{"id":"efcf32ab-ee35-4a62-84c6-85725c41bde5","arxiv_id":"2501.10968","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"Predicted charm-strange hadronic molecules decay with widths from a few to about two hundred MeV, dominated by specific two-body channels.","lead":"This paper computes how hypothetical particles made of a charmed baryon and a kaon would decay into ordinary hadrons. It predicts widths and dominant decay channels that experiments could look for at LHCb and similar facilities.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"For the broad predicted states the decay width exceeds the binding energy by an order of magnitude, so the bound-state wavefunction plus first-order width formula are internally inconsistent; this should be checked before relying on the 100–200 MeV predictions.","rationale":"The paper's central predictions are the width magnitudes and dominant channels. The reader's SU(4) concern is legitimate: Table 4 shows that rescaling charmed couplings by 0.8–1.2 moves some widths by a factor of about 5 (4.5 vs 22 MeV for the first state), which can cross the 'several MeV' vs 'tens of MeV' boundary. I therefore partially agree with the reader. But the more fundamental obstacle is the bound-state approximation itself. A width of 159 MeV with a 4.75 MeV binding energy means the state, if it exists, is a broad resonance rather than a weakly bound molecule; the real wavefunction used in Eq. (1) is not the correct object. The paper acknowledges in Sec. 1 that Ref. [16] omitted the lower channels because they were assumed weakly coupled 'generally', yet the present calculation shows exactly those channels giving widths of order 100 MeV for several states. That tension is an internal consistency problem, not just a parameter-uncertainty problem. A pole search with open channels is the decisive check. If it confirms the broad states, the paper should present them as resonances and justify the width calculation accordingly; if not, the 'roughly 200 MeV' claim should be withdrawn. Either way the verdict remains conditional pending this check, so I do not change the reader's CONDITIONAL verdict.","tokens_in":13115,"tokens_out":9990,"duration_ms":116992,"concrete_test":"Repeat the bound-state calculation of Ref. [16] for the \\Sigma_c K^* 1/2(1/2^-) candidate in a Lippmann-Schwinger or complex-scaling framework that explicitly includes the open two-body channels D_s N, \\Lambda_c K, and \\Sigma_c K with the same OBE interactions. Locate the resonance pole in the complex energy plane and compare its real and imaginary parts with the bound-state binding energy and with the perturbative widths of Table 3 and Fig. 5. If the pole shifts by more than its width or disappears, the first-order bound-state calculation is invalid; if a pole with roughly the predicted width survives, the concern is resolved.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The decay-width calculation treats every predicted YcK(*) state as a real bound state: it takes wavefunctions from the coupled-channel Schrödinger equation of Ref. [16] and evaluates two-body amplitudes in first-order perturbation theory (Eqs. (1)–(4)). That treatment is internally consistent only if the state is narrow compared with its binding energy and with the energy gap to the omitted lower channels. For the single \\Sigma_c K^* state with I(J^P)=1/2(1/2^-), Table 3 and Fig. 5 give \\Gamma=(50–245) MeV for binding energies E=(0 to −12) MeV; at E=−4.75 MeV, Table 4 gives \\Gamma=159 MeV. The width is therefore roughly 30 times the binding energy. Similar ratios occur for the \\Sigma_c K^* 1/2(3/2^-) state (\\Gamma up to 30 MeV, E=−12 MeV) and the coupled \\Lambda_c K^* / \\Sigma_c K^* 1/2(3/2^-) state (\\Gamma~70 MeV, E~2.5 MeV). For such broad poles the imaginary part of the pole position is comparable to or larger than the binding energy, so a normalizable real wavefunction and a first-order width formula are not justified. Moreover, Ref. [16] intentionally omitted the lower channels D_s N, \\Lambda_c K, and \\Sigma_c K that are precisely the decay channels computed here; the large widths show that those channels are not weakly coupled, so the resonance pole may be shifted or absent. The headline 'roughly 200 MeV width' for the single \\Sigma_c K^* state is thus not robust even before considering SU(4) coupling uncertainties.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This manuscript computes two-body strong decay widths for seven predicted YcK(*) molecular pentaquark candidates using the effective Lagrangian approach. The initial wave functions are taken from the authors' previous coupled-channel bound-state calculation [16], the transition amplitudes for S-wave decays are tabulated in Table 1, and the coupling constants are fixed by SU(4) flavor symmetry from nucleon couplings (Table 2). The authors report total and partial widths as functions of binding energy for each state, including a rescaling of the heavy-quark couplings by 0.8, 1.0, and 1.2 (Table 4). The main results are: the coupled Sigma_c K / Lambda_c K* / Sigma_c K* 1/2(1/2^-) state is narrow, with D_s N dominant; the coupled Lambda_c K* / Sigma_c K* states have widths of tens of MeV with Sigma_c K and Sigma_c^* K dominant; the single Sigma_c K* 1/2(1/2^-) state can be as broad as about 200 MeV; and the branching ratios are nearly independent of the binding energy.","tokens_in":13473,"tokens_out":7367,"duration_ms":76893,"significance":"If the predictions were reliable, the paper would provide concrete decay signatures for as-yet-unobserved charm-strange molecular pentaquarks and a way to distinguish molecular from compact interpretations. The authors provide explicit amplitude tables, check that D-wave admixtures affect the widths by less than 2%, and demonstrate that the branching ratios are stable under binding-energy variation and under a modest rescaling of the couplings. These are genuine strengths. The main significance is limited by the fact that no external data exist for the predicted states and, more importantly, by the internal inconsistency of the bound-state treatment for the broadest states, which is the subject of the major comments below.","major_comments":[{"comment":"The bound-state assumption is internally inconsistent for the broad states. For the single Sigma_c K* 1/2(1/2^-) molecule, Table 4 gives Gamma=159 MeV at E=-4.75 MeV, and Table 3/Fig. 5 give Gamma up to 245 MeV over E in (0,-12) MeV; the imaginary part of the would-be pole, Gamma/2, is thus 30-80 times larger than the binding energy. A normalizable bound-state wave function combined with a first-order width formula [Eqs. (1)-(4)] is not justified in this regime. The same problem affects the coupled Lambda_c K* / Sigma_c K* 1/2(3/2^-) state (Gamma=54.6 MeV at E=-1.14 MeV) and the coupled 1/2(1/2^-) state (Gamma=30.5 MeV at E=-4.88 MeV). The headline 'one hundred MeV' width therefore needs a complex-pole or full scattering treatment before it can be considered a prediction.","section":"§3, Table 4 and Fig. 5"},{"comment":"The large computed widths also show that the lower channels omitted when obtaining the wave functions are not weakly coupled. Reference [16] solved the coupled-channel Schrodinger equation without D_s N, Lambda_c K, and Sigma_c K, yet for the single Sigma_c K* 1/2(1/2^-) state Table 3 assigns 54% of the width to Sigma_c K and 38% to Lambda_c K. When the decay channels carry a width comparable to or larger than the binding energy, their feedback on the pole position and on the wave-function composition cannot be neglected; the predicted existence and mass of the broad states are therefore not robust. The authors should either include these channels in a coupled-channel scattering calculation or restrict the claims to parameter ranges where Gamma/2 is much smaller than |E|.","section":"§3 and Ref. [16]"},{"comment":"The claimed 'less than 20%' uncertainty from SU(4) breaking is not reflected in the numerical spread. Rescaling g_H from 0.8 g_H to 1.2 g_H changes the total width of the Sigma_c K* 1/2(1/2^-) state from 102.7 to 227.0 MeV (Table 4), a factor of 2.2, and the other rows show factors close to 2 as well. This likely results from coherence and cancellations among amplitudes, but the manuscript does not explain why a 20% coupling uncertainty produces such a large width uncertainty. The paper should quote the resulting uncertainty bands or justify why the estimate does not propagate.","section":"§3, Table 4 and Sec. 4"}],"minor_comments":[{"comment":"In Eq. (19) the tensor term contains gamma_alpha gamma_beta - gamma_alpha gamma_beta, which appears to be a typo for gamma_alpha gamma_beta - gamma_beta gamma_alpha.","section":"Eq. (19)"},{"comment":"There are numerous typographical errors, including 'V ol.', 'effective Largrangians', 'can be play an important role', 'the the binding energy', and 'Branch ratios' in the Fig. 5 caption; these should be corrected.","section":"Throughout"},{"comment":"References 53 and 56 are the same paper (Z. L. Wang, C. W. Shen, D. Ronchen et al., Eur. Phys. J. C 82, 497 (2022)) and should be merged or cross-referenced.","section":"References"},{"comment":"The phrase 'observed in the zai decay channel' in the Introduction appears to be a corrupted or incomplete sentence and should be rephrased.","section":"Introduction"}],"recommendation":"major_revision","confidential_remarks":"The broad-width inconsistency is the main obstacle. If the authors can rederive the widths for the broad states in a scattering framework or convincingly argue that the first-order result is valid despite Gamma much larger than E, the paper could become publishable. The paper fits the journal's scope. I did not find evidence of intentional misrepresentation; the SU(4) issue is an overstatement rather than a fabrication."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Jin-Yu and Rui have extended their OBE study to decay widths. What's new: first computation of two-body strong decay widths for the specific YcK* molecules from PRD 108, 054011, including coupled-channel amplitudes and branching ratios. The effective-Lagrangian machinery is standard, but the application is coherent and the amplitude tables are complete. They check D-wave effects (<2% effect) and show the main qualitative pattern is stable to a factor of 1.2 rescaling of couplings (Table 4). The branching ratios being nearly independent of binding energy is a useful experimental handle. Credit where due: the paper is honest about SU(4) breaking, flags three-body modes, and does not oversell.\n\nThe most serious soft spot is internal consistency for the broad states. For the single Sigma_c K* 1/2(1/2-) state, Table 4 gives Gamma = 159 MeV at binding energy E = -4.75 MeV, so the width exceeds the binding by a factor of 30. The first-order width formula and a normalizable real wavefunction are not justified when the imaginary part of the pole is comparable to or larger than the binding. Worse, Ref [16] deliberately omitted the lower channels (Ds N, Lambda_c K, Sigma_c K) that are exactly the dominant decay channels here. The large widths show those channels are not weakly coupled, so the resonance poles may shift substantially or not exist. This applies to the Sigma_c K* 1/2(1/2-) and 1/2(3/2-) states, and to some extent to the coupled Lambda_c K*/Sigma_c K* 1/2(3/2-) state (Gamma ~70 MeV at E ~ -1 MeV). The paper should either present these as resonance widths computed with a method that accommodates a complex pole, or restrict claims to the narrower states (e.g., the coupled Sigma_c K / Lambda_c K* / Sigma_c K* 1/2(1/2-) state with Gamma ~10 MeV, though even there Gamma/E is order one at small binding).\n\nSecond, the SU(4) breaking estimate rests on one comparison (Sigma_c(*) -> Lambda_c pi). That gives a 20% handle, but it is a single channel. A sensitivity check with a different spin-dependent coupling set would strengthen the claim. Third, no wavefunctions or code are released; the results depend on Ref [16]'s wavefunctions. That is model dependence, not circularity—the widths are new observables—but it limits independent verification.\n\nBottom line: the paper is a useful contribution for hadron spectroscopy, and the narrower states' predictions are probably worth taking seriously. The broad states need a disclaimer or a self-consistent treatment. I would send it to a serious referee, with the instruction to probe the width-vs-binding consistency.\n\nWho this is for: hadron spectroscopists in the molecular interpretation business. A reader there gets value from the pattern of dominant channels and the branching-ratio stability. Recommendation: accept with major revision, or at minimum require the authors to address the broad-state consistency issue and add explicit caveats.","headline":"First decay-width predictions for the YcK* molecular candidates, with a clear pattern of dominant channels, but the broad states with Gamma >> binding energy are not self-consistently treated as bound states.","tokens_in":13954,"tokens_out":3322,"would_cite":true,"duration_ms":37710,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["14.20.Pt","13.30.Eg"],"model":"deepseek-v4-flash","headline":"Predicted charm-strange molecular pentaquarks decay with widths from a few MeV to about 200 MeV, and their branching ratios are nearly binding-energy-independent.","keywords":["hadronic molecules","charm-strange pentaquarks","effective Lagrangian approach","two-body strong decays","Lambda_c K* molecule","Sigma_c K* molecule","decay widths","SU(4) flavor symmetry"],"falsifier":"Look for a $1/2(1/2^-)$ state near the $\\Sigma_c K^*$ threshold in the $\\Lambda_b \\to \\Lambda_c K \\bar K \\pi$ reaction: with a binding energy near $-5$ MeV the calculation predicts a total width of about 159 MeV and branching ratios of roughly 54\\% $\\Sigma_c K$ and 38\\% $\\Lambda_c K$; a measured width below about 50 MeV, or a dominant mode other than $\\Sigma_c K$, would contradict the prediction.","tokens_in":12928,"feed_emoji":"⚛️","tokens_out":11088,"duration_ms":104604,"temperature":0.7,"pith_summary":"The paper tries to establish concrete two-body strong decay signatures for six predicted charm-strange molecular pentaquarks, each made of a charmed baryon ($\\Lambda_c$ or $\\Sigma_c$) bound to a kaon or vector kaon $K^*$. Using an effective Lagrangian approach with wave functions from an earlier one-boson-exchange study, it computes total and partial widths for the allowed $S$-wave decay channels. The central finding is a strong quantum-number dependence: widths run from a few MeV for the coupled $\\Sigma_c K/\\Lambda_c K^*/\\Sigma_c K^*$ state with $1/2(1/2^-)$, where $D_s N$ dominates, up to about 200 MeV for the single $\\Sigma_c K^*$ $1/2(1/2^-)$ state. In every channel the branching ratios are nearly independent of binding energy, which makes the predicted channel ratios a stable fingerprint for experimental searches. These numbers give experiments a quantitative way to tell a loosely bound molecule from a compact pentaquark.","feed_headline":"Pentaquark molecule decays charted from a few to 200 MeV","feed_subtitle":"Branching ratios barely move with binding energy, giving a stable experimental fingerprint.","key_machinery":"The central machinery is the effective Lagrangian description of the $S$-wave two-body decay of a hadronic molecule, where the total amplitude is a coherent sum over the molecular channels of the transition amplitude for each constituent pair, weighted by the channel wave function. The paper uses meson-exchange and baryon-exchange amplitudes built from the effective Lagrangians $\\mathcal{L}_{PPV}$, $\\mathcal{L}_{VVP}$, $\\mathcal{L}_{VVV}$, $\\mathcal{L}_{BBP}$, $\\mathcal{L}_{BBV}$, $\\mathcal{L}_{BDP}$, and $\\mathcal{L}_{BDV}$, with all charmed coupling constants fixed by SU(4) flavor symmetry from tabulated nucleon couplings. The wave functions for the six predicted molecules come from a previous one-boson-exchange study, and coupled-channel effects enter by summing the individual channel contributions with their $S$-wave probabilities. This setup converts a molecular prediction into a definite list of partial widths whose pattern is robust to the binding energy.","core_discovery":"On the paper's own terms, the discovery is a decay-width hierarchy for the predicted $Y_c K^{(*)}$ molecules. The coupled $\\Sigma_c K/\\Lambda_c K^*/\\Sigma_c K^*$ state with $I(J^P)=1/2(1/2^-)$ has a total width of about 4--13 MeV, dominated by $D_s N$ (about 91\\%). The coupled $\\Lambda_c K^*/\\Sigma_c K^*$ states have widths of 14--33 MeV for $1/2(1/2^-)$, with $\\Sigma_c K$ (about 54\\%) and $\\Lambda_c K$ (about 36\\%) leading, and 25--70 MeV for $1/2(3/2^-)$, dominated by $\\Sigma_c^* K$ (about 90\\%). The single $\\Sigma_c K^*$ molecule with $1/2(1/2^-)$ is the broadest, reaching 50--245 MeV with $\\Sigma_c K$ (about 54\\%) and $\\Lambda_c K$ (about 38\\%) as the main modes; its $1/2(3/2^-)$ and $3/2(1/2^-)$ partners are narrower, with widths of 5--30 MeV and 10--39 MeV, respectively. In all cases the branching ratios stay almost flat as the binding energy varies over the plotted ranges. The paper attributes the large widths to light pion and rho exchange between the constituents, and it shows that coupled-channel effects, especially the small $\\Sigma_c K^*$ component in the $\\Lambda_c K^*/\\Sigma_c K^*$ states, can change the width through partial coherence.","pith_inferences":["If a future measurement resolves a candidate near a $Y_c K^{(*)}$ threshold with a width outside the predicted window, the molecular interpretation of that state would be in tension; a width inside the window would support it over a compact-pentaquark picture.","The SU(4) coupling relations are the main systematic uncertainty; a direct lattice computation of a charmed-baryon coupling such as $\\Lambda_c \\to \\Sigma_c \\pi$ would test the paper's 20% symmetry-breaking estimate.","The same effective-Lagrangian machinery could be applied to bottom partners built from $Y_b$ and $K^{(*)}$ mesons, where the heavier quark mass should make the molecular picture more reliable.","The binding-energy insensitivity of the branching ratios suggests a future analysis could invert the calculation and use measured channel ratios to constrain which coupled-channel component dominates the wave function."],"forward_implications":["Searches in $B \\to \\Lambda_c (\\Sigma_c) \\bar\\Lambda_c K$ and $\\Lambda_b \\to \\Lambda_c K \\bar K \\pi$ should look for the predicted width ranges; a $1/2(1/2^-)$ $\\Sigma_c K^*$ molecule should appear as a broad structure near threshold with $\\Sigma_c K$ and $\\Lambda_c K$ as the leading final states.","The near-constancy of branching ratios means experimental identification can rely on relative rates rather than on a precise knowledge of the binding energy.","The width hierarchy is a discriminating test: states with different spin-parity have different dominant decay modes ($\\Sigma_c K$ versus $\\Sigma_c^* K$), so the measured final state identifies the quantum numbers.","Coupled-channel effects matter for the $\\Lambda_c K^*/\\Sigma_c K^*$ predictions: ignoring the small $\\Sigma_c K^*$ component would remove the partial coherence that shifts the total width.","Three-body modes through $K^* \\to K\\pi$ may be significant for the $K^*$-containing molecules and are flagged by the paper as the next step."],"supporting_citations":[{"why":"Supplies the predicted six molecular candidates and their channel wave functions, which are the objects whose decays are computed.","marker":"[16]"},{"why":"Provides the effective Lagrangians and the base nucleon coupling constants used to build the decay amplitudes.","marker":"[56]"},{"why":"Earlier effective-Lagrangian decay study whose treatment of SU(4)-broken couplings is adapted here.","marker":"[22]"},{"why":"Recent application of the same coupling scheme that the paper follows for charmed hadrons.","marker":"[28]"},{"why":"Shows how SU(4) symmetry relations are corrected by using physical meson masses, the scheme adopted in Table 2.","marker":"[55]"},{"why":"Independent quark-model prediction of $\\Sigma_c K^*$ bound-state widths with which the paper compares its spin dependence.","marker":"[54]"},{"why":"Reports the observed charm-strange tetraquark candidates that motivate searching for charm-strange molecular partners.","marker":"[9]"},{"why":"Companion measurement of the same charm-strange resonances, supporting the near-threshold molecular discussion.","marker":"[10]"}],"fun_headline_variants":["Charmed molecule decay widths span 4–245 MeV, branching steady","Binding energy leaves charmed molecule decay branching unchanged","Coupled-channel molecules decay from a few to 245 MeV wide","Pentaquark-like states: decay width hierarchy with flat branching","Heavy hadron molecules: decay patterns independent of binding"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The calculation assumes that SU(4) flavor symmetry sets every charmed-baryon coupling from well-known nucleon couplings, with deviations under about 20%; if charm couplings break the symmetry more strongly, the computed widths and the ordering of dominant channels could change.","fun_headline_variants_meta":{"raw":{"variants":["Charmed molecule decay widths span 4–245 MeV, branching steady","Binding energy leaves charmed molecule decay branching unchanged","Coupled-channel molecules decay from a few to 245 MeV wide","Pentaquark-like states: decay width hierarchy with flat branching","Heavy hadron molecules: decay patterns independent of binding"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001,"raw_usage":{"total_tokens":4365,"prompt_tokens":1213,"completion_tokens":3152,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":829,"completion_tokens_details":{"reasoning_tokens":3066}},"tokens_in":829,"tokens_out":3152,"duration_ms":24963,"temperature":1.0,"reasoning_tokens":3066,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T18:46:32.052766+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Look for a $1/2(1/2^-)$ state near the $\\Sigma_c K^*$ threshold in the $\\Lambda_b \\to \\Lambda_c K \\bar K \\pi$ reaction: with a binding energy near $-5$ MeV the calculation predicts a total width of about 159 MeV and branching ratios of roughly 54\\% $\\Sigma_c K$ and 38\\% $\\Lambda_c K$; a measured width below about 50 MeV, or a dominant mode other than $\\Sigma_c K$, would contradict the prediction.","supporting_citations":[{"cited_title":"Chen and Q","cited_arxiv_id":null,"evidence_quote":"Supplies the predicted six molecular candidates and their channel wave functions, which are the objects whose decays are computed."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the effective Lagrangians and the base nucleon coupling constants used to build the decay amplitudes."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Recent application of the same coupling scheme that the paper follows for charmed hadrons."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Independent quark-model prediction of $\\Sigma_c K^*$ bound-state widths with which the paper compares its spin dependence."}],"review_version":1}