y,c2}$ result.","marker":"[69]"},{"why":"Provides the two-sub-event method used to estimate the first- and second-order event-plane resolutions.","marker":"[51]"},{"why":"Establishes spectator-neutron flow as the first-order event plane estimator that defines the reaction-plane direction.","marker":"[50]"},{"why":"Provides the model connecting Lambda-anti-Lambda polarization difference to a late-stage magnetic field and quantifies feed-down dilution.","marker":"[26]"},{"why":"Supplies the decay parameters $\\alpha_\\Lambda$ and $\\alpha_\\Xi$ used to convert angular asymmetries into polarizations.","marker":"[52]"},{"why":"Predicts larger polarization in smaller collision systems, the system-size dependence the isobar versus Au+Au comparison targets.","marker":"[29]"}],"fun_headline_variants":["Hyperon polarization now measured angle-by-angle in isobar collisions","First measurement of hyperon polarization's angular modulation at RHIC","In-plane emission boosts Lambda polarization in isobar collisions","Xi polarization signal at 2.9 sigma hints at strange baryon hierarchy"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The extraction assumes that the measured second-order event plane from charged tracks faithfully represents the true reaction plane, with any resolution smearing either negligible or already absorbed into the measured $v_2$ and acceptance factors; if that resolution is not fully accounted for, the size and significance of the 2.4$\\sigma$ in-plane polarization could shift.","fun_headline_variants_meta":{"raw":{"variants":["Hyperon polarization now measured angle-by-angle in isobar collisions","First measurement of hyperon polarization's angular modulation at RHIC","In-plane emission boosts Lambda polarization in isobar collisions","Xi polarization signal at 2.9 sigma hints at strange baryon hierarchy"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000995,"raw_usage":{"total_tokens":4291,"prompt_tokens":1102,"completion_tokens":3189,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":718,"completion_tokens_details":{"reasoning_tokens":3117}},"tokens_in":718,"tokens_out":3189,"duration_ms":24113,"temperature":1.0,"reasoning_tokens":3117,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T23:15:25.447540+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Recompute $P_{y,c2}$ after applying the second-order event-plane resolution correction $1/\\mathrm{Res}(\\Psi_2)$ or a scalar-product estimator; if the corrected value moves by more than the quoted 0.058 percent systematic uncertainty or its significance falls below roughly 2$\\sigma$, the in-plane enhancement claim fails. A second decisive check is to repeat the extraction using $\\Psi_2$ from each sub-event separately and compare the two results.","supporting_citations":[{"cited_title":"$\\Lambda$ and $\\bar{\\Lambda}$ spin interaction with meson fields generated by the baryon current in high energy nuclear collisions","cited_arxiv_id":"1807.11521","evidence_quote":"Gives the (3+1)D hydrodynamic model with shear-induced polarization whose equilibrium and s-quark-memory scenarios are compared to the data."},{"cited_title":"Zyzak, Online selection of short-lived particles on many-core com- puter architectures in the CBM experiment at FAIR, Ph.D","cited_arxiv_id":null,"evidence_quote":"Establishes spectator-neutron flow as the first-order event plane estimator that defines the reaction-plane direction."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Predicts larger polarization in smaller collision systems, the system-size dependence the isobar versus Au+Au comparison targets."}],"review_version":1}