{"id":"f0a3a1fc-9744-4de2-b2dd-3263773905af","arxiv_id":"2506.19101","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"The iHKMe model reproduces pion HBT radii at RHIC BES energies with a crossover equation of state, while a first-order phase transition predicts too-large R_long at higher energies.","lead":"Researchers simulated gold-on-gold collisions at RHIC energies from 7.7 to 39 GeV per nucleon pair using a hydrokinetic model, then computed pion interferometry radii and compared them to STAR data. The crossover equation of state matched the data better than a first-order phase transition, with the largest difference in the longitudinal radius at higher energies.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The claimed EoS sensitivity is not isolated: the crossover and first-order parameter sets in Table I differ in eta/s and eps_sw as well as in the equation of state, so the R_long difference cannot yet be attributed to the EoS.","rationale":"The reader identified the same load-bearing assumption: the comparison in Table I changes eta/s and eps_sw together with the EoS, so the observed R_long difference cannot be unambiguously assigned to the equation of state. I confirmed this by reading the parameter table and the model description. The effect is not merely a stylistic caveat: eps_sw controls the particlization hypersurface energy density, and lowering it from 0.50 to 0.35 GeV/fm^3 extends the hydrodynamic expansion before the cascade stage begins, which by itself can increase the emission duration and therefore R_long. The different shear viscosities (0.14 vs 0.08) provide an additional channel through which the two scenarios differ dynamically, independent of the phase-transition structure. The paper's conclusion in Section IV, that the crossover EoS 'yields a better description' and that the PT excess is 'caused by the increased system's lifetime during the mixed-phase stage,' goes beyond what the current setup can demonstrate. That said, the work has genuine strengths: it uses a full dynamical model with UrQMD initial conditions, viscous hydrodynamics, and afterburner, and it presents a sizable event sample (30,000 events per parameter set). The visual comparison of the two scenarios does suggest some sensitivity, but the confounding of parameters means the central claim is conditional rather than established. I therefore agree with the reader's CONDITIONAL verdict and recommend no change: the strongest claim should be treated as a promising but unproven indication, pending a matched-parameter comparison. The proposed concrete test would resolve the ambiguity with a modest number of additional simulations at the two lowest energies.","tokens_in":10940,"tokens_out":2879,"duration_ms":30886,"concrete_test":"Perform a controlled 2x2 parameter scan at 7.7 and 11.5 GeV: (a) the crossover EoS with the PT values eta/s = 0.08 and eps_sw = 0.35, and (b) the PT EoS with the CO values eta/s = 0.14 and eps_sw = 0.50, keeping all other Table I parameters at their stated values. Compare the resulting R_long(m_T) curves with the original CO and PT curves. If the R_long excess follows the eta/s and eps_sw choices rather than the EoS, the central EoS-sensitivity claim is confounded; if the excess persists for the same EoS regardless of the parameter swap, the attribution is supported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that the crossover EoS describes interferometry radii better than the first-order PT EoS, with the PT scenario producing noticeably larger R_long at higher BES energies due to a longer mixed-phase stage. However, Table I shows that the two scenarios are not varied solely in the EoS. For example, at 7.7 GeV the PT set uses eta/s = 0.08 and eps_sw = 0.35 GeV/fm^3, while the CO set uses eta/s = 0.14 and eps_sw = 0.50 GeV/fm^3; similar differences appear at 11.5 and 14.5 GeV, including different tau_th values. A lower eps_sw delays the switch from hydrodynamics to the hadronic cascade, extending the duration of particle emission and thereby increasing R_long independently of the EoS. The higher shear viscosity in the CO set may also affect the expansion history. Since these parameters were fixed in the prior spectra study [22] and are not varied independently here, the attribution of the R_long excess to the mixed-phase stage of the first-order EoS rests on the unverified assumption that the eta/s and eps_sw differences are negligible for HBT radii. The paper also provides no quantitative comparison metric or uncertainties, but the parameter confound is the more fundamental issue: without isolating the EoS, the stated conclusion that femtoscopic radii favor a crossover transition is not established.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper applies the extended integrated HydroKinetic Model (iHKMe) to Au+Au collisions at RHIC BES energies, sqrt(s_NN) = 7.7-39 GeV, and computes the pion interferometry radii R_out, R_side, and R_long. The model combines UrQMD initial conditions, a relaxation stage, viscous hydrodynamics, particlization, and a hadronic cascade. The parameters are taken from a prior spectra-calibration study [22], so the HBT radii are genuine predictions rather than fitted quantities. Two equations of state are compared at 7.7, 11.5, and 14.5 GeV: a crossover EoS and a first-order phase-transition EoS. The central claim is that the crossover EoS describes the STAR interferometry data better, especially at higher BES energies, and that the first-order EoS produces too large R_long because of an extended mixed-phase stage; the paper also notes that the model overestimates the energy growth of R_long at high energies.","tokens_in":11267,"tokens_out":4042,"duration_ms":42962,"significance":"If the central claim were established, this would be a valuable result: femtoscopic radii from a realistic dynamical model, with parameters fixed by spectra, would provide independent evidence about the nature of the QCD transition at moderate baryon density. The work covers a broad energy range, uses two EoS scenarios, and reports a substantial number of events per parameter set. The main strength is that the HBT radii are computed from previously calibrated parameters rather than fitted to the femtoscopic data, giving the comparison with STAR a predictive character. However, the comparison is qualitative, and the two EoS scenarios differ in several other model parameters, so the attribution of the R_long difference to the EoS is not currently supported.","major_comments":[{"comment":"The model \"noticeably overestimates the increase of the long radii with energy\" at 19.6, 27, and 39 GeV, yet Sec. IV summarizes the results as giving a \"satisfactory description ... across the entire energy range.\" This acknowledged discrepancy is not analyzed in terms of its physical origin, nor is its impact on the overall conclusion discussed. The authors should report a quantitative measure for the high-energy R_long deviation and state explicitly whether this discrepancy weakens the claim that the crossover EoS scenario reproduces the femtoscopic data.","section":"Sec. III, Fig. 3; Sec. IV"}],"minor_comments":[{"comment":"The 5% most central events are selected using 20,000 standalone UrQMD events, while the hydrodynamic simulations are a separate batch of 150 events. The possible bias from this two-step centrality selection is not quantified; a brief estimate of its effect on the extracted radii would be useful.","section":"Sec. III, centrality definition"}],"recommendation":"major_revision","confidential_remarks":"The paper relies heavily on the authors' own previous work [19,22] for the parameterization and the model setup; that is appropriate given the target journal, but the EoS comparison should be framed as testing the complete parameter sets rather than the EoS alone. No citation-pattern concerns beyond this. The manuscript is within scope for a heavy-ion theory journal, but the load-bearing confound in Table I must be addressed before the main claim is acceptable."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this paper does something worth doing. It takes the iHKMe model, whose parameters were fixed by spectra fits in the authors' earlier paper, computes pion HBT radii at RHIC BES energies for a crossover and a first-order EoS, and compares to STAR data. That is a real prediction, not a fit, and it is the first BES application of this model to femtoscopy. The crossover scenario tracks the data reasonably; the first-order scenario produces visibly larger R_long at higher BES energies. That is a clear and publishable-in-principle observation.\n\nWhat is new: previous iHKM HBT work was at top RHIC/LHC energies, and the recent BES work in [22] covered spectra. This paper extends the same calibrated parameter sets to HBT radii, and it is honest about the high-energy trend, admitting the model overestimates the growth of R_long.\n\nThe soft spots are real, and they sit on the main claim. The conclusion that femtoscopic radii favor a crossover EoS is not actually isolated. Table I shows the CO and PT parameter sets differ not only in the EoS but in eta/s (0.14 vs 0.08) and eps_sw (0.50 vs 0.35 GeV/fm^3), and sometimes tau_th. A lower eps_sw delays the switch from hydro to cascade and lengthens the emission duration; a different shear viscosity changes the expansion history. Either can change R_long independently of the EoS. The authors inherited these parameter sets from their spectra paper, so this is not a straw man—it is a confound that has to be addressed before the EoS attribution is established. There is also no quantitative agreement metric; model points carry no error bars, and the high-energy R_long overshoot is visible by eye. Comparing 14.5 GeV results against 11.5 and 19.6 GeV data is a reasonable expedient but weakens the lower-energy statements.\n\nNone of this kills the paper as a modeling contribution. The chain is concrete (UrQMD + hydro + cascade), the predictions are reproducible in principle, and the comparison to STAR is straightforward. What is established is that HBT radii are sensitive to the model scenario; what is not yet established is that they favor a crossover transition specifically.\n\nWho it is for: people doing hybrid-model femtoscopy at BES energies, and anyone using HBT radii to constrain the QCD phase structure. A serious referee should ask for an EoS scan at fixed eta/s and eps_sw, or at least a sensitivity study, plus uncertainties. I would send it to review, not desk reject; the central claim needs revision but the work is substantial. Self-citations are to the model's own development, not a concern here.","headline":"A genuine prediction of HBT radii from an already-calibrated model, but the central EoS-sensitivity claim is confounded because the crossover and first-order scenarios also differ in eta/s and eps_sw.","tokens_in":11781,"tokens_out":2664,"would_cite":true,"duration_ms":30000,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Pion interferometry radii at RHIC BES energies favor a crossover QCD transition over a first-order phase transition.","keywords":["pion femtoscopy","HBT radii","integrated HydroKinetic Model","RHIC Beam Energy Scan","equation of state","QCD phase transition","relativistic heavy-ion collisions","two-pion correlations"],"falsifier":"A decisive check is to rerun the 11.5 and 14.5 GeV cases with the crossover equation of state but the first-order scenario's viscosity and particlization density (and vice versa); if $R_{long}$ follows those parameters rather than the equation of state, the paper's EoS-sensitivity conclusion would collapse. A new measurement of interferometry radii at 14.5 GeV would also test the model's prediction at an energy now interpolated between 11.5 and 19.6 GeV.","tokens_in":10746,"feed_emoji":"⚛️","tokens_out":7784,"duration_ms":68531,"temperature":0.7,"pith_summary":"This paper tries to establish that pion interferometry radii measured in RHIC Beam Energy Scan collisions can be reproduced by the extended integrated HydroKinetic Model (iHKMe), and that these radii are sensitive enough to the equation of state to tell a smooth crossover from a first-order phase transition. The model couples UrQMD initial conditions, a gradual relaxation stage, viscous hydrodynamics, and a hadronic cascade, and the authors compute three-dimensional Gaussian radii $R_{out}$, $R_{side}$, $R_{long}$ for 5% central Au+Au collisions at $\\sqrt{s_{NN}}=7.7$–$39$ GeV. They find the crossover equation of state gives better agreement with measured data overall, while the first-order equation of state predicts a noticeably larger $R_{long}$ because the mixed-phase stage lengthens the system's lifetime; the discrepancy grows with collision energy. At 7.7 GeV the first-order scenario still gives reasonable agreement, leaving the low-energy transition type undecided.","feed_headline":"Pion source sizes favor a crossover QCD transition","feed_subtitle":"A full-evolution model reproduces femtoscopy radii better with a smooth transition than with a first-order phase change.","key_machinery":"The central object is the extended integrated HydroKinetic Model (iHKMe), which joins five stages: UrQMD-generated initial conditions, a pre-equilibrium relaxation stage in which the energy-momentum tensor and baryon current interpolate between UrQMD and hydrodynamic forms through a weight function $P(\\tau)$, viscous hydrodynamics with a chosen equation of state, Cooper-Frye particlization on a constant-energy-density hypersurface, and a final UrQMD hadron cascade that runs to $t=400$ fm/c. The free parameters ($R$, $\\tau_0$, $\\tau_{rel}$, $\\tau_{th}$, $\\eta/s$, $\\varepsilon_{sw}$) are taken from earlier spectra calibrations, and the interferometry radii are extracted from Gaussian fits to the two-pion correlation function in the out–side–long (Bertsch–Pratt) parametrization. Comparing the crossover and first-order equations of state is what carries the argument: the first-order scenario's mixed phase lengthens the emission duration, and $R_{long}$ is the observable that registers this lengthening.","core_discovery":"The central claim is that femtoscopic radii at intermediate collision energies can discriminate between equations of state. Within iHKMe, the crossover chiral equation of state reproduces the measured $R_{out}$, $R_{side}$, and $R_{long}$ across $\\sqrt{s_{NN}}=7.7$–$39$ GeV, while the first-order phase transition equation of state, calibrated separately to match particle spectra, yields $R_{long}$ values noticeably above the data at 11.5 and 14.5 GeV and above. The authors trace this excess to a prolonged mixed-phase stage that extends emission duration. They conclude that the crossover scenario describes the interferometry radii better, especially at higher BES energies, and that both scenarios remain compatible with the 7.7 GeV data.","pith_inferences":["The paper's EoS comparison is partly entangled with other parameter differences: the first-order sets use $\\eta/s=0.08$ and $\\varepsilon_{sw}=0.35$ while the crossover sets use $0.14$ and $0.50$, so a decisive test would vary the equation of state while holding these parameters fixed.","The paper's own trend implies a testable prediction for future low-energy collider programs: below 7.7 GeV the first-order scenario should make $R_{long}$ rise more steeply with energy, which precise low-energy femtoscopy could confirm.","Because no experimental 14.5 GeV data exist, the model's prediction at that energy is a direct, currently untested discriminator between the two equations of state.","Combining $R_{long}$ with $R_{out}$ and $R_{side}$ as a lifetime-versus-geometry diagnostic may sharpen EoS discrimination in future correlation analyses, including non-Gaussian source shapes."],"forward_implications":["Above roughly 11.5 GeV, the crossover equation of state describes the measured interferometry radii better than the first-order phase transition, which overpredicts $R_{long}$.","At 7.7 GeV both equations of state remain consistent with data, so low-energy femtoscopy alone cannot yet rule out a first-order transition.","The model reproduces the observed pattern of $R_{long}$ rising with collision energy while $R_{side}$ and $R_{out}$ stay roughly flat, supporting the picture that higher energies mainly extend emission duration.","The successful description from 7.7 to 39 GeV indicates that iHKMe's smooth stage coupling handles long nuclear overlap times and partial thermalization adequately.","The trend seen in the comparison suggests that at even lower energies (around 2–4 GeV) the first-order equation of state could become the preferred description."],"supporting_citations":[{"why":"Defines the extended integrated HydroKinetic Model with a smooth relaxation stage, which supplies the dynamical framework for all calculations.","marker":"[19]"},{"why":"Provides the calibrated model parameters for each collision energy and equation of state, the inputs on which the HBT results rest.","marker":"[22]"},{"why":"Gives the chiral crossover equation of state used as one of the two scenarios.","marker":"[23]"},{"why":"Gives the first-order phase transition equation of state used as the alternative scenario.","marker":"[24]"},{"why":"Provides the experimental Au+Au pion interferometry radii used as the comparison benchmark.","marker":"[43]"},{"why":"Supplies the UrQMD transport model used for initial conditions and for the final hadronic cascade.","marker":"[20]"}],"fun_headline_variants":["Pion radii favor a smooth QCD crossover","Pion femtoscopy supports crossover over first-order at BES","At RHIC BES, pion sizes point to crossover transition","Crossover QCD transition wins in pion source sizes","BES pion radii favor smooth QCD phase change"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The claim that the equation of state drives the better fit assumes that the two scenarios' other parameter differences—shear viscosity $\\eta/s$ of 0.14 vs 0.08 and the energy density $\\varepsilon_{sw}$ of 0.50 vs 0.35 at which the fluid becomes a hadron cascade—do not themselves explain the $R_{long}$ difference.","fun_headline_variants_meta":{"raw":{"variants":["Pion radii favor a smooth QCD crossover","Pion femtoscopy supports crossover over first-order at BES","At RHIC BES, pion sizes point to crossover transition","Crossover QCD transition wins in pion source sizes","BES pion radii favor smooth QCD phase change"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000641,"raw_usage":{"total_tokens":2978,"prompt_tokens":1001,"completion_tokens":1977,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":617,"completion_tokens_details":{"reasoning_tokens":1898}},"tokens_in":617,"tokens_out":1977,"duration_ms":14606,"temperature":1.0,"reasoning_tokens":1898,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T18:36:31.680315+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A decisive check is to rerun the 11.5 and 14.5 GeV cases with the crossover equation of state but the first-order scenario's viscosity and particlization density (and vice versa); if $R_{long}$ follows those parameters rather than the equation of state, the paper's EoS-sensitivity conclusion would collapse. A new measurement of interferometry radii at 14.5 GeV would also test the model's prediction at an energy now interpolated between 11.5 and 19.6 GeV.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines the extended integrated HydroKinetic Model with a smooth relaxation stage, which supplies the dynamical framework for all calculations."},{"cited_title":"Thermalization, evolution and LHC observables in an integrated hydrokinetic model of A+A collisions","cited_arxiv_id":"1508.07204","evidence_quote":"Provides the calibrated model parameters for each collision energy and equation of state, the inputs on which the HBT results rest."},{"cited_title":"Matching of nonthermal initial conditions and hydrodynamic stage in ultrarelativistic heavy-ion collisions","cited_arxiv_id":"0912.4180","evidence_quote":"Gives the chiral crossover equation of state used as one of the two scenarios."},{"cited_title":"Initialization of hydrodynamics in relativistic heavy ion collisions with an energy-momentum transport model","cited_arxiv_id":"1411.4490","evidence_quote":"Gives the first-order phase transition equation of state used as the alternative scenario."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the experimental Au+Au pion interferometry radii used as the comparison benchmark."},{"cited_title":"Effects of hadronic mean-field potentials on Hanbury-Brown-Twiss correlations in relativistic heavy-ion collisions","cited_arxiv_id":"1707.07272","evidence_quote":"Supplies the UrQMD transport model used for initial conditions and for the final hadronic cascade."}],"review_version":2}