{"id":"392d87fc-3a96-4be3-b5bd-cedfd6a11e81","arxiv_id":"2506.17973","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"Heavy-ion collision data, analyzed with a transport model, favor m*_n > m*_p for low kinetic energy nucleons and m*_n < m*_p for high kinetic energy nucleons.","lead":"This paper uses simulations of tin-on-tin collisions to show that low- and high-energy nucleon emission data favor opposite signs for the neutron-proton effective mass splitting. The findings suggest that a single value of this key nuclear-matter parameter cannot describe both regimes, which would affect neutron star models and heavy ion collision theory.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Two-window slope extraction with a model that fails to reproduce the full spectrum makes the opposite-sign Δm*_np claim binning-dependent; a varying-window reanalysis would settle it.","rationale":"The paper's methodological contribution—showing a strong within-model correlation between S_n/p and f_I (r up to 0.928)—is credible and useful. The point at which the argument becomes load-bearing is the step from that correlation to the claim that the data require opposite signs of Δm*_np/δ below and above 60 MeV. That step uses S_n/p computed from only two pairs of energies in the data, with the boundary at 60 MeV chosen after the model-data comparison, and it uses a model that the authors state does not reproduce the measured R_n/p spectra. The authors also list the high-momentum tail of the initial momentum distribution as an alternative explanation for the high-energy behavior, which is an internal admission that the sign flip is not uniquely determined by Δm*_np. Therefore the weakest assumption is not the correlation but the extraction/comparison procedure. The proposed sliding-window or full-spectrum test directly targets this assumption: if the inferred sign is stable under reasonable variations of the window, the concern is resolved; if not, the central physical conclusion is not supported. Since the reader's verdict was already CONDITIONAL and our concern supports that conditionality, the verdict should remain UNCHANGED.","tokens_in":10202,"tokens_out":4582,"duration_ms":46007,"concrete_test":"Re-extract S_n/p from the published data of Ref. [31] using a sliding 35 MeV window (or the full data) and recompute the inferred Δm*_np/δ with the same 189 parameter-set model outputs, varying the window position across the available energy range. If the inferred sign is not stable when the window boundaries move by ±5–10 MeV, or if a single-signed Δm*_np/δ can reproduce the full spectrum within errors, the claimed opposite-sign low/high constraints are an artifact of the chosen bins.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim—that low-kinetic-energy data favor m*_n > m*_p while high-kinetic-energy data favor m*_n < m*_p—rests on the two-point slopes S_n/p defined in Eq. (9), computed in the hand-selected windows 45–60 MeV and 60–95 MeV. This is the weakest structural link in the argument. The paper admits (Sec. 2, Fig. 2) that the model does not exactly reproduce the measured R_n/p spectrum, especially for S_n/p as a function of E_k/A. Because the model-data difference is not small, the slope over a chosen window can be dominated by the systematic model error rather than by sensitivity to f_I. The two windows also share the boundary at 60 MeV, so the low- and high-energy constraints are not independent, and the authors themselves attribute possible high-energy behavior to the high-momentum tail of the initial momentum distribution. With extracted central values of Δm*_np/δ = +0.28 to +0.41 (low) and −0.33 to −0.12 (high), and error estimates that depend strongly on the method (hatched vs shaded regions in Fig. 4), the sign flip is at most a 1–2 sigma separation. Without a pre-registered binning or a full-spectrum fit, the conclusion that the symmetry potential is non-monotonic in momentum is not settled.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript uses the ImQMD transport model with standard and extended Skyrme momentum-dependent interactions to study the neutron-proton effective mass splitting (Δm*_np). A Latin-hypercube sample of 189 parameter sets is generated in the space (S0, L, m*_s/m, f_I), and the slope S_n/p of the neutron-to-proton yield ratio with respect to kinetic energy is computed in two selected windows, 45–60 MeV and 60–95 MeV, via the two-point formula in Eq. (9). The authors report a strong linear correlation between S_n/p and Δm*_np/δ, with correlation coefficients up to 0.928 for 124Sn+124Sn, and compare the model slopes with data from Ref. [31]. They find that the low-energy window favors m*_n > m*_p with Δm*_np/δ between +0.28 and +0.41, while the high-energy window favors m*_n < m*_p with values between -0.33 and -0.12. The paper concludes that a fixed-Δm*_np Skyrme interaction cannot describe both windows, that the momentum-dependent symmetry potential may be non-monotonic, and that the high-momentum tail of the initial momentum distribution could also affect the high-energy part of the spectrum.","tokens_in":10515,"tokens_out":4925,"duration_ms":48584,"significance":"If the central claim is correct, the analysis would provide a path toward reconciling heavy-ion collision constraints on Δm*_np with nucleon-nucleus scattering analyses, and it would motivate momentum-dependent symmetry potentials beyond the standard Skyrme form. The paper has several genuine strengths: it carries out a multi-parameter sensitivity study rather than varying only L and Δm*_np; it tests both standard and extended Skyrme MDI; it demonstrates with correlation coefficients that S_n/p is much more sensitive to f_I than to S0, L, or m*_s/m in the model; and it applies the correlation to an external dataset rather than only to model-generated data. These features make the correlation analysis useful regardless of the final constraint values. However, the quantitative constraints are only as reliable as the slope extraction from a spectrum that the model itself does not reproduce, and the sign-flip claim is currently sensitive to window choices and to the error prescription used. The paper is therefore significant but not yet conclusive.","major_comments":[{"comment":"The two-point slopes S_n/p are computed in windows E1=45/E2=60 MeV and E1=60/E2=95 MeV that appear to be selected after inspecting the data, and the two windows share the same 60 MeV boundary, so the low- and high-energy constraints are not independent. Because the model does not exactly reproduce the measured R_n/p spectrum, as the paper itself states in Section 2 and as is visible in Fig. 2, the extracted slopes can be dominated by the model-data mismatch rather than by f_I sensitivity. Please provide a varying-window scan (for example, moving E1 and E2 over the available energy range) or a full-spectrum fit, and show that the sign of the extracted Δm*_np/δ does not depend on the chosen binning.","section":"Section 2, Eq. (9) and Fig. 3"},{"comment":"The two error prescriptions for the data S_n/p lead to constraints that are not mutually consistent. With the error-propagation method, the low-energy Δm*_np/δ values are 0.28±0.27 (standard MDI) and 0.31±0.22 (extended MDI), while the high-energy values are -0.12±0.22 and -0.21±0.23; under this error treatment the low- and high-energy constraints are statistically compatible with each other at roughly the 1σ level. With the alternative hatched-area method the separation is larger. Because the choice of error method changes the conclusion from a clear sign flip to at most a marginal one, the paper should justify one error prescription over the other and report the significance of the observed sign change under both methods.","section":"Table II and Fig. 4"},{"comment":"The authors state that a χ2 analysis was performed to obtain the optimal parameter sets shown as blue curves in Fig. 2, but the minimized reduced χ2 values are never reported. Since the model visibly fails to reproduce the full R_n/p spectrum, the reader cannot assess whether the remaining model-data discrepancy is small compared with the S_n/p sensitivity to f_I. Please report the χ2 values and residuals, and quantify how much of the two-point slope in each window is attributable to the systematic model deficiency rather than to the f_I dependence.","section":"Section 2, Fig. 2"},{"comment":"The paper acknowledges that the high-momentum tail of the nucleon momentum distribution in the initial nucleus can influence R_n/p at high kinetic energies and thereby affect the interpretation of the data. Since the high-energy window is precisely where the claim m*_n < m*_p is made, this alternative explanation is load-bearing and needs a quantitative test. Concretely, the authors should vary the initial momentum distribution or remove the highest-energy bins and show that the extracted high-energy Δm*_np/δ remains negative; otherwise the non-monotonic symmetry potential conclusion is not yet supported.","section":"Discussion (final paragraphs)"}],"minor_comments":[{"comment":"The notation f_I = (1/(2δ))(m/m*_n - m/m*_p) = m/m*_s - m/m*_v is surprising because the first expression depends on δ while the second does not; the equivalence should be stated explicitly or the definitions of m*_s and m*_v should be given in the text.","section":"Eq. (6)"},{"comment":"The text says the high-energy S_H_n/p results are presented in panels (e)-(f), but the Fig. 3 caption indicates panels (a)-(h) are for S_L,H_n/p; please correct the panel reference.","section":"Fig. 3 caption and text"},{"comment":"There is a typo: 'subjec to large uncertainties' should be 'subject to large uncertainties', and 'wealky correlated' should be 'weakly correlated'.","section":"Section 2, text near Eq. (9)"},{"comment":"The correlation coefficient quoted in the text changes between f_I and Δm*_np/δ (r=0.798/0.904 for f_I versus 0.80/0.928 for Δm*_np/δ); since the two quantities are linearly related in the model, this should be clarified so the reader does not perceive an inconsistency.","section":"Fig. 4 and Fig. 5"},{"comment":"The column headings D_L^Ext, D_L^Stand, D_H^Ext, D_H^Stand are not defined in the caption; please add a sentence explaining that D denotes the data window and Ext/Stand the two MDI forms.","section":"Table II"}],"recommendation":"major_revision","confidential_remarks":"The central claim is interesting and the correlation analysis is a useful contribution, but the sign-flip conclusion rests on hand-selected windows and on an error treatment that the paper itself shows to be ambiguous. I do not recommend rejection because the issues are addressable with additional analysis, but the current manuscript does not yet make the case that the non-monotonic momentum dependence is established."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things worth knowing upfront. The durable piece here is the correlation analysis: across 189 parameter sets sampled in {S0, L, m*_s/m, f_I}, S_n/p tracks Δm*_np/δ with r ≈ 0.93 for 124Sn+124Sn at high E_k, while S_DR does not. That is a genuinely useful message for the transport community and is the paper's real contribution. The second thing is that the central claim—that low-energy data favor m*_n > m*_p and high-energy data favor m*_n < m*_p—is not settled by the analysis as presented.\n\nThe correlation itself is convincing; the conversion to constraints is not. The energy windows (45–60 MeV and 60–95 MeV) are chosen after looking at the data, they share a boundary, and the two-point slopes are computed from a spectrum the authors explicitly say the model does not exactly reproduce. The high-energy window is additionally fragile because the authors themselves point to the high-momentum tail of the initial momentum distribution as a possible explanation for the same behavior. Given that the extracted central values differ by about 0.5 in Δm*_np/δ (from +0.28–0.41 to −0.33 to −0.12) and the quoted uncertainties are method-dependent, the sign flip is at most a one-to-two-sigma effect. The claim that the symmetry potential is non-monotonic in momentum is therefore a hypothesis to test, not a constraint to adopt.\n\nWhere they deserve credit: the scan is broad, standard and extended Skyrme interactions are both checked, the sensitivity to S_DR is honestly reported as weak, and the limitations are acknowledged in the text. There is no code release, which limits independent verification, but this is a modeling paper with a finite computation and the key qualitative correlation should be reproducible in principle.\n\nWho is this for? Anyone working on effective mass splitting constraints from heavy-ion collisions. It would be a reasonable journal article after revision. A serious referee should request a varying-window or sliding-window reanalysis to show the sign flip is not binning-dependent, a check of the extracted slopes against a full-spectrum fit, and preferably a cross-check with another transport code. I would not yet cite this work for a sign flip; I would cite it as a sensitivity study of S_n/p.","headline":"Useful sensitivity study, but the headline opposite-sign Δm*_np claim is not established: it rests on hand-picked energy windows and a model that misses the full spectrum.","tokens_in":11106,"tokens_out":2936,"would_cite":false,"duration_ms":29566,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["21.65.Ef","25.70.-z","24.10.Cn","21.30.Fe"],"model":"deepseek-v4-flash","headline":"In tin-on-tin collisions, the kinetic-energy slope of the neutron-to-proton yield ratio is dominated by the neutron-proton effective mass splitting, and the data favor $m_n^*>m_p^*$ below 60 MeV but $m_n^*<m_p^*$ above 60 MeV.","keywords":["neutron-proton effective mass splitting","heavy-ion collisions","symmetry energy","neutron-to-proton yield ratio","Skyrme interactions","quantum molecular dynamics","isospin asymmetry","transport model"],"falsifier":"Measure $R_{n/p}$ for $^{124}$Sn+$^{124}$Sn at 120 MeV/u with fine kinetic-energy bins from 40 to 100 MeV; if the slope $S_{n/p}$ does not change sign near 60 MeV when the bins and errors are handled consistently, the central claim of a sign-flipping constraint is refuted.","tokens_in":9973,"feed_emoji":"⚛️","tokens_out":10513,"duration_ms":93160,"temperature":0.7,"pith_summary":"This paper tries to pin down the neutron-proton effective mass splitting—how differently neutrons and protons effectively respond to moving through dense nuclear matter—by simulating $^{112,124}$Sn+$^{112,124}$Sn collisions at 120 MeV/u with the improved quantum molecular dynamics model and comparing them with published yield-ratio data. The authors find that the slope of the neutron-to-proton yield ratio with respect to kinetic energy, $S_{n/p}$, is almost linearly controlled by the splitting, with correlation coefficients up to $r=0.928$ for $^{124}$Sn+$^{124}$Sn. The same data favor $m_n^*>m_p^*$ for nucleons emitted below 60 MeV, matching nucleon-nucleus scattering analyses, and $m_n^*<m_p^*$ above 60 MeV. If this is right, no single fixed Skyrme interaction can describe both energy windows, and the momentum-dependent symmetry potential must change from decreasing to increasing with momentum.","feed_headline":"Tin collisions: neutron-proton mass splitting flips sign at 60 MeV","feed_subtitle":"Low-energy nucleons say neutrons are heavier; high-energy ones say neutrons are lighter.","key_machinery":"The load-bearing quantity is $S_{n/p}$, the two-point slope of the logarithm of the neutron-to-proton yield ratio across a kinetic-energy window. The paper uses the proportionality $S_{n/p} \\propto -(m/m_s^*)^2 \\Delta m^*_{np}$, feeds the model with the inverse-effective-mass difference $f_I = (1/2\\delta)(m/m_n^* - m/m_p^*)$ rather than $\\Delta m^*_{np}$ directly, and samples 189 parameter sets in the four-dimensional space $S_0$, $L$, $m_s^*$, $f_I$ using Latin hypercube sampling. The transport model is the improved quantum molecular dynamics (ImQMD) model with standard and extended Skyrme momentum-dependent interactions; extended interactions are fit to optical-potential data. The observable is computed for two kinetic windows, 45–60 MeV and 60–95 MeV, chosen from the available data points.","core_discovery":"The central claim is that the kinetic-energy slope of the logarithm of the neutron-to-proton yield ratio, $S_{n/p} = \\partial \\ln R_{n/p}/\\partial E_k$, is a direct and nearly linear observable for the neutron-proton effective mass splitting, and that comparing it with existing data from $^{112,124}$Sn+$^{112,124}$Sn at 120 MeV/u yields two different signs depending on the nucleon kinetic energy. With 189 parameter sets covering $S_0$, $L$, $m_s^*$, and $f_I$, the authors obtain $\\Delta m^*_{np}/\\delta \\approx 0.28$–$0.41$ from the 45–60 MeV window and $\\Delta m^*_{np}/\\delta \\approx -0.33$ to $-0.12$ from the 60–95 MeV window. They interpret the sign flip as evidence that the isovector potential is non-monotonic in momentum, a behavior standard Skyrme interactions cannot produce but finite-range Gogny forces already predict. The paper also notes that the model does not exactly reproduce the measured $R_{n/p}$ spectrum, and that a high-momentum tail from short-range correlations in the initial nucleus could compete with the high-energy interpretation.","pith_inferences":["If the energy-window dependence is genuine, average constraints on $\\Delta m^*_{np}$ obtained from the full spectrum will tend to cancel two opposite signs and could look artificially close to zero; separate bin-by-bin constraints would be the safer route.","The correlation analysis suggests that single ratios are far more informative than double ratios for this question, since $S_{DR}$ correlates only weakly with $f_I$; future analyses could therefore prioritize single-ratio measurements.","A decisive separation of the two explanations the paper leaves open—non-monotonic mean-field momentum dependence versus short-range-correlation high-momentum tails—would come from a transport calculation that adds high-momentum tails to the initial nucleus while holding $\\Delta m^*_{np}$ fixed and checking whether both windows can then be reproduced without a sign flip."],"forward_implications":["Low-energy heavy-ion data and nucleon-nucleus scattering now point the same way, $m_n^*>m_p^*$, which removes one longstanding source of disagreement.","Constraints on the effective mass splitting must be quoted per kinetic-energy window rather than as a single number, because the same Skyrme-type interaction cannot describe both windows.","The sign reversal at about 60 MeV implies the symmetry (isovector) potential is non-monotonic in nucleon momentum, a qualitative feature that standard Skyrme forces do not contain.","The strong, stable correlation between $S_{n/p}$ and $\\Delta m^*_{np}$ (up to $r=0.928$) makes the yield-ratio slope a practical observable for future heavy-ion experiments aimed at the effective mass splitting."],"supporting_citations":[{"why":"Derives the proportionality between $S_{n/p}$ and $\\Delta m^*_{np}$ and supplies the ImQMD model version used here.","marker":"[35]"},{"why":"Provides the published $R_{n/p}$ and $DR(n/p)$ spectra from which the $S_{n/p}$ data points and their errors are extracted.","marker":"[31]"},{"why":"Gives the nucleon-nucleus scattering result $\\Delta m^*_{np}=(0.41\\pm0.15)\\delta$ that the low-energy constraint is said to reconcile.","marker":"[26]"},{"why":"Fits the extended momentum-dependent interaction coefficients to Hama optical potential data.","marker":"[38]"},{"why":"Supplies the relations and prior ranges connecting $S_0$, $L$, $m_s^*$, and $f_I$ to the Skyrme parameters.","marker":"[39]"},{"why":"Predicts a non-monotonic momentum-dependent symmetry potential with finite-range Gogny interactions, cited as the expected behavior behind the sign flip.","marker":"[45]"},{"why":"Also predicts non-monotonic effective-mass behavior from Gogny forces, supporting the interpretation of the high-energy constraint.","marker":"[46]"}],"fun_headline_variants":["Neutron-proton mass splitting flips sign at 60 MeV in tin","Heavy ion tin collisions reveal sign flip in neutron-proton mass splitting","Momentum-dependent neutron-proton mass splitting from tin collisions","Tin collision data show neutron mass switches lighter or heavier at 60 MeV"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the two-point slopes $S_{n/p}$ computed from the published data in the selected 45–60 MeV and 60–95 MeV windows are unbiased probes of $\\Delta m^*_{np}$, even though the model does not exactly reproduce the measured neutron-to-proton spectrum and the high-energy window could also be explained by the unmodeled high-momentum tail of the initial nucleon distribution.","fun_headline_variants_meta":{"raw":{"variants":["Neutron-proton mass splitting flips sign at 60 MeV in tin","Heavy ion tin collisions reveal sign flip in neutron-proton mass splitting","Momentum-dependent neutron-proton mass splitting from tin collisions","Tin collision data show neutron mass switches lighter or heavier at 60 MeV"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000166,"raw_usage":{"total_tokens":1276,"prompt_tokens":991,"completion_tokens":285,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":607,"completion_tokens_details":{"reasoning_tokens":206}},"tokens_in":607,"tokens_out":285,"duration_ms":3174,"temperature":1.0,"reasoning_tokens":206,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T18:57:14.641507+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure $R_{n/p}$ for $^{124}$Sn+$^{124}$Sn at 120 MeV/u with fine kinetic-energy bins from 40 to 100 MeV; if the slope $S_{n/p}$ does not change sign near 60 MeV when the bins and errors are handled consistently, the central claim of a sign-flipping constraint is refuted.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Derives the proportionality between $S_{n/p}$ and $\\Delta m^*_{np}$ and supplies the ImQMD model version used here."},{"cited_title":"Morfouace, C","cited_arxiv_id":null,"evidence_quote":"Provides the published $R_{n/p}$ and $DR(n/p)$ spectra from which the $S_{n/p}$ data points and their errors are extracted."},{"cited_title":"Li, W.-J","cited_arxiv_id":null,"evidence_quote":"Gives the nucleon-nucleus scattering result $\\Delta m^*_{np}=(0.41\\pm0.15)\\delta$ that the low-energy constraint is said to reconcile."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Fits the extended momentum-dependent interaction coefficients to Hama optical potential data."}],"review_version":2}