{"id":"15cbaf77-151d-4882-9df8-8e6175808494","arxiv_id":"2606.13333","paper_version":2,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":4.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"Lambda polarization in low-energy heavy-ion collisions depends on the equation of state in UrQMD simulations and arises from shear in the baryon current due to stopping.","lead":"The study uses the UrQMD transport model to calculate thermal vorticity-induced Lambda polarization in Ag+Ag and Au+Au collisions at energies from 2.24 to 7.7 GeV, comparing a hadron resonance gas EoS to a chiral mean field EoS. Polarization is smaller with the softer EoS and does not decrease at lower energies, attributed to shear from baryon stopping.","discovery_kind":"unclear","skeptic_critique":{"model":"grok-4.3","headline":"Unvalidated assumption that UrQMD thermal vorticity maps directly to observed Λ polarization at √sNN=2-8 GeV","rationale":"The reader's weakest_assumption directly identifies the same unvalidated step; the abstract's own caveat makes this the load-bearing point rather than any internal inconsistency in the reported numbers.","tokens_in":1738,"tokens_out":265,"duration_ms":5715,"concrete_test":"Recompute polarization using the same UrQMD runs but replace the thermal-vorticity formula with an independent estimator (e.g., direct angular-momentum transfer to Λs via spin-orbit coupling); if the EoS-induced difference shrinks below statistical significance, the sensitivity claim is model-dependent.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The headline claims (EoS sensitivity of polarization; non-decreasing polarization at lower energies; origin in baryon-current shear) rest on the premise that the model's thermal vorticity produces the correct polarization signal. The abstract explicitly states this relation 'remains to be validated,' yet the calculations compare two EoS implementations and draw mechanistic conclusions without additional checks. If the mapping contains model-specific artifacts (e.g., from hadronic rescattering or vorticity definition), the reported EoS dependence and stopping mechanism are not robust.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The manuscript employs the UrQMD transport model to compute thermal vorticity-induced global polarization of Λ hyperons in Ag+Ag and Au+Au collisions at √sNN = 2.24–7.7 GeV across centralities. Two equations of state are compared: a hadron resonance gas and a chiral mean field (CMF) model incorporating a chiral transition. The polarization is reported to be sensitive to the EoS (softer EoS yields smaller values), does not decrease at lower energies within experimental acceptance, and is attributed to shear in the baryon current arising from stopping.","tokens_in":1848,"tokens_out":408,"duration_ms":13826,"significance":"If the thermal vorticity to polarization mapping is robust, the EoS sensitivity and non-decreasing low-energy behavior could provide a new observable for dense nuclear matter at FAIR/RHIC-BES energies. The mechanistic link to baryon stopping offers a testable interpretation of vorticity generation.","major_comments":[{"comment":"Abstract: the text explicitly states that 'the relation between hadronic polarization and the medium's collective rotation remains to be validated,' yet proceeds to report quantitative EoS dependence and a specific shear mechanism without supplying validation against data, alternative polarization mechanisms, or model cross-checks; this assumption is load-bearing for all headline claims.","section":"Abstract"},{"comment":"Results section (comparison of EoS implementations): the reported sensitivity of polarization to the CMF versus HRG EoS lacks accompanying error bars, explicit centrality cuts, or quantitative model validation metrics, making it impossible to assess whether the difference exceeds statistical or systematic uncertainties.","section":"Results"}],"minor_comments":[{"comment":"Notation for thermal vorticity and polarization definitions should be cross-referenced to prior UrQMD literature for clarity.","section":null}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for the constructive comments, which help improve the clarity of our manuscript. We respond to each major comment below.","responses":[{"response":"The abstract already states that the polarization-rotation relation remains to be validated, and our work operates strictly within the standard thermal-vorticity framework employed throughout the literature. The quantitative EoS dependence and shear interpretation are presented as model predictions under that assumption, not as experimentally validated results. To address the concern we will revise the abstract and introduction to explicitly note that the mapping is an assumption (with references to its use at higher energies) and that alternative mechanisms are outside the present scope.","revision_made":"partial","referee_comment":"[Abstract] Abstract: the text explicitly states that 'the relation between hadronic polarization and the medium's collective rotation remains to be validated,' yet proceeds to report quantitative EoS dependence and a specific shear mechanism without supplying validation against data, alternative polarization mechanisms, or model cross-checks; this assumption is load-bearing for all headline claims."},{"response":"We agree that the presentation can be improved. In the revised manuscript we will add statistical error bars to all polarization results, state the exact centrality intervals used for each data set, and include a short discussion quantifying the size of the EoS-induced difference relative to the statistical uncertainties. Because both EoS implementations are run inside the identical UrQMD code, the comparison is internal; we will clarify this point to avoid implying external validation.","revision_made":"yes","referee_comment":"[Results] Results section (comparison of EoS implementations): the reported sensitivity of polarization to the CMF versus HRG EoS lacks accompanying error bars, explicit centrality cuts, or quantitative model validation metrics, making it impossible to assess whether the difference exceeds statistical or systematic uncertainties."}],"tokens_in":1343,"tokens_out":399,"duration_ms":18281,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The main thing to know is that this UrQMD study finds Lambda polarization sensitive to the choice of equation of state at FAIR/RHIC-BES energies, with a softer EoS giving smaller polarization, and that the polarization in the measured acceptance does not drop at the lowest beam energies.\n\nThe paper compares a hadron resonance gas EoS to the chiral mean field EoS in the same transport framework for Ag+Ag and Au+Au collisions from 2.24 to 7.7 GeV. It extracts thermal vorticity and converts it to polarization, then applies experimental cuts. This extends prior UrQMD polarization work by including the CMF model and focusing on the energy range where baryon stopping is strong. The indication that large vorticity comes from shear in the stopped baryon current follows from the runs.\n\nThe model runs are standard and the comparison is straightforward. The authors flag that the polarization-vorticity connection still needs validation, which keeps the claims in proportion.\n\nThe soft spot is the same one the stress-test note highlights. They state the relation remains to be validated yet draw mechanistic conclusions from the EoS dependence and the stopping process. Without extra tests, such as varying the vorticity definition or checking against hadronic effects, it is not clear how robust the reported sensitivity is. The abstract gives no quantitative values or uncertainties, so the practical size of the EoS effect is not shown.\n\nThis paper is for nuclear physicists already working with UrQMD or similar codes on polarization at a few GeV. It supplies a direct EoS comparison they can use. It is not aimed at a broader audience.\n\nI would send it to peer review. The topic is relevant and the calculation is well-defined, even though the validation issue will likely come up in review.","headline":"UrQMD runs show EoS-dependent Lambda polarization at 2-8 GeV that holds steady at low energies, but the vorticity-to-polarization step is flagged as unvalidated.","tokens_in":2324,"tokens_out":446,"would_cite":false,"duration_ms":19197,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"Lambda polarization in heavy-ion collisions depends on the stiffness of the nuclear equation of state, with softer equations yielding smaller values.","keywords":["Lambda polarization","equation of state","heavy-ion collisions","thermal vorticity","baryon stopping","UrQMD model","FAIR energies","RHIC-BES"],"falsifier":"An experimental measurement at these energies showing Lambda polarization that is either independent of equation-of-state stiffness or that decreases sharply below 2.24 GeV would contradict the central claim.","tokens_in":2660,"feed_emoji":"","tokens_out":721,"duration_ms":12019,"temperature":0.7,"pith_summary":"The paper calculates the global polarization of Lambda hyperons induced by thermal vorticity in non-central Ag+Ag and Au+Au collisions at beam energies from 2.24 to 7.7 GeV using the UrQMD transport model. It compares two equations of state, one resembling a hadron resonance gas and the other incorporating a chiral mean-field description with a transition consistent with lattice QCD. The results show that polarization is sensitive to the equation of state, with the softer version producing smaller polarization, and that polarization in experimental acceptance does not fall at lower energies. The authors trace the large vorticity to shear in the baryon current arising from its stopping. A sympathetic reader would care because this links an observable polarization signal directly to the medium's collective rotation and its underlying equation of state at energies relevant to FAIR and RHIC-BES.","feed_headline":"Lambda polarization shrinks with softer nuclear equation of state","feed_subtitle":"UrQMD calculations at 2-8 GeV show the effect persists at lower energies because baryon stopping creates the driving shear.","key_machinery":"Thermal vorticity-induced polarization of Lambdas calculated in the UrQMD model under two equations of state (hadron resonance gas versus chiral mean-field).","core_discovery":"Using the UrQMD transport model with two different equations of state, the thermal vorticity-induced Lambda polarization is found to be sensitive to the equation of state, with a softer EoS producing smaller polarization values. The Lambda polarization within experimental acceptance and centrality cuts does not decrease at even lower beam energies. The large vorticity arises from the shear in the baryon current created by baryon stopping.","pith_inferences":["If the relation holds, future polarization data at FAIR could constrain the location of the chiral transition in dense matter.","The stopping-induced shear mechanism may also affect other observables such as directed flow or elliptic flow at the same energies.","Extending the calculation to include additional hadrons or different centrality bins could test whether the polarization signal is robust across species."],"forward_implications":["Polarization measurements can distinguish between stiff and soft equations of state in the baryon-rich regime.","The absence of a decrease in polarization at lower energies implies that vorticity remains large even as beam energy drops.","Baryon stopping is identified as the dominant source of the shear that generates the observed vorticity.","The chiral mean-field equation of state, which includes a lattice-consistent transition, yields systematically different polarization than a pure hadron resonance gas."],"fun_headline_variants":["Softer EoS cuts Lambda polarization in UrQMD simulations","Lambda polarization persists at low energies from baryon shear","Thermal vorticity polarization sensitive to nuclear equation of state","Baryon current shear causes large vorticity in low energy runs"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"The UrQMD transport model with the two chosen equations of state correctly produces the thermal vorticity and the resulting polarization from baryon stopping without dominant contributions from other mechanisms.","fun_headline_variants_meta":{"raw":{"variants":["Softer EoS cuts Lambda polarization in UrQMD simulations","Lambda polarization persists at low energies from baryon shear","Thermal vorticity polarization sensitive to nuclear equation of state","Baryon current shear causes large vorticity in low energy runs"]},"model":"grok-4.3","cost_usd":0.004785,"raw_usage":{"total_tokens":2352,"prompt_tokens":661,"num_sources_used":0,"completion_tokens":64,"cost_in_usd_ticks":47849500,"prompt_tokens_details":{"text_tokens":661,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":1627,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":661,"tokens_out":64,"duration_ms":10714,"temperature":1.0,"reasoning_tokens":1627,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-27T05:23:44.351878+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"An experimental measurement at these energies showing Lambda polarization that is either independent of equation-of-state stiffness or that decreases sharply below 2.24 GeV would contradict the central claim.","supporting_citations":[],"review_version":1}