{"id":"c8a71a08-5302-4ae9-a260-1d2bb3c7de77","arxiv_id":"2412.12729","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":9,"one_line_summary":"Hyperon interactions tuned to femtoscopic data still yield neutron star maximum masses of only 1.3-1.4 solar masses, leaving the hyperon puzzle unresolved.","lead":"This paper uses hyperon interactions constrained by ALICE femtoscopy data and lattice QCD to compute neutron star equations of state, and finds that stars with hyperons still only reach 1.3 to 1.4 solar masses. The result confirms that the 'hyperon puzzle' remains unsolved if only two-body interactions are included, strengthening the case for three-body forces or new physics in dense matter.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Maximum mass range may depend on the non-self-consistent inclusion of the 3NF: Eq. (5) adds the nucleonic 3NF after the G-matrix calculation, so single-particle potentials and in-medium correlations omit 3NF effects.","rationale":"The paper is careful to state that its conclusion applies only when two-body hyperon–nucleon and hyperon–hyperon interactions are considered, and the hyperonic-three-body-force omission is an explicit scope condition rather than a hidden flaw. The central numerical claim is also consistent with earlier BHF results using different YN/YY models, giving independent support. However, the weakest internal link is the treatment of the nucleonic 3NF: Eq. (5) is appended to the energy density after the G-matrix has been solved, so the in-medium single-particle potentials and the G-matrix itself are computed without 3NF effects. The reader's weakest_assumption correctly identifies this concern, along with the related but distinct hyperonic-3BF and P-wave issues. Among these, the 3NF self-consistency is the most load-bearing because it affects the high-density EoS that determines M_max and because it is an approximation internal to the calculation rather than an external scope condition. The proposed test—switching to the standard density-dependent-two-body-force implementation—would settle whether this approximation shifts the result. Given the paper's explicit scoping and the robustness of the qualitative conclusion, the reader's CONDITIONAL verdict remains appropriate; no change to the verdict is needed, but the conditional acceptance should require validation or clear reporting of the 3NF treatment's effect.","tokens_in":16039,"tokens_out":10814,"duration_ms":102139,"concrete_test":"Repeat the full BHF calculation using the standard implementation where the phenomenological 3NF of Eq. (5) is converted into a density-dependent two-body force and included in the Bethe–Goldstone equation (as in Refs. [49,50,51]), keeping all hyperon interactions and the fitted a,b parameters fixed. Recompute the TOV maximum mass for the hyperonic EoS. If M_max changes by more than ∼0.1 M_sun, the reported 1.3–1.4 M_sun range is not robust to the 3NF treatment; if it remains within that range, the simplification is validated.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim, M_max ≈ 1.3–1.4 M_sun for stars with S=-1 and S=-2 hyperons, rests on the BHF EoS built in Sect. 3. The Bethe–Goldstone equation (1) and single-particle potentials (3) are solved using only two-body NN, YN, and YY interactions; the nucleonic 3NF is then added purely as an energy-density term, Eq. (5), after the G-matrix is obtained. Consequently, the 3NF does not enter the G-matrix or the single-particle spectrum, even though the chemical potentials μ_i = ∂ε/∂ρ_i used for beta-equilibrium do receive 3NF contributions. This mixed procedure is a deliberate simplification, but it is not the standard BHF treatment of 3NFs, where an effective density-dependent two-body force is inserted into the Bethe–Goldstone equation (as the paper itself notes from Refs. [49,50,51]). Because the maximum mass is controlled by the EoS at several times saturation density, the non-self-consistent 3NF treatment could shift M_max or the reported bands, which are already acknowledged to be lower bounds (Sect. 4). The two K0 values only vary the parameters a,b in Eq. (5); they do not test whether the post-hoc addition itself is adequate.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript constructs the equation of state (EoS) of hypernuclear matter in the Brueckner–Hartree–Fock approach using the NLO19 chiral ΛN–ΣN interaction and its variants tuned to ALICE Λp femtoscopic data, together with HAL QCD lattice potentials for the ΛΛ and ΞN channels that reproduce ΛΛ and Ξ−p correlations. The nucleonic part uses the Argonne v18 potential plus a phenomenological density- and isospin-dependent three-nucleon-force term fitted to the saturation binding energy and to two values of the incompressibility (K0 = 160 and 270 MeV). Beta-equilibrated compositions, EoSs, mass–radius relations, and tidal deformabilities are obtained by solving the TOV equations. The central result is that the maximum mass of neutron stars containing S = −1 and S = −2 hyperons is about 1.3–1.4 M⊙, almost independent of the nucleonic EoS, so the hyperon puzzle persists if only two-body hyperon–nucleon and hyperon–hyperon interactions are included. The hyperonic EoSs satisfy the GW170817 tidal-deformability constraint only in the mass range 1.1–1.3 M⊙.","tokens_in":16302,"tokens_out":5921,"duration_ms":53254,"significance":"The result is significant because it uses state-of-the-art hyperon interactions constrained by femtoscopy and lattice QCD, rather than older phenomenological potentials, and still finds a maximum mass incompatible with the observed ~2 M⊙ pulsars. This sharpens the hyperon puzzle and gives a concrete falsifiable prediction: if the two-body interactions used here are correct, the observed high-mass pulsars cannot contain hyperons without additional repulsive many-body forces. The paper is also useful as a detailed propagation of interaction uncertainties (Λp scattering-length variations and regulator cutoff dependence) into neutron-star observables. The BHF equations are presented explicitly, and the construction of the uncertainty bands is explained. The main limitations—the post-hoc inclusion of the nucleonic three-nucleon force and the neglect of P-wave YN uncertainty—are acknowledged by the authors, but they are load-bearing for the quantitative claim and need further scrutiny.","major_comments":[{"comment":"The three-nucleon force is added only to the energy density after the G-matrix and single-particle potentials are computed, rather than being inserted into the Bethe–Goldstone equation as an effective density-dependent two-body force, as in Refs. [49–51]. Because the maximum mass is the central quantitative claim, this non-self-consistent treatment could shift the quoted 1.3–1.4 M⊙ range; the authors should estimate the systematic effect by comparing with the standard BHF implementation of Refs. [49–51], or at least provide a quantitative argument that the post-hoc addition does not affect the hyperonic maximum mass. The two K0 values only vary the coefficients a and b in Eq. (5); they do not test the form of the 3NF or the self-consistency of its inclusion.","section":"Sec. 3, Eq. (5)"},{"comment":"The paper explicitly states that the uncertainty from the ΛN interaction in P- and higher partial waves is not considered, although it could be about ±3 MeV in the Λ single-particle potential at saturation density. Since the paper's stated aim is to propagate uncertainties from the hyperon interactions to neutron-star properties, omitting this known source makes the displayed bands incomplete; the authors should either include an estimate of its effect on the EoS and on M_max or justify why it cannot affect the central conclusion.","section":"Sec. 4, final paragraph"},{"comment":"The claim that the maximum mass is 'quite insensitive to the nucleonic part of the EoS' is based on only two K0 values with the same phenomenological 3NF form. The isospin dependence (1+β^2) in Eq. (5) is an ad hoc ansatz; a different symmetry-energy behavior of the 3NF could change radii and tidal deformabilities, and possibly the maximum mass. This should be discussed or tested with an alternative 3NF parametrization.","section":"Sec. 4, Fig. 3"}],"minor_comments":[{"comment":"The x-axis label in all four panels appears garbled ('0 ρ/ρ4'); please fix the typography.","section":"Fig. 1"},{"comment":"The caption says 'panels (e) and (d)' where it should say 'panels (e) and (f)'.","section":"Fig. 3 caption"},{"comment":"The reference 'Primate communication' should be 'private communication'.","section":"Ref. [44]"},{"comment":"The phrase 'interior of neutrons of neutron stars' should be 'interior of neutron stars'.","section":"Sec. 5"},{"comment":"The statement that different ΛΛ and ΛΛ–ΞN parameterizations lead to identical results appears twice; consider consolidating to avoid redundancy.","section":"Sec. 4 and Sec. 5"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is likely within scope for EPJ A. The main concern is that the central numerical claim rests on a non-self-consistent 3NF treatment and on incomplete uncertainty accounting; both are fixable with additional calculations or careful discussion. I would not reject, but the revision should address these points."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is a careful, honest extension of the standard BHF treatment of hyperonic matter. What is new is not the qualitative conclusion—the 1.3–1.4 Msun maximum mass has been around since Schulze et al.—but the inputs: NLO19 variants tuned to ALICE femtoscopy and HAL QCD lattice potentials for Lambda-Lambda and XiN, with explicit uncertainty bands from data errors and cutoff variation. The paper does exactly what it says: it propagates those uncertainties to composition, EoS, mass-radius, and tidal deformability. The calculation is not circular; no parameter is adjusted to neutron star observables, and the prediction misses the 2 Msun pulsars, which is informative.\n\nThe core logic holds up. Within the stated scope (two-body YN/YY only), the result is a genuine prediction, and the paper flags the natural escape hatches: hyperonic three-body forces and P-wave YN uncertainty. The bands are lower bounds and the authors say so. That should count as credit, not a hidden flaw.\n\nThe main soft spot is exactly what the stress-test note identifies: the nucleonic 3NF is added after the G-matrix as an energy-density term, Eq. (5), rather than inserted as an effective density-dependent two-body force into the Bethe–Goldstone equation. That is a deliberate simplification, stated in Section 3, and the K0 variation only changes the two coefficients in Eq. (5), so it does not test whether the post-hoc addition is adequate. For the central conditional claim this is a caveat, not a knock-down objection, but the maximum mass could shift if the 3NF were treated self-consistently.\n\nTwo minor issues: the text around Fig. 2 refers to t/a=12 while footnote 2 says only t/a=11 was used, and the exact XiN parameter sets come from a private communication (ref. 44, with the typo 'Primate'), with no code or data deposit. Neither changes the conclusion, but both should be cleaned up.\n\nBottom line: a useful paper for the neutron-star EoS and strangeness community. The literature is handled fairly, and earlier results are properly credited. I would send it to a serious referee and would cite it for the uncertainty propagation, with the caveats understood.","headline":"Solid, honest BHF propagation of modern femtoscopic and lattice hyperon interactions to neutron stars; confirms the 1.3–1.4 solar mass ceiling and is worth refereeing, with the 3NF caveat kept in proportion.","tokens_in":16965,"tokens_out":3141,"would_cite":true,"duration_ms":28840,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["97.60.Jd","13.75.Ev"],"model":"deepseek-v4-flash","headline":"Femtoscopy-tuned and lattice-QCD hyperon interactions leave neutron-star maximum masses at 1.3–1.4 solar masses, so the hyperon puzzle persists if only two-body forces act.","keywords":["neutron star","hyperon puzzle","equation of state","Brueckner–Hartree–Fock","hyperon-nucleon interaction","femtoscopy","tidal deformability","strangeness"],"falsifier":"Repeat the identical Brueckner–Hartree–Fock calculation with a microscopically derived three-nucleon force replacing the fitted phenomenological term of Eq. (5); if the hyperonic maximum mass rises above roughly 1.4 solar masses, the reported ceiling is an artifact of the nucleonic parametrization rather than a consequence of the two-body hyperonic interactions. An observed neutron star above 1.4 solar masses with confirmed hyperons in its interior would also falsify the claim.","tokens_in":15731,"feed_emoji":"🌌","tokens_out":13055,"duration_ms":112213,"temperature":0.7,"pith_summary":"The paper tries to establish whether modern, data-driven hyperon interactions still make neutron stars too soft to reach two solar masses. Using a chiral hyperon-nucleon force tuned to femtoscopic Lambda-proton correlations and lattice-QCD Lambda-Lambda and Xi-N potentials that reproduce femtoscopic data, it computes hypernuclear equations of state and derives neutron-star structure. The central finding is that, no matter how stiff or soft the nucleonic part is, the maximum mass with S=-1 and S=-2 hyperons is 1.3–1.4 solar masses. That is far below the observed roughly two-solar-mass pulsars, so the hyperon puzzle persists if only two-body hyperon-nucleon and hyperon-hyperon interactions are at work. Hyperonic tidal deformabilities agree with the GW170817 constraint only in the 1.1–1.3 solar-mass range.","feed_headline":"Hyperons still cap neutron stars at 1.4 solar masses","feed_subtitle":"Femtoscopy-tuned and lattice-QCD interactions soften the equation of state, so the hyperon puzzle persists.","key_machinery":"The load-bearing machinery is the Brueckner–Hartree–Fock (BHF) many-body method in the strange sector: coupled-channel Bethe–Goldstone equations produce in-medium G-matrices for the NN, Lambda-N–Sigma-N, and Lambda-Lambda–Xi-N systems, and self-consistent single-particle potentials are iterated until convergence. The resulting energy density is combined with a phenomenological three-nucleon term, Eq. (5), chosen to reproduce saturation binding and two values of the nuclear incompressibility, and beta-equilibrium with leptons fixes the composition. The Tolman–Oppenheimer–Volkoff equations then give the mass–radius relation and a Love-number equation gives the tidal deformability.","core_discovery":"The paper shows that the currently best-constrained two-body hyperonic interactions produce a maximum neutron-star mass of 1.3–1.4 solar masses once hyperons appear. This value is almost independent of the nucleonic equation of state: the onset of Lambda, Sigma-minus, and Xi-minus hyperons triggers compensating softening mechanisms that wash out the nucleonic uncertainty. Consequently none of the considered hyperonic equations of state reproduces the observed roughly two-solar-mass pulsars, and the paper concludes that two-body-only hyperonic interactions leave the hyperon puzzle unsolved. The same equations of state predict tidal deformabilities compatible with GW170817 only up to about 1.3 solar masses, which is exactly the mass range the lower maximum mass allows.","pith_inferences":["If hyperonic three-body forces supply the missing repulsion, their required strength can be quantified by demanding that the maximum mass reach the observed two-solar-mass scale, turning the puzzle into a concrete target for three-body-force calculations.","Since the paper finds the maximum mass insensitive to nucleonic stiffness, radius and tidal-deformability measurements are likely to discriminate hyperonic from purely nucleonic equations of state better than mass measurements alone.","The paper notes in passing that P-wave hyperon-nucleon scattering is unconstrained; tightening that input could widen the uncertainty bands, so the 1.3–1.4 solar-mass peak should be read with that caveat.","Future precise tidal-deformability or radius measurements on stars below 1.4 solar masses could distinguish among the attractive and repulsive variants of the hyperon interactions explored here."],"forward_implications":["Adding strangeness through the studied two-body interactions softens the equation of state and lowers the maximum mass to 1.3–1.4 solar masses.","The maximum mass of hyperonic stars is nearly independent of the stiffness of the nucleonic equation of state, collapsing a wide spread in pure-nucleonic predictions.","None of the considered hyperonic equations of state can reproduce the observed roughly two-solar-mass pulsars; only pure nucleonic equations of state reach those masses.","Hyperonic stars have smaller radii and tidal deformabilities at a given mass than pure nucleonic stars, so hyperonic predictions match the GW170817 tidal constraint only below about 1.3 solar masses.","Because the maximum mass stays low, the hyperon puzzle remains open: some additional repulsion beyond two-body hyperonic forces is required."],"supporting_citations":[{"why":"supplies the chiral next-to-leading-order hyperon-nucleon potential that defines the S=-1 interaction.","marker":"[24]"},{"why":"provides the femtoscopy-tuned variants and the scattering-length uncertainty band used for the YN interaction.","marker":"[22]"},{"why":"supplies the lattice-QCD Lambda-Lambda and Xi-N potentials used for the S=-2 sector.","marker":"[23]"},{"why":"is the two-nucleon potential used for the nucleonic part of the BHF calculation.","marker":"[46]"},{"why":"is the femtoscopic Xi-minus-proton correlation data used to select attractive and repulsive Xi-N potentials.","marker":"[18]"},{"why":"is the femtoscopic Lambda-proton correlation data used to tune and test the S=-1 interaction.","marker":"[19]"},{"why":"is one of the earlier BHF hyperonic-star calculations that found the same insensitivity of the maximum mass to the nucleonic EoS.","marker":"[31]"},{"why":"is a later BHF study with meson-exchange hyperon interactions whose maximum-mass result is compared and confirmed.","marker":"[32]"},{"why":"provides the GW170817 tidal-deformability constraints that the paper compares with its hyperonic predictions.","marker":"[67]"},{"why":"is the roughly two-solar-mass pulsar observation that sets the incompatibility target for the hyperonic EoSs.","marker":"[17]"}],"fun_headline_variants":["Hyperon-only forces cap neutron stars at 1.4 solar masses","Femtoscopic data keep hyperon puzzle alive in neutron stars","Max neutron star mass drops to 1.4 with hyperons","Hyperon puzzle unsolved: two-body forces limit mass","Neutron star mass capped by hyperon onset at 1.4 suns"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing assumption is that a Brueckner–Hartree–Fock calculation using only two-body hyperon-nucleon and hyperon-hyperon forces, plus a fitted three-nucleon term, describes dense matter up to the central density of the maximum-mass star; if hyperonic three-body forces supply extra repulsion, the 1.3–1.4 solar-mass ceiling would rise.","fun_headline_variants_meta":{"raw":{"variants":["Hyperon-only forces cap neutron stars at 1.4 solar masses","Femtoscopic data keep hyperon puzzle alive in neutron stars","Max neutron star mass drops to 1.4 with hyperons","Hyperon puzzle unsolved: two-body forces limit mass","Neutron star mass capped by hyperon onset at 1.4 suns"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001025,"raw_usage":{"total_tokens":4342,"prompt_tokens":988,"completion_tokens":3354,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":604,"completion_tokens_details":{"reasoning_tokens":3261}},"tokens_in":604,"tokens_out":3354,"duration_ms":19601,"temperature":1.0,"reasoning_tokens":3261,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T13:48:11.154432+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Repeat the identical Brueckner–Hartree–Fock calculation with a microscopically derived three-nucleon force replacing the fitted phenomenological term of Eq. (5); if the hyperonic maximum mass rises above roughly 1.4 solar masses, the reported ceiling is an artifact of the nucleonic parametrization rather than a consequence of the two-body hyperonic interactions. An observed neutron star above 1.4 solar masses with confirmed hyperons in its interior would also falsify the claim.","supporting_citations":[{"cited_title":"Schulze, A","cited_arxiv_id":null,"evidence_quote":"is one of the earlier BHF hyperonic-star calculations that found the same insensitivity of the maximum mass to the nucleonic EoS."},{"cited_title":"Kumar et al., Liv","cited_arxiv_id":null,"evidence_quote":"provides the GW170817 tidal-deformability constraints that the paper compares with its hyperonic predictions."}],"review_version":1}