{"id":"50910d05-8d0a-4901-817e-56620e551626","arxiv_id":"2504.13640","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"The predicted yield ratio of 4ΛHe to 4ΛH is sharply different depending on whether the unconfirmed neutron-lambda bound states 2Λn and 3Λn exist, making this ratio a proposed experimental probe of their existence.","lead":"This paper applies a coalescence model to predict how often three types of lambda hypernuclei form in gold-gold collisions at 3 GeV, including channels that start from deuterons, tritons, and two proposed neutron-lambda bound states. It proposes using the yield ratio of the two four-body hypernuclei as a test of whether those neutron-lambda bound states exist.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The inference of 2Λn/3Λn from the 4ΛH deficit hinges on the freeze-out ordering that excludes 3ΛH+N coalescence; if that ordering is wrong, the missing 4ΛH yield could come from 3ΛH+n, weakening the central claim.","rationale":"The reader's weakest assumption correctly identifies the freeze-out ordering of 3ΛH as the most load-bearing condition. My stress-test agrees: the entire inference of 2Λn and 3Λn existence from the 4ΛH underprediction depends on excluding 3ΛH + N coalescence channels. If 3ΛH is not actually the last species to freeze out, the missing yield could be filled by ordinary two-body coalescence of a measured, well-established hypernucleus with a nucleon, making the exotic-state conclusion non-unique. The paper itself flags this assumption in Sec. III D, so it is not an oversight, but its centrality is not adequately mitigated by independent support. The proposed concrete test—computing the 3ΛH + n -> 4ΛH yield within the same formalism—would directly quantify whether the assumption is avoidable. I do not see a reason to move the verdict away from CONDITIONAL; the paper remains a useful, testable prediction exercise, but the load-bearing assumption needs explicit validation before the existence-constraint claim can be considered robust. The reader also mentioned the model-output nature of 2Λn/3Λn abundances, which is a secondary concern; the freeze-out ordering is the more decisive issue because it undermines the uniqueness of the channel attribution. Hence, no change to the reader's verdict is needed.","tokens_in":24968,"tokens_out":7902,"duration_ms":70299,"concrete_test":"Compute the two-body coalescence yields for 3ΛH + n -> 4ΛH and 3ΛH + p -> 4ΛHe using Eq. (17) with the measured 3ΛH spectrum as f_h1 and the primordial neutron/proton spectra as f_h2, assuming 3ΛH is present before freeze-out. Compare the resulting 4ΛH dN/dy to the gap between the STAR data and the no-exotic-channel total (2.188e-3). If the 3ΛH+n channel alone produces more than 50% of that gap, the central claim that the deficit implies 2Λn/3Λn existence is not robust.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Sec. III D explicitly asserts that 3ΛH cannot participate in forming 4ΛH or 4ΛHe because it is 'likely to be formed after 4ΛH and 4ΛHe due to its relatively loosely-bound structure' (citing Ref. [52]). This freeze-out ordering is load-bearing: the central claim that the 56% deficit in 4ΛH requires 2Λn and 3Λn channels assumes that no other channel can fill the gap. If 3ΛH is available before freeze-out, the two-body coalescence 3ΛH + n -> 4ΛH (Eq. 17) would contribute to 4ΛH without involving any exotic bound states. Given the measured 3ΛH yield (dN/dy ≈ 1.13e-2) and the neutron surplus (Znp=1.34), even a small coalescence probability could produce a yield comparable to the deficit (data minus no-exotic total ≈ 2.77e-3), making the inferred 2Λn/3Λn contribution non-unique. The paper's own text flags this as an assumption rather than a derived result. Furthermore, even after including 2Λn and 3Λn, the theoretical 4ΛH yield at RMS=2.0 fm is 4.00e-3, still about 19% below the STAR central value, so the residual discrepancy leaves room for additional channels and weakens the claim that the exotic-state channels are specifically required.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript extends an analytical coalescence model to the production of Λ-hypernuclei (3ΛH, 4ΛH, 4ΛHe) in central Au-Au collisions at sqrt(s_NN) = 3 GeV. The model combines nucleon+Λ and nucleus+nucleon(Λ) coalescence channels in a two-step scheme designed to avoid double counting, and the authors present channel-by-channel pT spectra, rapidity densities, and mean transverse momenta. Without the hypothetical bound states 2Λn and 3Λn, the model underpredicts the STAR 4ΛH yield by about 56% (Table I); including these states through the channels p+n+2Λn, d+2Λn, and p+3Λn brings the yield closer to data but leaves a residual deficit (Table IV). The authors propose the yield ratios 4ΛHe/4ΛH and (4ΛH−4ΛHe)/(4ΛH+4ΛHe) as observables that could discriminate between scenarios with and without these neutron-Λ bound states.","tokens_in":25372,"tokens_out":9545,"duration_ms":76338,"significance":"The paper's strengths are its analytic, transparent coalescence formalism, the explicit channel decomposition, and the fact that no new free parameters are introduced beyond those fixed by light-nucleus data in the previous work. The proposed asymmetry ratios are a falsifiable prediction that could in principle constrain the existence of 2Λn and 3Λn. However, the central inference is conditional: it depends on the assumption that 3ΛH freezes out after 4ΛH and 4ΛHe, and the no-exotic baseline asymmetry is essentially a restatement of the fitted neutron-to-proton ratio Znp. The exotic-state contributions also inherit the model's uncertainty in the unmeasured 2Λn/3Λn multiplicities. With a sensitivity study and an uncertainty estimate, the paper would provide a valuable constraint; in its present form, the conclusion is suggestive rather than decisive.","major_comments":[{"comment":"The exclusion of 3ΛH from the formation of 4ΛH is load-bearing. The paper assumes that 3ΛH freezes out after all other light (hyper-)nuclei and therefore cannot participate in 4ΛH production; this is stated as 'likely' in Sec. III B and as a definite exclusion in Sec. III D, with Ref. [52] cited but no quantitative justification. If the ordering is wrong and the two-body channel 3ΛH + n → 4ΛH (which the formalism of Eq. (17) would describe) operates, then the measured 3ΛH yield dN/dy ≈ 1.13×10-2 (Table I) and the neutron surplus Znp = 1.34 imply that a modest coalescence probability suffices to produce a yield comparable to the no-exotic deficit of ≈ 2.77×10-3, so the inferred need for 2Λn and 3Λn would be non-unique. The authors should either provide a dynamical reason for the ordering or test the alternative scenario.","section":"Sec. III B and III D (Eq. (17))"},{"comment":"The no-exotic baseline asymmetry is essentially a fitted input restated as a prediction. For the four-body channels, Eqs. (53)-(54) give 4ΛHe/4ΛH = 1/Znp = 0.746 and (4ΛH−4ΛHe)/(4ΛH+4ΛHe) = (Znp−1)/(Znp+1) = 0.145, with Znp = 1.34 fixed by the t/3He ratio (Sec. III A). Consequently the 'neither 2Λn nor 3Λn' entries in Table V (≈0.71 and ≈0.17) are not independent predictions; the predictive content is in the deviations caused by the exotic channels. The paper should state this explicitly and should assess how robust those deviations are to the assumed RMS radii, binding energies, and spins of 2Λn and 3Λn, since the abundances in Table II are outputs of the same model.","section":"Sec. III E, Eqs. (53)-(54), Table V"},{"comment":"The scenario-dependent ratios rest on unmeasured 2Λn and 3Λn multiplicities computed with the same fitted inputs, and no theoretical uncertainty is propagated from the fits of the blast-wave parameters, Znp, Rf, or the adopted RMS radii. Moreover, after including the exotic states the model still does not fully reproduce the data: at the nominal RMS = 2.0 fm the total dN/dy for 4ΛH is 4.00×10-3, about 19% below the STAR central value of 4.95×10-3, and at RMS = 2.5 fm it is 3.30×10-3, below the lower bound of the combined experimental uncertainty. This residual deficit leaves room for other channels, such as decays of excited hypernuclei, which the paper mentions only in passing. A sensitivity analysis and an uncertainty estimate are needed to support the claim that 2Λn and 3Λn are specifically required.","section":"Secs. III C-III D, Tables II, IV, V"}],"minor_comments":[{"comment":"The phrase 'baryonic interactions do minate' contains a typo and should read 'dominate'.","section":"Sec. I"},{"comment":"The term 'perdue states' appears to be a typo for 'putative states'.","section":"Sec. III B"},{"comment":"The phrase 'dividing protons in Fig. 1 (a) by 80%' is ambiguous; since the measured protons are about 80% of the primordial ones, the primordial spectrum should be obtained by dividing by 0.80 (equivalently multiplying by 1.25), and this should be stated unambiguously.","section":"Sec. III A"},{"comment":"The numerical value of the RMS radius of 2Λn obtained from RMS = 1/sqrt(4 μ BΛ) is not quoted; the paper would be more reproducible if the value (about 2 fm) were given.","section":"Sec. III C"},{"comment":"The value N3He/Nt = 0.687 is taken from central values of Ref. [33]; quoting the experimental uncertainty would help readers gauge the robustness of the two-body-channel asymmetry.","section":"Sec. III E, Eq. (55)"},{"comment":"Theoretical results are quoted without any uncertainty; adding a sensitivity range over Rf and the assumed RMS radii would make the comparison with data more informative.","section":"Tables I, III, IV"}],"recommendation":"major_revision","confidential_remarks":"For the editor: the manuscript is within the scope of the journal and the analytical framework is clean, but the central inference is more fragile than the abstract suggests. The key issue is the freeze-out ordering assumption, which is cited to a previous paper but not tested; the authors should be asked to relax it or justify it quantitatively. I would also encourage the editor to ask for quantitative uncertainty estimates, because the apparent agreement with the 4ΛH data after including 2Λn/3Λn is sensitive to the assumed RMS radii. With those revisions, the paper could be a solid contribution; in its current form, the claim that 2Λn and 3Λn are needed is not uniquely established."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is a useful paper, not a conclusive one. The authors extend their analytic coalescence model to 3ΛH, 4ΛH, and 4ΛHe at sqrt(s_NN)=3 GeV, decompose production into each coalescence channel, and show that the measured 4ΛH yield is underpredicted by about 56% unless channels through the possible bound states 2Λn and 3Λn are included. The scenario-dependent predictions for 4ΛHe/4ΛH and (4ΛH−4ΛHe)/(4ΛH+4ΛHe) are new and cleanly testable with STAR data. That is the real value: a single ratio measurement could discriminate between existence scenarios for two unconfirmed states.\n\nThe model work is competent. The analytic formulas for 2-, 3-, and 4-body coalescence are laid out explicitly, the channel bookkeeping is careful, and no new free parameters are introduced: Znp and Rf are fixed by light-nucleus data. I also credit the paper for reporting the residual underprediction even after adding 2Λn and 3Λn, and for mentioning excited-hypernucleus decays as an alternative source of the yield.\n\nThe soft spots are real. The strongest caveat is the freeze-out ordering assumption in Sec. III D: the paper asserts that 3ΛH forms after 4ΛH and 4ΛHe, and therefore cannot coalesce with a nucleon to make 4ΛH. If 3ΛH + n → 4ΛH is allowed instead, the apparent deficit that motivates 2Λn and 3Λn could be filled without any exotic bound states. The paper cites Zhang and Ko for this ordering, but it does not quantify how sensitive the conclusion is to that ordering. This is a load-bearing assumption, not a minor detail.\n\nSecond, the baseline asymmetry is close to circular. Equations (53)–(54) show that the no-exotic 4ΛHe/4ΛH ratio is essentially 1/Znp, and Znp is fit to the measured t/3He ratio. So the prediction that the ratio is about 0.71 is largely a restatement of an input. The exotic-state abundances are also computed from the same fitted inputs, so the scenario ratios are model-dependent in a way the paper does not quantify. There is no propagation of theoretical uncertainties anywhere.\n\nThird, even with both exotic states, the central 4ΛH yield remains about 19% below the STAR central value at RMS=2.0 fm. The paper is honest about this, but it means the exotic-state interpretation is only partially supported, not required.\n\nWho is this for: people working on hypernucleus production in heavy-ion collisions and on the existence of neutron-Lambda bound states. It deserves a serious referee. The right outcome is revision, not rejection: the freeze-out ordering should be tested by allowing 3ΛH + n and checking how much 2Λn and 3Λn are still needed, and the uncertainty band on the ratio predictions should be shown.","headline":"Useful channel decomposition and cleanly testable ratio predictions, but the case for 2Λn and 3Λn depends on an untested freeze-out ordering and the baseline asymmetry is close to a fitted input.","tokens_in":25933,"tokens_out":4014,"would_cite":true,"duration_ms":34741,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["21.80.+a","25.75.Dw","25.75.-q"],"model":"deepseek-v4-flash","headline":"At $\\sqrt{s_{NN}}=3$ GeV, the measured $^4_{\\Lambda}$H yield is underestimated by about 56% unless unconfirmed $^2_{\\Lambda}n$ and $^3_{\\Lambda}n$ bound states join coalescence; future $^4_{\\Lambda}{\\rm He}/^4_{\\Lambda}{\\rm H}$…","keywords":["hypernuclei","Lambda hypernuclei","coalescence mechanism","neutron-Lambda bound states","production asymmetry","yield ratios","Au-Au collisions","heavy-ion collisions"],"falsifier":"Measure the two yield ratios $^4_{\\Lambda}{\\rm He}/^4_{\\Lambda}{\\rm H}$ and $(^4_{\\Lambda}{\\rm H}-^4_{\\Lambda}{\\rm He})/(^4_{\\Lambda}{\\rm H}+^4_{\\Lambda}{\\rm He})$ at midrapidity in the same 0–10% central Au-Au collisions at $\\sqrt{s_{NN}}=3$ GeV. The paper's four scenarios place the pairs at about (0.71, 0.17) with neither bound state, (0.63–0.64, 0.22) with only $^2_{\\Lambda}n$, (0.55–0.57, 0.27–0.29) with only $^3_{\\Lambda}n$, and (0.46–0.49, 0.34–0.37) with both; a measured pair falling clearly in one band and excluding the others would settle which states exist. A direct measurement of the $^2_{\\Lambda}n$ and $^3_{\\Lambda}n$ yields in the same system (predicted $dN/dy\\approx1.4\\times10^{-1}$ and $\\approx4.8\\times10^{-2}$) would confirm the mechanism independently.","tokens_in":24726,"feed_emoji":"⚛️","tokens_out":28240,"duration_ms":199508,"temperature":0.7,"pith_summary":"The paper asks whether the coalescence mechanism—which builds light nuclei by combining hadrons that fly out of a heavy-ion collision close in momentum and position—can account for the measured yields of the strangeness-bearing hypernuclei $^3_{\\Lambda}$H, $^4_{\\Lambda}$H, and $^4_{\\Lambda}$He at the low collision energy $\\sqrt{s_{NN}}=3$ GeV. In the authors' coalescence model, $^3_{\\Lambda}$H is reproduced within uncertainties, but the computed $^4_{\\Lambda}$H yield falls short of the measured value by about 56%. The central proposal is that the missing yield comes from coalescence channels built on two unconfirmed neutron-$\\Lambda$ bound states, $^2_{\\Lambda}n$ and $^3_{\\Lambda}n$; because these feed $^4_{\\Lambda}$H more than they feed $^4_{\\Lambda}$He, their existence would visibly enlarge the production asymmetry between the two $A=4$ hypernuclei. The paper predicts the yield ratios $^4_{\\Lambda}{\\rm He}/^4_{\\Lambda}{\\rm H}$ and $(^4_{\\Lambda}{\\rm H}-^4_{\\Lambda}{\\rm He})/(^4_{\\Lambda}{\\rm H}+^4_{\\Lambda}{\\rm He})$ under four scenarios, ranging from about 0.71 and 0.17 with no bound states to about 0.46–0.49 and 0.34–0.37 with both. A sympathetic reader would care because the collisions that already measured $^4_{\\Lambda}$H can, with one more yield-ratio measurement, place existence constraints on neutron-$\\Lambda$ bound states that direct searches have not yet settled.","feed_headline":"A 56% yield gap hints at two unseen neutron-Λ bound states","feed_subtitle":"Two yield ratios, ⁴ΛHe/⁴ΛH from 0.71 to 0.46 and the asymmetry from 0.17 to 0.37, tell which states exist.","key_machinery":"The load-bearing object is the analytical $N$-body coalescence formula (Eq. (44)), a closed expression for the invariant transverse-momentum spectrum of a hypernucleus formed from $N$ primordial hadrons: the product of $N$ single-hadron spectra, each evaluated at a share $m_i/(m_1+\\cdots+m_N)$ of the cluster momentum, times a spin degeneracy factor and a product of Gaussian overlap integrals whose widths combine the cluster's root-mean-square radius (2.0 fm for $^4_{\\Lambda}$H, 4.9 fm for $^3_{\\Lambda}$H) with the hadronic freeze-out radius $R_f=3.27$ fm. The formula follows from Wigner-transforming a spherical harmonic-oscillator wave function and approximating the momentum kernel by a delta function, justified by the kernel's small width. On top of this sits a two-step bookkeeping scheme that avoids double counting: first nucleons and $\\Lambda$'s coalesce into $d$, $t$, $^3$He, and $^3_{\\Lambda}$H, then those nuclei capture remaining hadrons. The channel inventory for $A=4$—which species can feed $^4_{\\Lambda}$H versus $^4_{\\Lambda}$He—is what converts the measured deficit into constraints on $^2_{\\Lambda}n$ and $^3_{\\Lambda}n$. The asymmetry argument runs through the analytic ratios Eqs. (53)–(58), where the neutron-surplus factor $Z_{np}=1.34$ fixes the baseline and the $^2_{\\Lambda}n$/$^3_{\\Lambda}n$ channels push the ratio toward 0.","core_discovery":"The discovery claim is that, in the coalescence picture applied to central Au-Au collisions at $\\sqrt{s_{NN}}=3$ GeV, the measured abundance of the hypernucleus $^4_{\\Lambda}$H cannot be reproduced by channels made of measured species alone: direct four-body $p+n+n+\\Lambda$ coalescence, $n+d+\\Lambda$, and $t+\\Lambda$ together give $dN/dy\\approx2.2\\times10^{-3}$ against a measured $(4.95\\pm0.43\\pm1.01)\\times10^{-3}$, a shortfall of about 56% that extends below the data's lower error bar. The paper attributes the gap to participation of the unconfirmed neutron-$\\Lambda$ bound states $^2_{\\Lambda}n$ and $^3_{\\Lambda}n$: $^2_{\\Lambda}n$ can enter $^4_{\\Lambda}$H through $p+n+^2_{\\Lambda}n$ and $d+^2_{\\Lambda}n$ but enters $^4_{\\Lambda}$He through only $p+p+^2_{\\Lambda}n$, while $^3_{\\Lambda}n$ contributes to $^4_{\\Lambda}$H only, via $p+^3_{\\Lambda}n$. Because these channels add asymmetrically, the $^4_{\\Lambda}$H-to-$^4_{\\Lambda}$He asymmetry grows from the baseline set by the neutron surplus alone ($^4_{\\Lambda}{\\rm He}/^4_{\\Lambda}{\\rm H}\\approx0.71$, asymmetry $\\approx0.17$) to $^4_{\\Lambda}{\\rm He}/^4_{\\Lambda}{\\rm H}\\approx0.46$–$0.49$ with asymmetry $\\approx0.34$–$0.37$ when both states exist. The paper also predicts the states' own yields, $dN/dy\\approx1.4\\times10^{-1}$ for $^2_{\\Lambda}n$ and $\\approx4.8\\times10^{-2}$ for $^3_{\\Lambda}n$, and shows that including them brings the $^4_{\\Lambda}$H total to within a residual deficit that it attributes to decays of excited hypernuclei.","pith_inferences":["Because the two proposed ratios compare particles measured in the same collision sample, acceptance and decay-branching uncertainties largely cancel; a few-percent measurement would already separate the 'no bound states' column from the 'both bound states' column, and a ten-percent measurement would separate 'no states' from 'only $^2_{\\Lambda}n$', which differ by only about ten percent in $^4_{\\L","The same channel-inventory logic could be exported to $\\Xi$-hypernuclei or to $A=4$ hypernuclei at other beam energies, where the neutron surplus and the relative weight of the $^2_{\\Lambda}n$/$^3_{\\Lambda}n$ channels change, providing independent cross-checks of the existence constraints.","The predicted $^2_{\\Lambda}n$ yield, $dN/dy\\approx0.14$, is an order of magnitude above the $^4_{\\Lambda}$H yield and well above the $^3_{\\Lambda}$H yield; a dedicated search for the state in the same collision system—through its decay products or through correlation measurements—could test the bound state's existence directly, rather than only through the asymmetry ratios."],"forward_implications":["If both $^2_{\\Lambda}n$ and $^3_{\\Lambda}n$ exist, their channels raise the computed $^4_{\\Lambda}$H yield from about $2.2\\times10^{-3}$ to about $4.0\\times10^{-3}$ at RMS 2.0 fm, closing most of the 56% gap; the remaining deficit is attributed to decays of excited hypernuclei.","The two ratios are scenario-dependent by design: about 0.71 and 0.17 with no bound states, falling to about 0.46–0.49 and 0.34–0.37 with both, so a single future measurement distinguishes the cases.","Because $^3_{\\Lambda}n$ feeds only $^4_{\\Lambda}$H while $^2_{\\Lambda}n$ feeds both $^4_{\\Lambda}$H and $^4_{\\Lambda}$He, the four columns of Table V separate the 'only $^2_{\\Lambda}n$' from 'only $^3_{\\Lambda}n$' scenarios, letting the two states be constrained independently rather than jointly.","The model's inputs—$R_f=3.27$ fm, $Z_{np}=1.34$, blast-wave fits to proton and $\\Lambda$ spectra—are all fixed by light-nucleus and hyperon data, so the hypernucleus predictions are parameter-free tests of the coalescence mechanism extended to strangeness."],"supporting_citations":[{"why":"Supplies the measured $^3_{\\Lambda}$H and $^4_{\\Lambda}$H spectra and yields that the model must reproduce; the comparison exposes the roughly 56% deficit.","marker":"[18]"},{"why":"The authors' earlier work establishing the two-step coalescence model for light nuclei and fixing the input parameters $Z_{np}$ and $R_f$ that the present calculation inherits.","marker":"[36]"},{"why":"Measured proton, $t$, and $^3$He spectra at the same collision energy used to fix the neutron-surplus factor and freeze-out radius, including the $t/^3$He ratio behind the asymmetry baseline.","marker":"[33]"},{"why":"Measured $\\Lambda$ spectrum at the same collision energy, fitted with the blast-wave model to provide the primordial $\\Lambda$ momentum input.","marker":"[49]"},{"why":"The basis for the freeze-out ordering assumption that $^3_{\\Lambda}$H forms last and therefore cannot coalesce into $^4_{\\Lambda}$H or $^4_{\\Lambda}$He.","marker":"[52]"},{"why":"Derives the analytical two-body and multi-body coalescence formulas, including the delta-function momentum approximation, used for every channel.","marker":"[38]"},{"why":"Supplies the root-mean-square radii of $^3_{\\Lambda}$H, $^4_{\\Lambda}$H, and $^4_{\\Lambda}$He used in the Gaussian overlap widths.","marker":"[12]"},{"why":"The blast-wave model used to convert measured proton and $\\Lambda$ spectra into the primordial momentum distributions feeding the coalescence integrals.","marker":"[48]"}],"fun_headline_variants":["56% yield gap in ⁴ΛH hints at two unseen neutron-Λ states","Hypernucleus yield shortfall points to exotic Λ-neutron clusters","Coalescence gap predicts ²Λn and ³Λn bound states","Asymmetric hypernuclei yields reveal neutron-Λ states","Missing ⁴ΛH channels suggest unseen neutron-Λ bound states"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The result rests on the freeze-out ordering assumption that $^3_{\\Lambda}$H forms after all other light (hyper-)nuclei, so it cannot coalesce into $^4_{\\Lambda}$H or $^4_{\\Lambda}$He; if $^3_{\\Lambda}$H were available earlier, extra channels such as $^3_{\\Lambda}{\\rm H}+n\\to{}^4_{\\Lambda}{\\rm H}$ would take up part of the missing yield, and the inferred roles of $^2_{\\Lambda}n$ and $^3_{\\Lambda}n$—whose abundances are themselves model outputs—would have to be re-mapped.","fun_headline_variants_meta":{"raw":{"variants":["56% yield gap in ⁴ΛH hints at two unseen neutron-Λ states","Hypernucleus yield shortfall points to exotic Λ-neutron clusters","Coalescence gap predicts ²Λn and ³Λn bound states","Asymmetric hypernuclei yields reveal neutron-Λ states","Missing ⁴ΛH channels suggest unseen neutron-Λ bound states"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001336,"raw_usage":{"total_tokens":5601,"prompt_tokens":1284,"completion_tokens":4317,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":900,"completion_tokens_details":{"reasoning_tokens":4216}},"tokens_in":900,"tokens_out":4317,"duration_ms":28120,"temperature":1.0,"reasoning_tokens":4216,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T12:02:38.137159+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the two yield ratios $^4_{\\Lambda}{\\rm He}/^4_{\\Lambda}{\\rm H}$ and $(^4_{\\Lambda}{\\rm H}-^4_{\\Lambda}{\\rm He})/(^4_{\\Lambda}{\\rm H}+^4_{\\Lambda}{\\rm He})$ at midrapidity in the same 0–10% central Au-Au collisions at $\\sqrt{s_{NN}}=3$ GeV. The paper's four scenarios place the pairs at about (0.71, 0.17) with neither bound state, (0.63–0.64, 0.22) with only $^2_{\\Lambda}n$, (0.55–0.57, 0.27–0.29) with only $^3_{\\Lambda}n$, and (0.46–0.49, 0.34–0.37) with both; a measured pair falling clearly in one band and excluding the others would settle which states exist. A direct measurement of the $^2_{\\Lambda}n$ and $^3_{\\Lambda}n$ yields in the same system (predicted $dN/dy\\approx1.4\\times10^{-1}$ and $\\approx4.8\\times10^{-2}$) would confirm the mechanism independently.","supporting_citations":[{"cited_title":"Momentum dependence of light nuclei production in pp, p-Pb and Pb-Pb collisions at the CERN Large Hadron Collider","cited_arxiv_id":"2007.05745","evidence_quote":"The basis for the freeze-out ordering assumption that $^3_{\\Lambda}$H forms last and therefore cannot coalesce into $^4_{\\Lambda}$H or $^4_{\\Lambda}$He."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the root-mean-square radii of $^3_{\\Lambda}$H, $^4_{\\Lambda}$H, and $^4_{\\Lambda}$He used in the Gaussian overlap widths."}],"review_version":1}