{"id":"7363097c-abff-4518-a741-fed80ad92ec0","arxiv_id":"2411.18285","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":7,"one_line_summary":"A fixed-center Faddeev calculation predicts five N D* K̄* bound states with spin 1/2, 3/2, 5/2 and binding energies of 10 to 30 MeV.","lead":"The authors predict five new weakly bound three-body particles made of a nucleon and an exotic D* K̄* meson pair, using an approximation to the Faddeev equations. The predicted states have binding energies of 10 to 30 MeV and could be searched for in heavy-meson decay experiments.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The five-state claim rests on a spin-degenerate NK* amplitude (Eq. 11) that assigns the same Lambda(1800) pole to both S=1/2 and S=3/2, although Table I weights these spin channels differently.","rationale":"The reader's verdict correctly flags the dependence of the result on fitted two-body inputs. My stress-test agrees with that identification but sharpens it to a specific, less obvious feature: Eq. (11) treats the NK* amplitude as spin-independent, while the spin recoupling coefficients in Table I place most of the weight on the S=3/2 component for several total spins. This is not an internal inconsistency of the paper, but it is a load-bearing assumption because the abstract's claim of five states, and in particular the 3/2 and 5/2 peaks, would be qualitatively changed if the S=3/2 NK* amplitude differs from the S=1/2 one. The calculation is otherwise a clear and honest application of the standard FCA formalism, and the paper does not hide its reliance on prior two-body models; however, no uncertainty estimate or alternative-parameterization check is given, which is exactly why the CONDITIONAL verdict is appropriate. The proposed concrete test isolates whether the spin-degenerate input is actually indispensable, and would settle the concern without requiring a full three-body Faddeev calculation. I therefore do not recommend changing the reader's CONDITIONAL verdict; the concern reinforces the need for a robustness check rather than overturning the central claim.","tokens_in":9954,"tokens_out":8590,"duration_ms":76953,"concrete_test":"Recompute |T|^2 for the Table I rows Jtot=3/2, Jclu=1 and Jtot=3/2, Jclu=2 using two separate NK* amplitudes: keep t2^{S=1/2} as Lambda(1800) but set t2^{S=3/2} either to zero or to a pole shifted by, say, 50 MeV with width 200 MeV. If the 3/2 and 5/2 peaks do not both survive with binding energies within 10 MeV of the quoted values, the five-state claim is not robust to the spin decomposition of the NK* input. A second useful check is to vary qmax in Eq. (7) from 0.8 to 1.4 GeV to test cutoff sensitivity.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central prediction of five bound states with 10-30 MeV binding is obtained from the FCA equations, whose input amplitudes t1 and t2 are controlled by resonance parameters in Eqs. (10)-(12). The weakest element is the NK* amplitude: Eq. (11) uses the identical Breit-Wigner pole, Lambda(1800) with width 205 MeV, for both S=1/2 and S=3/2. But Table I assigns different weights to these spin channels; for example, the Jtot=3/2, Jclu=1 row gives 5/6 weight to the S=3/2 NK* amplitude, so the existence of that peak depends essentially on an S=3/2 amplitude that is not independently established. If Lambda(1800) is a spin-1/2 resonance, or if the S=3/2 NK* interaction has a different pole position or strength, the predicted 3/2 and 5/2 states would shift or disappear. No uncertainty is provided for the resonance masses, widths, or couplings, and no variation of these inputs is shown; the abstract's quantitative five-state claim therefore rests on a single, spin-degenerate Breit-Wigner assumption for the NK* subsystem.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript studies the three-body N D* anti-K* system using the Fixed Center Approximation (FCA) to the Faddeev equations, treating the D* anti-K* pair as a cluster in J_clu=0,1,2 states and allowing the nucleon to scatter on D* and anti-K*. The two-body input amplitudes are Breit-Wigner forms for Lambda_c(2910) and Lambda_c(2940) in the ND* subsystem and for Lambda(1800) in the N anti-K* subsystem, with couplings fixed by compositeness or taken from Ref. [67]. Solving the FCA equations yields five peaks in |T|^2: one J=1/2 state from J_clu=0, two states from J_clu=1, and two states from J_clu=2, with reported bindings of 10-30 MeV and widths of 30-60 MeV. The paper proposes DKN, D*KN, and DK*N as the decay channels where these states could be observed experimentally.","tokens_in":10286,"tokens_out":3888,"duration_ms":36253,"significance":"If the five states are real, they would be a new family of three-body molecular exotica and a useful extension of the FCA method to a system with a heavy-light exotic cluster. The paper's strengths are its concrete, falsifiable predictions (masses, widths, and decay channels) and its use of a well-established formalism. However, the quantitative five-state claim is not yet robust: the N anti-K* amplitude is taken to be spin-degenerate, several resonance parameters are adopted from earlier analyses without variation, and no systematic uncertainties are provided. These issues do not invalidate the framework, but they mean the paper presently overstates the certainty of the abstract's 'five states with bindings from 10 to 30 MeV and widths below 60 MeV' conclusion.","major_comments":[{"comment":"The N anti-K* amplitude in Eq. (11) is taken to be the same Lambda(1800) Breit-Wigner for S=1/2 and S=3/2, but Table I shows that the Jtot=3/2 (Jclu=1) and Jtot=5/2 (Jclu=2) peaks are dominated by the S=3/2 component, with coefficients 5/6 and 1, respectively. If Lambda(1800) is only a spin-1/2 state, or if the S=3/2 N anti-K* interaction has a different pole position or strength, the predicted 3/2 and 5/2 states would shift or disappear. The authors should test this by using spin-dependent N anti-K* amplitudes or by varying the S=3/2 pole within a plausible range; without such a test, the five-state claim is not fully supported.","section":"II, Eq. (11) and Table I"},{"comment":"The input parameters entering the FCA equations are taken from previous works with no variation: the resonance masses and widths in Eqs. (10)-(11), the couplings from Eq. (12) and Ref. [67], the cluster masses from Ref. [45], and the cutoff qmax=1.1 GeV in Eq. (7). The abstract's quantitative claim of 10-30 MeV bindings and widths below 60 MeV is therefore a single-parameter-set result. A sensitivity study, even a simple scan over the resonance masses, widths, couplings, and qmax, is needed to determine whether the five peaks are robust or merely reflect the choices of input parameters.","section":"II, Eqs. (7), (10)-(12)"},{"comment":"The FCA loop of Eq. (4) relies on a cluster form factor whose parameters are inherited from Ref. [45], and the xi factor in Eq. (13), which distributes cluster binding between D* and anti-K* proportionally to their masses, is introduced without validation against an alternative prescription. Because the D* anti-K* cluster is a relatively shallow bound state, the accuracy of the fixed-center approximation for this kinematics is not self-evident. A comparison with a few-body calculation or, at minimum, a variation of xi and qmax would strengthen the central claim.","section":"II, Eqs. (4) and (13)"}],"minor_comments":[{"comment":"The phrase 'D* anti-K N system' near the start of Section I appears to be missing a star on the K and should read 'D* anti-K* N system'.","section":"I (Introduction)"},{"comment":"The word 'landshapes' should be 'lineshapes'.","section":"IV (Summary and Outlook)"},{"comment":"The acknowledgment 'Natural Science Foundation of Chian' contains a typo and should read 'Natural Science Foundation of China'.","section":"Acknowledgments"},{"comment":"The symbol q0 in Eq. (4) denotes an energy, while q denotes a three-momentum; the text should explicitly clarify that q0 is not the zeroth component of the same four-vector to avoid confusion.","section":"II, Eq. (4)"},{"comment":"The compositeness formula in Eq. (12) uses a 'binding energy' B, but the text does not specify the sign convention for B; the authors should state whether B is taken as positive for a bound state.","section":"II, Eq. (12)"},{"comment":"Reference [81] cites a conference talk without author initials or publication details; this reference should be completed or replaced with a citable source.","section":"References"}],"recommendation":"major_revision","confidential_remarks":"The paper fits the journal's scope and the authors are well known in this line of work. I do not see the use of previously fitted resonance parameters as circular in a disqualifying sense, because the FCA calculation does combine them into new three-body predictions; however, the spin-degenerate treatment of the N anti-K* amplitude is a genuine load-bearing point. The requested sensitivity studies and a spin-dependent N anti-K* amplitude test should be feasible within the manuscript's scope, so I recommend major revision rather than rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"First thing to know: this is a solid, straightforward extension of the Fixed Center Approximation program to a new three-body system, and it gives five concrete, falsifiable predictions. The novelty is real but modest—it is the first FCA study of N D* K̄*, and the results (bindings 10-30 MeV, widths 30-60 MeV, decay channels) are something BESIII and LHCb could look for. The paper does a good job of citing the prior work and being transparent about where each input comes from.\n\nThe main soft spot is exactly what the stress-test flags: the N K̄* amplitude in Eq. (11) uses the same Λ(1800) pole for both S=1/2 and S=3/2, but Table I gives these spin channels different weights. For the Jtot=3/2, Jclu=1 state, the S=3/2 amplitude carries weight 5/6. If Λ(1800) is only a spin-1/2 state, or if the S=3/2 amplitude differs from the S=1/2 one, then the 3/2 and 5/2 states are not on solid ground. That is not a reason to desk-reject, but it is a reason a referee should ask for a sensitivity study or a more careful treatment of the spin structure.\n\nSecond soft spot: there are no uncertainties anywhere. No variation of resonance masses, widths, couplings, or the cutoff qmax. The cluster masses come from Ref. [45] and are treated as exact. Given that the input amplitudes are Breit-Wigner forms with fitted parameters, the five-state claim is only as strong as those inputs. The paper should say what happens if the inputs move by their quoted errors.\n\nI disagree a bit with the reader's circularity concern: yes, many inputs are from papers by overlapping authors, but they are published, and the method is not circular—the three-body peaks are computed, not input. The concern is more about input uncertainty than circularity.\n\nWho is this for? Hadron spectroscopists, especially experimentalists. It deserves a serious referee: the calculation is well-posed, the predictions are concrete, and the central issue (spin structure of the NK* amplitude) is exactly the kind of thing peer review should catch. Send it out, and ask the referees to push on the spin issue and uncertainties.","headline":"Clean FCA extension with five concrete three-body predictions, but the 3/2 and 5/2 states lean on a spin-degenerate NK* input that needs scrutiny.","tokens_in":10778,"tokens_out":5149,"would_cite":false,"duration_ms":40733,"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":"Five bound states form when a nucleon meets the D*K̄* pair","keywords":["exotic hadrons","three-body bound states","Fixed Center Approximation","Faddeev equations","D* K̄* molecule","X0(2900)","heavy meson spectroscopy","molecular states"],"falsifier":"Perform a high-statistics search for narrow peaks in the $DKN$, $D^*KN$, and $DK^*N$ invariant-mass distributions produced in decays of heavy mesons; finding no peaks with binding energies of $10$-$30$ MeV and widths below $60$ MeV would rule out the prediction, as would a direct measurement of the $N D^*$ amplitude showing that $\\Lambda_c(2910)$ and $\\Lambda_c(2940)$ do not dominate.","tokens_in":9786,"feed_emoji":"⚛️","tokens_out":11160,"duration_ms":86983,"temperature":0.7,"pith_summary":"This paper predicts five bound states in the three-body system built from a nucleon ($N$), a $D^*$ meson, and an antikaon vector meson $\\bar K^*$. Treating the exotic $D^*\\bar K^*$ pair as a pre-existing cluster with spin $0$, $1$, or $2$, and letting the nucleon scatter off each component inside the cluster, the authors find total-spin $1/2$, $3/2$, and $5/2$ states with binding energies of $10$ to $30$ MeV and widths below $60$ MeV. The prediction matters because these states would be genuinely exotic: an ordinary baryon bound to a meson pair that is not a conventional quark-antiquark system. If the peaks appear in $DKN$, $D^*KN$, and $DK^*N$ invariant-mass distributions, they would be the first three-body hadrons built on an exotic two-body core.","feed_headline":"Five bound states predicted when a nucleon meets the D*K̄* pair","feed_subtitle":"Bindings of 10-30 MeV and widths below 60 MeV put the predicted states within reach of current experiments.","key_machinery":"The engine is the Fixed Center Approximation (FCA) to the Faddeev equations, in which the $D^*\\bar K^*$ pair is treated as a fixed cluster and the nucleon scatters successively off its two constituents. The summed amplitude is $T=(\\tilde t_1+\\tilde t_2+2\\tilde t_1\\tilde t_2\\tilde G_0)/(1-\\tilde t_1\\tilde t_2\\tilde G_0^2)$, with $\\tilde t_1$ and $\\tilde t_2$ the $N D^*$ and $N\\bar K^*$ scattering amplitudes renormalized by the cluster masses, and $\\tilde G_0$ the nucleon propagator weighted by the cluster form factor. The input $t_1$ is a Breit-Wigner amplitude for the $\\Lambda_c(2910)$ (spin $1/2$) and $\\Lambda_c(2940)$ (spin $3/2$) resonances, with couplings $g=3.71$ and $2.63$ fixed by the Weinberg compositeness condition; $t_2$ is a Breit-Wigner amplitude for $\\Lambda(1800)$ with coupling $g=3.3$. The cluster form factor $F_X(q)$ is computed from the $D^*\\bar K^*$ wave function with a cutoff $q_{\\max}=1.1$ GeV.","core_discovery":"The central claim is that the $N D^* \\bar K^*$ system is bound in five distinct channels. Starting from the previously computed $D^*\\bar K^*$ cluster states with $J_{\\rm clu}=0,1,2$ (the $J=0$ state identified with the observed $X_0(2900)$), the Fixed Center Approximation to the Faddeev equations generates one $J=1/2$ state from the $J=0$ cluster, two states ($J=1/2$ and $3/2$) from the $J=1$ cluster, and two states ($J=3/2$ and $5/2$) from the $J=2$ cluster. The binding energies range from about $10$ MeV (for the $5/2$ state) to about $30$ MeV, and the widths range from about $30$ to $60$ MeV. The paper argues that the states should show up as peaks in $DKN$, $D^*KN$, and $DK^*N$ invariant-mass distributions, not in the $N D^*\\bar K^*$ channel itself, because the three-body system is bound below that threshold.","pith_inferences":["A natural extrapolation not made in the paper is that other baryons ($\\Lambda$, $\\Sigma$) attached to the same $D^*\\bar K^*$ cluster would produce analogous families of bound states with shifted masses and widths.","The quoted binding energies and widths inherit the Breit-Wigner approximation for the input amplitudes; replacing those with more microscopic two-body inputs could change the numbers, so the existence of bound states is more robust than the precise values.","The extra peaks seen between the two thresholds resemble Efimov-like three-body enhancements, suggesting the system could serve as a hadronic test of universal three-body physics; measuring the spacing of those extra peaks would discriminate between molecular and threshold-effect interpretations."],"forward_implications":["Five experimentally accessible peaks are predicted in the three-body invariant-mass channels $DKN$, $D^*KN$, and $DK^*N$.","The $J=5/2$ state, with about $10$ MeV binding and about $30$ MeV width, is the narrowest and therefore the cleanest experimental target.","The states should be searched for in those decay channels, not in the $N D^*\\bar K^*$ component, because the three-body system is bound below that threshold.","Because the Fixed Center Approximation produces widths as well as binding energies, the prediction gives concrete peak shapes for experiments, going beyond methods that yield only binding energies.","Confirmation of all five states would extend the molecular picture already used for the $X_0(2900)$ to a complete three-body sector."],"supporting_citations":[{"why":"Supplies the $D^*\\bar K^*$ cluster bound states with $J_{\\rm clu}=0,1,2$ and the cluster masses $X(2866)$, $X(2861)$, $X(2775)$ used as input.","marker":"[45]"},{"why":"Original prediction of $J=0,1,2$ bound states in the $D^*\\bar K^*$ interaction, the basis of the molecular picture.","marker":"[42]"},{"why":"Reports the $X_0(2900)$ state in the $D^-K^+$ mass distribution, identified as the $J=0$ cluster state.","marker":"[43]"},{"why":"Second experimental observation of $X_0(2900)$ that motivated the refined cluster predictions.","marker":"[44]"},{"why":"Provides the $N D^*$ amplitudes tied to $\\Lambda_c(2910)$ and $\\Lambda_c(2940)$ and the FCA treatment of a similar three-body system.","marker":"[16]"},{"why":"Provides the $N\\bar K^*$ amplitude and the $\\Lambda(1800)$ resonance parameters, including the coupling $g=3.3$.","marker":"[67]"},{"why":"Weinberg compositeness formula used to fix the $N D^*$ couplings $g=3.71$ and $2.63$.","marker":"[80]"},{"why":"Defines the FCA normalization and cluster form factor used in the three-body equations.","marker":"[68]"}],"fun_headline_variants":["Five bound states found for nucleon plus D*K̄* pair","Predicted five bound N-D*K̄* states","Five new exotic states from N D*K̄* interactions","Nucleon binding to D*K̄* yields five states","Five bound states in N-D*K̄* system: 10-30 MeV binding"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The calculation assumes that the $N D^*$ interaction is fully described by the two resonances $\\Lambda_c(2910)$ and $\\Lambda_c(2940)$, and the $N\\bar K^*$ interaction by $\\Lambda(1800)$, with the masses, widths, and couplings taken from previous analyses; if any of these inputs is wrong or incomplete, the five predicted peaks would shift or disappear.","fun_headline_variants_meta":{"raw":{"variants":["Five bound states found for nucleon plus D*K̄* pair","Predicted five bound N-D*K̄* states","Five new exotic states from N D*K̄* interactions","Nucleon binding to D*K̄* yields five states","Five bound states in N-D*K̄* system: 10-30 MeV binding"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000871,"raw_usage":{"total_tokens":3778,"prompt_tokens":960,"completion_tokens":2818,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":576,"completion_tokens_details":{"reasoning_tokens":2724}},"tokens_in":576,"tokens_out":2818,"duration_ms":20536,"temperature":1.0,"reasoning_tokens":2724,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T11:20:35.887291+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Perform a high-statistics search for narrow peaks in the $DKN$, $D^*KN$, and $DK^*N$ invariant-mass distributions produced in decays of heavy mesons; finding no peaks with binding energies of $10$-$30$ MeV and widths below $60$ MeV would rule out the prediction, as would a direct measurement of the $N D^*$ amplitude showing that $\\Lambda_c(2910)$ and $\\Lambda_c(2940)$ do not dominate.","supporting_citations":[],"review_version":1}