{"id":"01c889a7-a1e2-4c6e-9b4f-c8b3875b16d4","arxiv_id":"2508.12686","paper_version":2,"verdict":"CONDITIONAL","confidence":"LOW","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"In the decay B+ to D*+ D- K+, a model with a D-bar* K* molecular state reproduces the 2870 MeV enhancement, while a D* D-bar molecular state does not account for the chi_c1(3872) peak.","lead":"This paper models the decay B+ to D*+ D- K+ and uses the result to argue that an enhancement near 2900 MeV comes from a D-bar* K* molecular state, while the chi_c1(3872) peak does not look like a D* D-bar molecule. The study is relevant to physicists trying to decide whether certain exotic hadrons are composite molecules of ordinary mesons or something else.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The 2900 MeV enhancement may be dominated by the T*_{c\\bar{s}1}(2900)^0 Breit-Wigner term added to match data, so the claimed support for the \\bar{D}^*K^* molecular interpretation is insecure.","rationale":"The reader's weakest assumption and my concern coincide: the ad hoc Breit-Wigner terms can mask or mimic the molecular signal. This is load-bearing because the paper's headline evidence is the 2900 MeV peak, and one of the added BW states sits at exactly 2900 MeV. The paper does not (in the available abstract/text) show the decomposition of the spectrum into molecular and BW contributions. This does not prove the claim false; it makes the claim conditional on an explicit test. Therefore the reader's CONDITIONAL verdict is appropriate and should remain unchanged.","tokens_in":12434,"tokens_out":5057,"duration_ms":45975,"concrete_test":"Refit the D^-K^+ spectrum with the T*_{c\\bar{s}1}(2900)^0 Breit-Wigner term removed (keeping the molecular amplitude and the other BW terms). If the 2900 MeV enhancement persists, the molecular interpretation is supported; if it disappears or is strongly reduced, the enhancement is attributable to the ad hoc BW term. In either case, report the separate contributions of the \\bar{D}^*K^* molecular amplitude and each Breit-Wigner term in the 2850–2950 MeV window.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The abstract states: 'To better reproduce the experimental data, additional Breit-Wigner contributions from T*_{c\\bar{s}1}(2900)^0, \\chi_{c1}(4010), and h_c(4300) are included.' The central evidence, a 'pronounced enhancement near 2900 MeV', is at the same mass as one of those added Breit-Wigner states (T*_{c\\bar{s}1}(2900)^0). Without a decomposition showing that the molecular amplitude alone produces the enhancement, the conclusion that the enhancement 'strongly support[s]' the \\bar{D}^*K^* molecular interpretation does not follow. The \\bar{D}^*K^* molecular pole is at 2870 MeV, below the D^*K^* threshold (~2902 MeV), so its contribution to the 2900 region should be a threshold/cusp effect; a simple resonance-like peak near 2900 is more naturally accounted for by the added BW term. This is a masking/circularity risk, not just a parameter uncertainty: the added BW was introduced to reproduce the data, and the same data are then cited as evidence for the molecular state.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies the three-body decay B^+ -> D^{*+} D^- K^+ as a probe of hadronic molecular states. Within a one-boson-exchange model, the authors construct interaction kernels for the \\bar{D}^*K^* and D^*\\bar{D} systems, solve the quasipotential Bethe-Salpeter equation to obtain rescattering amplitudes and poles, and then insert these amplitudes into a Monte Carlo simulation of the D^-K^+ and D^{*+}D^- invariant mass spectra. To match the data, the authors add incoherent Breit-Wigner contributions from T^*_{c\\bar{s}1}(2900)^0, \\chi_{c1}(4010), and h_c(4300). The central claim is that a pronounced enhancement near 2900 MeV in the D^-K^+ spectrum strongly supports interpreting T^*_{c\\bar{s}0}(2870)^0 as a \\bar{D}^*K^* molecular state, while the absence of a sizeable D^*\\bar{D} molecular effect disfavours a molecular interpretation of \\chi_{c1}(3872).","tokens_in":12809,"tokens_out":2789,"duration_ms":30329,"significance":"If the central claim were established, the paper would provide a useful new decay channel for testing the molecular hypothesis for T^*_{c\\bar{s}0}(2870)^0 and would add a quantitative negative result for the D^*\\bar{D} interpretation of \\chi_{c1}(3872). The model setup is concrete and the numerical machinery (quasipotential Bethe-Salpeter amplitudes plus Monte Carlo spectra) is appropriate for this type of analysis. However, the significance as presented is limited because the main phenomenological evidence, the 2900 MeV enhancement, sits at the same mass as one of the Breit-Wigner states that were added specifically to reproduce the data; the paper does not demonstrate that the molecular amplitude alone produces that enhancement.","major_comments":[{"comment":"The abstract states that, to better reproduce the experimental data, additional Breit-Wigner contributions from T^*_{c\\bar{s}1}(2900)^0, \\chi_{c1}(4010), and h_c(4300) are included. The same abstract then cites a pronounced enhancement near 2900 MeV as strongly supporting the \\bar{D}^*K^* molecular interpretation. Because 2900 MeV is the mass of one of the added Breit-Wigner states, this is a masking risk, not a cosmetic issue: the enhancement may be dominated by the added term rather than by the molecular amplitude. The paper should show the D^-K^+ spectrum with and without each of the Breit-Wigner terms, or provide a fit-fraction decomposition, before the molecular-support claim can be evaluated.","section":"Abstract"},{"comment":"The \\bar{D}^*K^* molecular pole is reported near 2870 MeV, below the \\bar{D}^*K^* threshold of about 2902 MeV. For a bound state below threshold, the contribution to the 2900 MeV region is expected to be a threshold/cusp-like enhancement rather than a clean resonance peak. The paper should display the molecular contribution alone in this region and compare its shape with the data. Without that decomposition, a peak near 2900 MeV is more naturally attributable to the added T^*_{c\\bar{s}1}(2900)^0 Breit-Wigner term.","section":"Results (spectra)"},{"comment":"The Breit-Wigner masses and widths, as well as the regulator/cutoff parameters in the one-boson-exchange form factors, are free inputs. The paper gives no uncertainty estimates, no fit-quality measure, and no sensitivity study for these parameters. Since the central claim relies on the decomposition of the 2900 MeV region, the authors should provide quantitative information on how the molecular contribution varies with the cutoff and how the fit quality changes when the added Breit-Wigner terms are varied. This is needed to support the word 'strongly' in the abstract.","section":"Model and fit"}],"minor_comments":[{"comment":"The states T^*_{c\\bar{s}0}(2870)^0 and T^*_{c\\bar{s}1}(2900)^0 should be introduced with their quantum numbers and experimental status at first use, and the notation should be checked for consistency throughout.","section":"Introduction"},{"comment":"Please specify whether the molecular amplitudes and the added Breit-Wigner amplitudes are combined coherently or incoherently. If they are added incoherently, a brief justification is needed, since interference effects can be important for three-body final states.","section":"Method"},{"comment":"The Monte Carlo description should state the number of generated events, the phase-space sampling method, and whether detector acceptance or efficiency effects are included. This information is necessary for the reader to interpret the statistical fluctuations visible in the spectra.","section":"Monte Carlo simulation"},{"comment":"The spectra figures should identify each curve (full result, molecular contribution alone, each Breit-Wigner contribution separately) with a legend, and the experimental data points should be referenced with their source and luminosity.","section":"Figures"}],"recommendation":"major_revision","confidential_remarks":"The supplied manuscript text contains extensive encoding corruption in the body, which made independent verification of the equations and section numbering impossible. If the submitted PDF is similarly affected, the authors should be asked to correct it. The referee report above is based on the abstract and the readable portions of the text."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"You should know two things about this paper. First, it is a genuine new application: nobody has run the quasipotential Bethe-Salpeter molecular framework on B+ -> D*+ D- K+ before, and the negative conclusion about chi_c1(3872) as a D*Dbar molecule is a distinct, useful result. Second, the main positive claim—that a 2900 MeV enhancement in the D^-K+ spectrum 'strongly supports' interpreting T*_{cbar s0}(2870)^0 as a Dbar*K* molecule—is not secure from the abstract alone. The abstract says the authors added a Breit-Wigner contribution from T*_{cbar s1}(2900)^0 to reproduce the data. That is the same mass region as the claimed molecular signal. Without a figure or table separating the molecular amplitude from the added BW term, the enhancement might be mostly the ad hoc resonance, not the molecule. The reader flagged this, and I think the flag lands.\n\nWhat the paper does well: the setup is standard and appropriate. Constructing OBE potentials, solving the qBSE for poles, then folding those amplitudes into the three-body decay is a coherent, reproducible scheme. The negative result for chi_c1(3872) is interesting because it argues against a popular molecular interpretation and does not depend on the added BW terms. The Monte Carlo simulation of invariant mass spectra is also the right way to compare with data.\n\nSoft spots, in proportion: the masking/circularity risk at 2900 MeV is real, and it is the central issue. The molecular pole at 2870 MeV sits below the D*K* threshold, so a peak near 2900 is naturally a threshold/cusp effect; a simple resonance-like bump is more economically explained by the added BW. The authors need to show how much of the peak comes from the molecular amplitude alone, not just the total. There is also the usual set of free parameters—cutoff in the OBE form factors, plus masses and widths of the three added BW states—and the abstract gives no uncertainties. That is not damning in this field, but it limits what a reader can conclude. The full text I received was garbled, so I could not check whether the decomposition is already there; if it is, much of this criticism dissolves.\n\nWho this is for: hadron spectroscopists working on molecular exotics and the T*_{cbar s0}(2870)/chi_c1(3872) debate. It deserves a serious referee: the question is timely, the method is established, and the negative chi_c1 result alone is worth publishing if it survives scrutiny. The referee should demand a clear decomposition of the 2900 MeV peak and a sensitivity study over the BW parameters.\n\nRecommendation: send to peer review, with the decomposition as a required revision.","headline":"A plausible molecular-state analysis of B+ -> D*+ D- K+, but the headline claim about the 2870 state is undermined by an added Breit-Wigner term at 2900 MeV unless the paper shows a decomposition.","tokens_in":13174,"tokens_out":1167,"would_cite":false,"duration_ms":15001,"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":"The authors use the decay $B^+\\to D^{*+}D^-K^+$ to argue that the enhancement near 2900 MeV in the $D^-K^+$ spectrum identifies $T^*_{\\bar{c}\\bar{s}0}(2870)^0$ as a $\\bar{D}^*K^*$ molecular state, while the $D^*\\bar{D}$ molecule leaves no…","keywords":["B+ -> D*+ D- K+ decay","hadronic molecules","T*_{cbar s0}(2870)^0","chi_{c1}(3872)","one-boson-exchange model","quasipotential Bethe-Salpeter equation","invariant mass spectrum","exotic hadrons"],"falsifier":"Re-run the Monte Carlo simulation with the extra $T^*_{\\bar{c}\\bar{s}1}(2900)^0$ resonance removed while keeping the $\\bar{D}^*K^*$ molecular amplitude. If the 2900 MeV enhancement vanishes, the claimed molecular signal is an artifact of the added resonance; if it persists, the molecular pole is doing the work.","tokens_in":12209,"feed_emoji":"⚛️","tokens_out":13352,"duration_ms":112179,"temperature":0.7,"pith_summary":"This paper tests whether two exotic states can be understood as hadronic molecules by computing the decay $B^+\\to D^{*+}D^-K^+$. The $\\bar{D}^*K^*$ molecular amplitude produces a pronounced enhancement near 2900 MeV in the $D^-K^+$ invariant mass spectrum, which the authors read as support for identifying $T^*_{\\bar{c}\\bar{s}0}(2870)^0$ as a $\\bar{D}^*K^*$ molecule. The $D^*\\bar{D}$ molecular amplitude, in contrast, leaves the $D^-K^+$ and $D^{*+}D^-$ spectra essentially unchanged, so the paper concludes that $\\chi_{c1}(3872)$ is not naturally a $D^*\\bar{D}$ molecule. If correct, the decay becomes a direct experimental probe of molecular internal structure, and the 2900 MeV peak is a specific prediction of the molecular picture.","feed_headline":"A 2900 MeV bump in B decays supports a hadronic molecule","feed_subtitle":"In B^+ -> D*+D^-K^+, the computed spectrum favors a Dbar*K* molecule and finds no D*Dbar signal for chi_c1(3872).","key_machinery":"The load-bearing machinery is the one-boson-exchange model for the $\\bar{D}^*K^*$ and $D^*\\bar{D}$ interactions, with effective Lagrangians supplying the vertices. Solving the quasipotential Bethe-Salpeter equation for these kernels yields the molecular pole positions and the rescattering amplitudes that enter the three-body decay. The decay amplitudes are then combined with Monte Carlo simulation to produce the $D^-K^+$ and $D^{*+}D^-$ invariant mass spectra. Additional Breit-Wigner terms for $T^*_{\\bar{c}\\bar{s}1}(2900)^0$, $\\chi_{c1}(4010)$, and $h_c(4300)$ are added to reproduce the measured shapes. The paper's central contrast is that the $\\bar{D}^*K^*$ pole generates the 2900 MeV structure while the $D^*\\bar{D}$ pole does not generate the $\\chi_{c1}(3872)$ structure.","core_discovery":"The central claim is that the $D^-K^+$ invariant mass distribution of $B^+\\to D^{*+}D^-K^+$ distinguishes the two molecular hypotheses. When the pole from the $\\bar{D}^*K^*$ system, obtained by solving the quasipotential Bethe-Salpeter equation with one-boson-exchange kernels, is included in the decay amplitude, the spectrum shows a clear enhancement near 2900 MeV that matches the state $T^*_{\\bar{c}\\bar{s}0}(2870)^0$. The authors conclude that this state is supported as a $\\bar{D}^*K^*$ molecular state. The analogous $D^*\\bar{D}$ molecular amplitude produces no significant structure in either spectrum, which the authors take as evidence against interpreting $\\chi_{c1}(3872)$ as a $D^*\\bar{D}$ molecule. To fit the data, the amplitude also includes Breit-Wigner contributions from $T^*_{\\bar{c}\\bar{s}1}(2900)^0$, $\\chi_{c1}(4010)$, and $h_c(4300)$.","pith_inferences":["Editorial inference: the same machinery could be applied to the charge-conjugate decay and to $B_s^0$ analogues; agreement of the predicted 2900 MeV line shape across channels would test the molecular assignment without additional parameter tuning.","Editorial inference: a robustness check the paper does not report is varying the cutoff of the one-boson-exchange potential and checking whether the 2900 MeV enhancement survives; if it moves or disappears, the molecular pole is not the stable origin of the signal.","Editorial inference: the negative result for the $D^*\\bar{D}$ molecule does not rule out other molecular or compact interpretations of $\\chi_{c1}(3872)$; it only speaks against this specific molecule in this decay."],"forward_implications":["If the $\\bar{D}^*K^*$ molecular interpretation is right, the 2900 MeV enhancement in $B^+\\to D^{*+}D^-K^+$ is produced by final-state rescattering and should reappear in related $B$-decay modes.","The absence of a $D^*\\bar{D}$ molecular signal weakens the case that $\\chi_{c1}(3872)$ is a $D^*\\bar{D}$ molecule, shifting molecular-model searches toward other configurations.","The $D^-K^+$ line shape near 2900 MeV becomes a quantitative observable for testing the molecular pole's mass and width against future high-statistics data.","The tuned Breit-Wigner terms are part of the model comparison, so the molecular claim can be checked by whether the extra terms remain necessary once the molecular amplitudes are included."],"supporting_citations":[],"fun_headline_variants":["2900 MeV bump in B+ decay supports bar-D*K* molecule","No D*Dbar molecular signal for chi_c1(3872) in B+ decay","B+ decay spectrum favors bar-D*K* molecule, not D*Dbar","B+ decay rules out D*Dbar molecule for chi_c1(3872)"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The analysis depends on the model's computed molecular poles being physical and on the extra resonance shapes added to match the data not being what actually creates the 2900 MeV bump.","fun_headline_variants_meta":{"raw":{"variants":["2900 MeV bump in B+ decay supports bar-D*K* molecule","No D*Dbar molecular signal for chi_c1(3872) in B+ decay","B+ decay spectrum favors bar-D*K* molecule, not D*Dbar","B+ decay rules out D*Dbar molecule for chi_c1(3872)"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000976,"raw_usage":{"total_tokens":4283,"prompt_tokens":1218,"completion_tokens":3065,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":834,"completion_tokens_details":{"reasoning_tokens":2974}},"tokens_in":834,"tokens_out":3065,"duration_ms":21153,"temperature":1.0,"reasoning_tokens":2974,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T17:18:10.201051+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Re-run the Monte Carlo simulation with the extra $T^*_{\\bar{c}\\bar{s}1}(2900)^0$ resonance removed while keeping the $\\bar{D}^*K^*$ molecular amplitude. If the 2900 MeV enhancement vanishes, the claimed molecular signal is an artifact of the added resonance; if it persists, the molecular pole is doing the work.","supporting_citations":[],"review_version":2}