{"id":"8c08b266-0c48-4fb4-98ea-3563dd0bdcbf","arxiv_id":"2505.03969","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"In HYDJET++ simulations of deformed Xe-Xe collisions, higher-order anisotropic flow harmonics v4-v7 are generated from elliptic and triangular flow via mode mixing and show centrality-dependent scaling that roughly matches ALICE and CMS data.","lead":"Using the HYDJET++ Monte Carlo model with a deformed xenon nucleus, the authors compute higher-order flow harmonics v4 through v7 in Xe-Xe collisions and compare them with LHC data. A generalist may read this to see how a widely used event generator handles nonlinear flow correlations in a deformed nuclear system.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The claimed v5-v7 correlations are imposed by construction: Sec. 2.1 sets v5 ∝ v2×v3 and v6 ∝ (v2^3 + v3^2) instead of letting them respond to their own eccentricities, so the central finding is not an emergent prediction.","rationale":"Reader's weakest_assumption is correct and matches the most load-bearing issue. The construction in Sec. 2.1 makes the v2-v7 correlation almost tautological: v5 and v6 are defined as products/powers of v2 and v3, so the reported strong correlations and scaling ratios in Figs. 4-5 contain no information beyond the model's input. This does not by itself make the data comparisons worthless—HYDJET++'s centrality shape of v4-v7 can still be compared with ALICE/CMS—but it means the central claim of 'strongly correlated' higher harmonics is not independently tested. The estimator mismatch (reaction-plane versus cumulants/scalar product) further prevents a quantitative conclusion. The paper admits no deposition of data and no code, and in Sec. 3 notes fluctuations are not well captured, so the test cannot be performed from the text. These limitations justify keeping the reader's CONDITIONAL verdict: accept only if the authors confirm that v5-v7 are genuinely emergent Fourier coefficients and compare like-for-like estimators. I agree with the reader's identification and do not change the verdict.","tokens_in":12887,"tokens_out":8300,"duration_ms":86210,"concrete_test":"Ask the authors to provide the modified HYDJET++ event-by-event flow calculation (source or deposited data) and check whether v5, v6, v7 are computed as independent Fourier coefficients of the final charged-particle azimuthal distribution or are assigned algebraically as c·v2·v3 and c′·(v2^3+v3^2). Then run the same Xe-Xe setup in an event-by-event viscous hydrodynamic code that includes linear and nonlinear responses (e.g., MUSIC + UrQMD) with the same 129Xe deformation parameters, and decompose v4-v7 into linear and nonlinear parts (e.g., regression on εn and products of ε2, ε3). If the linear fraction of v5-v7 exceeds ~20% in the 0-60% centrality range, the HYDJET++ construction suppresses a non-negligible physical contribution and the reported correlations/scaling ratios are not evidence for the model's physics.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central claim is that v4-v7 are centrality dependent and strongly correlated with v2 and v3 (abstract and Sec. 3). But Sec. 2.1 states that 'in HYDJET++ these higher Fourier harmonics do not generate their own intrinsic event planes,' with v5 generated by interference (v5 ∝ v2×v3) and v6 by v6 ∝ (v2^3 + v3^2). Thus the reported correlations are built into the observable rather than being a property of the collision dynamics. The only independent inputs are ρ3u and ρ4u (plus ν2), while v5-v7 are obtained from those inputs by mode-mixing formulas; no linear response to eccentricities ε5, ε6, ε7 is included. If real Xe-Xe collisions contain significant linear contributions to v5-v7, as viscous-hydrodynamic calculations indicate for v4-v7, the scaling ratios in Figs. 4-5 and the 'suitable match' with ALICE/CMS data are model-specific artifacts. The comparison is further weakened by mixing estimators: model v2/v3 use the reaction-plane method while ALICE/CMS data use 2-particle cumulants and ATLAS uses scalar product (Sec. 3). The manuscript itself concedes 'the role of fluctuations is not well expressed from the model' and the code is not deposited, so the construction cannot be audited.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript uses the Monte Carlo HYDJET++ event generator with a modified Woods-Saxon density profile for a deformed Xe nucleus to compute anisotropic flow harmonics v2 through v7 in Xe-Xe collisions at sqrt(s_NN) = 5.44 TeV. The authors report results for seven centrality classes and two kinematic ranges, and compare v_n, response ratios, and power-law scaled ratios v_n / v_m^(n/m) with ALICE, ATLAS, and CMS data. The paper's central claim is that higher-order harmonics v4-v7 are centrality dependent and strongly correlated with v2 and v3, and that the model reproduces the LHC data at mid-rapidity, while failing to describe ATLAS data at larger pseudorapidity.","tokens_in":13300,"tokens_out":4745,"duration_ms":54319,"significance":"If the reported correlations and scaling ratios were emergent predictions of the collision dynamics, this study would provide a useful phenomenological test of nonlinear mode-mixing in a deformed, smaller system at LHC energies. The paper has some strengths: it uses a large event sample (10^6 events per centrality class), presents two kinematic ranges, incorporates nuclear deformation parameters from the nuclear-data literature, and makes explicit comparisons with three LHC experiments. However, the central correlation claim for v5-v7 is not a dynamical prediction because the manuscript itself constructs these harmonics as nonlinear mode-mixing combinations of v2 and v3. The comparison with experimental data is also weakened by the use of different flow estimators in the model and in the data. Reproducibility is limited because the model code and simulation data are not deposited, and the tunable parameters are not given in full. With a clear reframing as a test of the mode-mixing ansatz rather than as an emergent prediction, the study could still be a useful benchmark for HYDJET++, but in its present form the main claim is largely tautological.","major_comments":[{"comment":"The central claim that v5-v7 are 'significantly correlated' with v2 and v3 is true by construction, not by dynamical prediction. Section 2.1 states explicitly that in HYDJET++ the harmonics v_n (n>=4) do not generate their own intrinsic event planes, with v5 proportional to v2 times v3 and v6 proportional to (v2^3 + v3^2), and that only rho3u and rho4u are treated independently among the higher-order anisotropy parameters. Consequently, the scaling ratios and response ratios for n=5-7 in Figs. 3-5 reduce to functions of the tuned lower-order harmonics and of the chosen mode-mixing coefficients; they do not constitute independent information about the collision geometry or the hydrodynamic response. The 'suitable match' with ALICE and CMS data for these harmonics is therefore weaker than presented, because the comparison tests the input ansatz and the tuning of v2 and v3 rather than the model's ability to generate higher harmonics from the initial state. I request that the paper be explicitly reframed as a test of the nonlinear-mode-mixing ansatz, that the circularity be acknowledged in the abstract and conclusions, and that any wording implying emergent predictions for v5-v7 be removed.","section":"Sec. 2.1; Abstract; Sec. 3"},{"comment":"The quantitative comparison of model results with experimental data mixes different flow estimators. The manuscript states that HYDJET++ v2 and v3 are obtained with the reaction-plane method and the higher harmonics via nonlinear mode-mixing, whereas ALICE and CMS data are 2-particle cumulants and ATLAS data are obtained with the scalar-product method. These estimators have different event-plane resolution corrections, different sensitivity to multiplicity fluctuations, and different nonflow contamination, so the agreement seen in Fig. 2 and the scaling comparisons in Figs. 4-5 are not apples-to-apples. Because HYDJET++ generates full events, the same experimental estimators could in principle be computed within the model; without that, the conclusions about 'suitable match' and the degree of agreement with each experiment are not firmly established.","section":"Sec. 3; Figs. 2-5"},{"comment":"The Data Availability Statement says that the model data will not be deposited, and the manuscript does not provide the full set of tuned centrality-dependent parameters (epsilon2(b), delta2(b), epsilon3(b), rho3u(b), rho4u(b)) or the code. Given that the numerical results depend on 10^6 events and on these input parameters, the central results cannot be reproduced or audited by an independent reader. For a model-based paper whose main conclusions depend on the details of the mode-mixing construction, I consider this a load-bearing reproducibility omission. At minimum, complete parameter tables and a description of the event-selection and averaging procedure should be provided, and ideally the modified HYDJET++ code should be released.","section":"Data Availability Statement; Sec. 3"}],"minor_comments":[{"comment":"The manuscript contains numerous typographical and OCR-style corruptions, e.g., equations rendered as '/equal1' and scaling relations written as 'vn/vn/m m'. These need to be corrected in the final version to make the mathematical content readable.","section":"Throughout"},{"comment":"The summary mentions '0 < pT < 5 GeV/c' as a kinematic range, while the body of the paper specifies '0.5 < pT < 60 GeV/c' for the high-pseudorapidity range and 'pT > 0.2 GeV/c' for the mid-rapidity range. This inconsistency should be resolved.","section":"Summary; Sec. 3"},{"comment":"The text states that smaller Xe-Xe systems have larger viscous effects, but also states that HYDJET++ uses parameterized ideal hydrodynamics with no dissipative effects. The presentation should clarify which statements are model results and which are motivations from data or viscous-hydrodynamics calculations.","section":"Sec. 3"},{"comment":"The figures do not show statistical uncertainties or any sensitivity of the model results to the input parameters. Adding at least statistical error bars, or stating that they are negligible after 10^6 events, would strengthen the quantitative comparisons.","section":"Figs. 2-5"}],"recommendation":"major_revision","confidential_remarks":"The manuscript appears to correspond to an already published article (Eur. Phys. J. Plus 139 (2024) 400). If this submission is intended as a post-publication version, the requested changes may need to take the form of an erratum or a substantially revised version rather than a standard revision. The main issue is not technical correctness of the HYDJET++ implementation but the framing: the correlation claims for v5-v7 are built into the observable definitions. I would support publication after the authors reframe the claims as tests of the mode-mixing ansatz and add the estimator and reproducibility caveats."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this is a legitimate but limited follow-up to the authors' earlier HYDJET++ work. The new piece is applying the deformed-xenon Woods-Saxon profile to generate v4–v7 and showing centrality-dependent scaling ratios alongside ALICE/CMS/ATLAS points. If you work with this event generator, the benchmark is useful.\n\nWhat the paper does well: the model setup is described in adequate detail, the deformation parameters come from a proper nuclear database, the centrality and pT cuts match the experiments, and the authors are upfront that the model doesn't handle fluctuations well and that the ATLAS comparison fails at forward rapidity. The qualitative match with ALICE/CMS in mid-rapidity is informative. The power-law scaling plots (vn/vm^(n/m)) are a clear way to present the centrality dependence.\n\nThe main soft spot is exactly what the stress-test note says: Sec. 2.1 defines v5 as proportional to v2×v3 and v6 as a combination of powers, with no intrinsic event planes for n≥4. So the 'strong correlation' reported in the abstract and Sec. 3 is not an emergent property of the collision dynamics; it is programmed into the model. That doesn't make the paper worthless, but it means the headline claim is overstated. The response ratios in Fig. 3 and the scaling in Figs. 4–5 are functions of the tuned v2 and v3 parameters, so they test the parameterization, not a dynamical hypothesis.\n\nA second issue is the estimator mismatch: model v2/v3 come from the reaction-plane method, while ALICE/CMS data are 2-particle cumulants and ATLAS uses scalar product. The comparison is qualitative at best, and the paper doesn't quantify systematic differences. Third, no code or data are deposited, so the tuning of epsilon2, delta2, rho3u, rho4u cannot be audited.\n\nWho is this for? Event-generator phenomenologists and people benchmarking HYDJET++ against LHC data. It won't change the physics picture, and it isn't a test of mode-coupling theory. But it is a competent model study that deserves a serious referee; the main request would be to reframe the claims and deposit the setup.","headline":"A competent HYDJET++ extension to v7 in deformed Xe–Xe, but the higher-harmonic correlations are built in by construction and the comparison mixes estimators.","tokens_in":13830,"tokens_out":2289,"would_cite":false,"duration_ms":22397,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["25.75.Ld"],"model":"deepseek-v4-flash","headline":"In HYDJET++ simulations of deformed Xe-Xe collisions, the higher-order flow harmonics v4-v7 are produced entirely by v2-v3 mode-mixing, and the resulting centrality-dependent scaling ratios match ALICE and CMS data.","keywords":["anisotropic flow","higher-order harmonics","HYDJET++","Xe-Xe collisions","nonlinear mode mixing","power-law scaling","deformed nuclei","flow response coefficients"],"falsifier":"Measure the linear and nonlinear parts of $v_5$, $v_6$, and $v_7$ separately in Xe-Xe collisions at 5.44 TeV using event-plane or multiparticle-cumulant methods; if the linear parts are non-negligible, the scaling ratios $v_n/v_m^m$ will differ from the HYDJET++ predictions in a centrality-dependent way.","tokens_in":12691,"feed_emoji":"⚛️","tokens_out":9098,"duration_ms":76626,"temperature":0.7,"pith_summary":"The paper aims to show that, in the Monte Carlo HYDJET++ model, all higher-order anisotropic flow harmonics $v_4$ through $v_7$ in deformed Xe-Xe collisions at 5.44 TeV are generated exclusively by nonlinear mode-mixing of the elliptic flow $v_2$ and triangular flow $v_3$. Because the model gives these high harmonics no independent event planes of their own, the response of $v_n$ to $v_2$ and $v_3$ can be studied through the power-law scaling ratios $v_n/v_m^m$ as a function of collision centrality. The authors report that these ratios are centrality dependent, that $v_2$ dominates the response, and that the computed $v_n$ agree qualitatively with ALICE and CMS data at mid-rapidity. If the picture holds, the scaling ratios become observables that isolate nonlinear hydrodynamic response coefficients while bypassing uncertainties in modeling the initial state.","feed_headline":"Higher harmonic flow in Xe-Xe is pure v2-v3 mode mixing","feed_subtitle":"Centrality-dependent ratios v_n/v_m^m isolate the nonlinear response and match LHC data at mid-rapidity.","key_machinery":"The load-bearing mechanism is the nonlinear mode-mixing construction built into HYDJET++: the flow harmonics $v_4$-$v_7$ are generated by superimposing the elliptic ($v_2$) and triangular ($v_3$) deformations of the freeze-out surface and the transverse flow rapidity, so that each $v_n$ with $n\\ge 4$ has no intrinsic event plane. The associated diagnostic is the power-law scaling ratio $v_n/v_m^m$, which isolates the individual response of each high harmonic to $v_2$ and $v_3$ across centrality. This construction makes the higher harmonics pure overtones of the lower ones, turning their correlations into a clean probe of nonlinear hydrodynamic response.","core_discovery":"The central claim is that in deformed Xe-Xe collisions simulated with HYDJET++, the higher Fourier harmonics $v_4$, $v_5$, $v_6$, and $v_7$ are not independent degrees of freedom: they emerge purely from the interference of the lower-order harmonics $v_2$ and $v_3$, with $v_5 \\propto v_2 v_3$ and $v_6 \\propto (v_2^3 + v_3^2)$. Consequently, the reaction plane of each high harmonic is inherited from the lower-order planes, and the normalized ratios $v_n/v_m^m$ provide a direct measure of the nonlinear response of the system. The paper presents these ratios across seven centrality classes in two pseudorapidity windows and finds a strong centrality dependence driven chiefly by $v_2$, with magnitudes that match ALICE and CMS data but underpredict ATLAS data at forward rapidity.","pith_inferences":["If $v_5$, $v_6$, and $v_7$ in real collisions receive linear contributions from their own participant-plane eccentricities, the deviations from the HYDJET++ scaling ratios would be largest in the most central classes, a falsifiable prediction that can be checked with existing LHC data using linear/nonlinear separation techniques.","Applying the same $v_n/v_m^m$ analysis to uranium-uranium collisions, where the intrinsic deformation is larger, should produce an even steeper centrality dependence of the response ratios; this is a direct extension the paper does not make.","Since HYDJET++ contains no viscous evolution, the agreement with data suggests the scaling ordering is governed by the mode-mixing algebra rather than by specific transport coefficients, so the ratios could serve as model-independent checks in full viscous hydrodynamic simulations.","The centrality window below 30% where the $v_6/v_2^3$ ratio is maximal may be the best region to search for sensitivity to the Xe deformation parameter $\\beta_2$, because the mode-mixing response is most distinct there."],"forward_implications":["The scaling ratios $v_n/v_2^{n/2}$ and $v_n/v_3^{n/3}$ provide a way to extract nonlinear response coefficients that are independent of initial-condition modeling.","The observed ordering, with $v_6/v_2^3$ largest and $v_3/v_2^{3/2}$ smallest in the 0-30% centrality interval, is a pattern that experiment can look for directly.","The match with ALICE and CMS data at mid-rapidity supports the mode-mixing picture as the dominant source of $v_4$- $v_7$ in Xe-Xe at 5.44 TeV.","The failure at high pseudorapidity against ATLAS data identifies a limitation of the Bjorken boost-invariant freeze-out treatment rather than of the mode-mixing idea itself."],"supporting_citations":[{"why":"Establishes the HYDJET++ description of flow harmonics in Xe-Xe that this work extends to higher harmonics.","marker":"[22]"},{"why":"Provides the model's anisotropic-flow parameterization and previously tuned comparisons for Xe-Xe collisions.","marker":"[23]"},{"why":"Demonstrates the v6 nonlinear mode-mixing analysis in Pb-Pb that the present study generalizes to v4-v7.","marker":"[24]"},{"why":"Documents the HYDJET++ model formalism, including freeze-out and jet treatment used here.","marker":"[25]"},{"why":"ALICE Xe-Xe flow data at 5.44 TeV used for the mid-rapidity comparison.","marker":"[45]"},{"why":"CMS Xe-Xe flow data at 5.44 TeV used for the mid-rapidity comparison.","marker":"[46]"},{"why":"ATLAS Xe-Xe flow data at 5.44 TeV used for the high-pseudorapidity comparison.","marker":"[47]"},{"why":"Argument that nonlinear response coefficients are independent of the initial density profile, motivating the scaling-ratio approach.","marker":"[19]"},{"why":"Source of the Xe deformation parameters β2 and β4 used in the modified Woods-Saxon profile.","marker":"[48]"}],"fun_headline_variants":["Xe-Xe higher harmonics are pure v2-v3 mode mixing","Why v4-v7 in Xe-Xe are echoes of v2 and v3","Nonlinear response in Xe-Xe: v_n/v_m^m isolates v2-v3 mixing","Xe-Xe flow: v4-v7 arise from v2-v3 mode coupling"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The entire analysis assumes that $v_5$, $v_6$, and $v_7$ have no intrinsic event planes, being generated solely by $v_2$-$v_3$ mode-mixing; real collisions with linear contributions would make the reported correlations and scaling ratios artifacts of the model.","fun_headline_variants_meta":{"raw":{"variants":["Xe-Xe higher harmonics are pure v2-v3 mode mixing","Why v4-v7 in Xe-Xe are echoes of v2 and v3","Nonlinear response in Xe-Xe: v_n/v_m^m isolates v2-v3 mixing","Xe-Xe flow: v4-v7 arise from v2-v3 mode coupling"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000841,"raw_usage":{"total_tokens":3688,"prompt_tokens":994,"completion_tokens":2694,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":610,"completion_tokens_details":{"reasoning_tokens":2600}},"tokens_in":610,"tokens_out":2694,"duration_ms":18002,"temperature":1.0,"reasoning_tokens":2600,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T23:40:59.475810+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the linear and nonlinear parts of $v_5$, $v_6$, and $v_7$ separately in Xe-Xe collisions at 5.44 TeV using event-plane or multiparticle-cumulant methods; if the linear parts are non-negligible, the scaling ratios $v_n/v_m^m$ will differ from the HYDJET++ predictions in a centrality-dependent way.","supporting_citations":[{"cited_title":"Pandey, S.K","cited_arxiv_id":null,"evidence_quote":"Establishes the HYDJET++ description of flow harmonics in Xe-Xe that this work extends to higher harmonics."},{"cited_title":"Pandey, B.K","cited_arxiv_id":null,"evidence_quote":"Provides the model's anisotropic-flow parameterization and previously tuned comparisons for Xe-Xe collisions."},{"cited_title":"Bravina, B.H.B","cited_arxiv_id":null,"evidence_quote":"Demonstrates the v6 nonlinear mode-mixing analysis in Pb-Pb that the present study generalizes to v4-v7."},{"cited_title":"Lokhtin, L","cited_arxiv_id":null,"evidence_quote":"Documents the HYDJET++ model formalism, including freeze-out and jet treatment used here."},{"cited_title":"Acharya, F","cited_arxiv_id":null,"evidence_quote":"ALICE Xe-Xe flow data at 5.44 TeV used for the mid-rapidity comparison."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"ATLAS Xe-Xe flow data at 5.44 TeV used for the high-pseudorapidity comparison."},{"cited_title":"Yan, J.-Y","cited_arxiv_id":null,"evidence_quote":"Argument that nonlinear response coefficients are independent of the initial density profile, motivating the scaling-ratio approach."},{"cited_title":"Möller, A","cited_arxiv_id":null,"evidence_quote":"Source of the Xe deformation parameters β2 and β4 used in the modified Woods-Saxon profile."}],"review_version":1}