{"id":"daa207f5-bc96-420e-b7c6-d30d22af0c47","arxiv_id":"2412.03216","paper_version":2,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"Photoproduction and electroproduction yields of Lambda_c(2940) as a molecule versus a three-quark state are predicted to be of the same order of magnitude at EicC and EIC, with total yields of 10^5 to 10^7 events.","lead":"This paper estimates how many excited charmed baryons and predicted D-bar-N molecules could be produced at two proposed electron-ion colliders, EicC in China and EIC in the US. It finds yields of 10^5 to 10^7 events depending on the state, suggesting the facilities could detect them, but that the structure of the Lambda_c(2940) baryon may not be distinguishable from production rates alone.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The central claim rests on the t-channel-only photoproduction approximation, which is weakest exactly in the near-threshold photon-energy region that dominates the EicC/EIC yield integrals.","rationale":"Read in good faith, this is a standard effective-Lagrangian feasibility estimate. The authors are transparent about several model choices, and the ratio-based argument for the two Λc(2940) pictures is a useful observation. However, the central quantitative claims — same-order production rates and yields sufficient for detection — inherit all of their sensitivity from the photoproduction amplitude. The paper's own Su2024 statement restricts to t-channel exchange and justifies this by an asymptotic-mass argument that is weakest precisely in the w ~ 5-10 GeV window where the equivalent-photon spectrum peaks. Since the two Λc(2940) models differ mainly in the coupling at the NΛcD* vertex, an additional production mechanism that accesses a different vertex could alter both the absolute yields and the model-discrimination ratio. The reader's weakest_assumption identifies the same issue, so my agreement is full. The unresolved numerical-input ambiguity (6.64 vs 1.63) reinforces that the central ratio is not yet uniquely pinned down. None of this makes the paper's approach fundamentally incorrect; it means the current results are conditional on a t-channel-only model, which is exactly the verdict the reader reached. Therefore no verdict change is recommended.","tokens_in":11618,"tokens_out":22176,"duration_ms":220729,"concrete_test":"Recompute the Λc(2940) cross sections with the full tree-level amplitude: add s-channel N* diagrams, u-channel Λc exchange, and the contact terms required by gauge invariance, using the same effective Lagrangians, form factors, and cutoff Λ2=2.5 GeV as Section II.B. Then re-integrate the EicC and EIC yields; if the integrated yields change by more than roughly 50% or the molecule/3P0 ratio moves outside the same-order band, the t-channel-only approximation is not safe and the conclusions of Tables II and IV need revision.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section II.B states 'we only consider t-channel particle exchange here,' and Section III.A justifies this by saying the center-of-mass energy is much higher than the nucleon mass. The yields in Tables II and IV are obtained by integrating the photoproduction cross section over the equivalent-photon spectrum, whose 1/ω weight emphasizes photon energies just above the Λc(2940)+Dbar threshold, i.e., w ~ 5-10 GeV. At these energies the t-channel D* exchange is not obviously dominant over s-channel nucleon-resonance diagrams, u-channel contributions, or the contact terms needed for electromagnetic gauge invariance with charged D/D* exchange. No estimate of these omitted contributions is given. If they contribute at the same order as the t-channel term, the absolute yields could shift by an order of magnitude, and the molecule-versus-three-quark ratio could change because the two Λc(2940) models enter through different NΛcD* couplings (1.63 vs 0.75). The 'same order of magnitude' and 'likely detectable' claims therefore depend on an unvalidated dominance assumption. A secondary ambiguity: Section II.B quotes excited-state couplings g_{ND*Λ*}=6.64 from Refs. [24,31], an order of magnitude larger than the compositeness value g_{Λc(2940)D*N}=1.63 used later; the manuscript does not explicitly state which value enters the numerics, and using 6.64 would invalidate the central ratio claim.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper estimates photoproduction and electroproduction yields for ground and excited Lambda_c states and predicted (Dbar N) hadronic molecules at the proposed EicC and EIC facilities. It uses t-channel D and D* exchange effective Lagrangians for gamma p -> Dbar0 Lambda_c^(*) and gamma p -> (Dbar N) D+, with couplings determined from SU(4) symmetry, the compositeness condition for molecular states, and the 3P0 model for quark-model states. The equivalent photon approximation converts photoproduction cross sections into electroproduction yields. The central quantitative claims are that Lambda_c(2940) production is of the same order of magnitude whether it is treated as a hadronic molecule or a three-quark state, and that with integrated luminosity the yields reach 10^6-10^7 for Lambda_c excited states and 10^5 for (Dbar N) molecular states, making them likely detectable.","tokens_in":11961,"tokens_out":4734,"duration_ms":42780,"significance":"If the calculation were robust, the paper would provide useful first estimates for charm-baryon searches at EicC and EIC, and its conclusion that photoproduction alone may not discriminate the structure of Lambda_c(2940) would be a valuable caution. The paper has concrete strengths: the ratio between channels is shown to be fairly stable under variation of the form-factor cutoff in Fig. 6; the compositeness condition and 3P0 model are implemented with explicit formulas; and the final yield tables are straightforward to use for experimental planning. However, the absolute yields, on which the detectability claim rests, inherit several unquantified model uncertainties, and the manuscript itself acknowledges the t-channel-only approximation and the use of the experimental mass for a quark-model state whose predicted mass is higher. The significance is therefore conditional on a quantitative assessment of these omitted and ambiguous contributions.","major_comments":[{"comment":"The central yield claims depend on the t-channel-only approximation, but the approximation is weakest exactly in the photon-energy region that dominates the yield integrals. Section II.B states 'we only consider t-channel particle exchange here,' and Section III.A justifies this by saying the center-of-mass energy is much higher than the nucleon mass. The equivalent photon spectrum in Eq. (5) has a 1/omega weight, so the yields in Tables II and IV receive substantial contributions from photon energies just above threshold, w ~ 5-10 GeV. At these energies, s-channel nucleon-resonance diagrams, u-channel contributions, and the contact terms required by electromagnetic gauge invariance for charged D/D* exchange are not obviously negligible. No estimate of these omitted contributions is given. Because the molecule-versus-three-quark comparison enters through different N Lambda_c D* couplings (1.63 vs 0.75), an order-of-magnitude shift in the t-channel contribution could change the central 'same order of magnitude' conclusion. I would ask the authors to provide at least a quantitative estimate of the omitted channels, or to phrase the claims explicitly as lower-bound estimates under a stated dominance assumption.","section":"II.B and III.A; Fig. 7; Tables II and IV"},{"comment":"There is an unresolved ambiguity in the coupling constant that enters the molecular Lambda_c(2940) amplitude. Section II.B states that 'the excited states coupling constants g_{ND Lambda*_c} = -0.54 and g_{ND* Lambda*_c} = 6.64 are used in Refs. [24,31].' Section II.C.1 instead derives g_{Lambda_c(2940) D*N} = 1.63 from the compositeness condition, Eq. (22). The manuscript never explicitly states which value is used in Eq. (9) for the molecular Lambda_c(2940) curve in Fig. 7 and the corresponding yields in Table II. If the value 6.64 is used, the molecular cross section scales by (6.64/1.63)^2 ~ 16.6 relative to the compositeness-based value, which would invalidate the claimed 'same order of magnitude' ratio with the 3P0 result (g = 0.75). This is a load-bearing numerical ambiguity and must be resolved in the text.","section":"II.B and II.C.1"},{"comment":"The 3P0-model prediction for Lambda_c(2940) uses the experimental mass while the quark model predicts the Lambda_c(1/2-, 2P) state to be roughly 40-60 MeV heavier, and this difference is acknowledged in the introduction. The mass enters the threshold and phase space of the t-channel amplitude, and the cross section of a near-threshold state is very sensitive to that input. Section III.A states 'we use this assignment along with the experimental mass [1] in our 3P0 model calculations,' but no sensitivity study is given. The same-order-of-magnitude comparison between the 3P0 and molecular models could change if the predicted mass were used instead. A simple check with the quark-model mass, or an estimate of the resulting shift in Table II, is needed before the comparison can be considered robust.","section":"III.A"},{"comment":"The yield ranges quoted in Tables II and IV reflect only the variation of collision energy and integrated luminosity between EicC and EIC, not the model uncertainties in the input couplings, the form-factor cutoff Lambda_2, or the molecular size parameter Lambda. Section III.A calibrates Lambda_2 = 2.5 GeV by 'comparing the charm production results [12-14,22]' but does not state the uncertainty of that calibration. Figure 6 shows that the ratios to the ground state are stable under Lambda_2 variation at w = 10 GeV, but ratios do not constrain the absolute normalization that determines the 'yields reach 10^5-10^7' claim. I request a propagated uncertainty estimate, or at least an explicit statement that the quoted yields are central values without model-systematic errors.","section":"Tables II and IV; Fig. 6"}],"minor_comments":[{"comment":"There are typos: 'descrping' should be 'describing', 'wav function' should be 'wave function', and 'repectively' should be 'respectively'.","section":"II.C.2"},{"comment":"The summary repeats the typo 'yeilds' for 'yields'.","section":"IV"},{"comment":"The sentence beginning 'We use Lambda_c and Lambda_c(2940) molecular state as examples' is grammatically incomplete; it likely should read 'We use the Lambda_c and Lambda_c(2940) molecular state as examples.'","section":"III.A"},{"comment":"The sentence 'even after taking into account reconstruction efficiency, the yields remain considerable large' would be clearer with a stated efficiency value or a more precise phrasing such as 'assuming a plausible reconstruction efficiency.'","section":"III.A"},{"comment":"References [4] and [45] are the same paper (Capstick and Isgur, Phys. Rev. D 34, 2809 (1986)); this duplication should be removed.","section":"References"}],"recommendation":"major_revision","confidential_remarks":"The manuscript's own stated limitations (t-channel-only amplitudes, use of the experimental mass for the quark-model assignment, and the unstated choice between g = 6.64 and g = 1.63) are precisely the points that control the central yield and ratio claims. I would like the revision to resolve the coupling ambiguity explicitly and to add quantitative sensitivity estimates for the omitted channels and the mass assignment. The paper is suitable for reconsideration after those points are addressed, but in its current form the absolute yields are not yet supported by the calculation."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Fairly standard feasibility estimate, but the new bits are genuinely useful. The first yield numbers for the (D-bar N) molecules at EicC and EIC, and the 3P0-model comparison of Lambda_c(2940) as a quark state vs a molecule in photoproduction, are not in the earlier literature. The calculation is coherent, and Fig. 6's cutoff-dependence check on the channel ratios is exactly the kind of robustness test this sort of model needs. The main conclusion—that the Lambda_c(2940) photoproduction rate can't tell a molecule from a three-quark state—is honestly stated and probably survives more refined treatment because it's a ratio comparison.\n\nSoft spots, in decreasing order. The t-channel-only assumption is the biggest one. The argument that 'the c.m. energy is much larger than the nucleon mass' is weak at w=5-10 GeV, and that is precisely the region the equivalent-photon integral samples; the standard WW spectrum carries a 1/omega factor. Incidentally, Eq. (5) as written appears to have lost that factor—the dn = N(omega) omega domega form gives dN/domega ~ omega ln(1/omega), which is not the usual WW result. The authors should check the normalization. No estimate is given for s-channel, u-channel, or contact contributions. That could shift absolute yields by an order of magnitude and even affect the molecule/quark ratio, since the two Lambda_c(2940) models enter through different couplings.\n\nSecond, the coupling-constant ambiguity: Section II.B quotes g_ND*Lambda* = 6.64 from Refs [24,31], and Section II.C.1 computes g_Lambda_c(2940)D*N = 1.63 from compositeness. The text never says which one enters the molecule cross sections. The Table II numbers are consistent with 1.63, but a reader shouldn't have to reverse-engineer that. If 6.64 were used, the 'same order of magnitude' claim would fail. A referee should push for an explicit statement.\n\nThird, the quoted yield ranges come from varying only the cutoff Lambda_2. The model also depends on gamma, the SHO parameters, and the molecular size parameter, with no uncertainty budget, so the ranges are optimistic. Minor items: the Lambda_c(2940)-3P0 row of Table II has a garbled value ('(4.5 ~ 2.3) x 10^7'), and using the experimental Lambda_c(2940) mass in the 3P0 calculation while the quark model expects 40-60 MeV higher is a simplification that could feed back into the coupling and phase space.\n\nWho should read this? Anyone planning a charm-baryon program at EicC/EIC or working on the Lambda_c(2940) molecular interpretation. It deserves a serious referee: the central claim is sound, the new yields are worth having, and the problems are clarity and omitted-model-checks, not a fatal flaw. I'd send it to peer review with a request for the coupling-constant clarification, a check of the WW spectrum, and a short discussion of omitted channels.","headline":"A useful feasibility estimate with one robust central claim, but the t-channel-only approximation and an ambiguous coupling-constant value need referee attention before the yield numbers can be taken at face value.","tokens_in":12479,"tokens_out":9162,"would_cite":true,"duration_ms":76936,"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 paper shows that yields of excited charm baryons at EicC and EIC reach 10^6 to 10^7 events, while Lambda_c(2940) production rates alone cannot distinguish a molecular from a three-quark structure.","keywords":["charm baryons","Lambda_c(2940)","hadronic molecules","Dbar-N molecular states","photoproduction","electroproduction","EicC and EIC","equivalent photon approximation"],"falsifier":"A measurement of the $\\gamma p\\to \\bar{D}^0\\Lambda_c(2940)$ cross section at a center-of-mass energy around 10 GeV would settle the central estimate: the paper's t-channel model places it in a specific band (the $\\Lambda_2=2.5$ GeV curve in Fig. 7), so a measured value an order of magnitude above or below that band would falsify the yield prediction.","tokens_in":11405,"feed_emoji":"⚛️","tokens_out":8675,"duration_ms":73674,"temperature":0.7,"pith_summary":"This paper asks whether the planned electron-ion colliders EicC and EIC can produce excited charmed baryons -- the ground state $\\Lambda_c$, the excitations $\\Lambda_c(2595)$ and $\\Lambda_c(2940)$, and the predicted $(\\bar{D}N)$ hadronic molecules -- in numbers large enough to study. Its central finding is that the production rate of $\\Lambda_c(2940)$ is essentially the same whether the state is modelled as a $J^P=1/2^-$ hadronic molecule or as the quark-model $\\Lambda_c(1/2^-,2P)$ state, so a rate measurement alone will not identify the state's internal structure. Using the Weizsäcker-Williams equivalent-photon approximation to go from real-photon to electron-proton collisions, the paper estimates that the excited $\\Lambda_c$ states are produced $10^6$ to $10^7$ times at both colliders after integrated luminosity, and the $(\\bar{D}N)$ molecular states about $10^5$ times, which would make them detectable. The authors conclude that EicC and EIC open a window on charm baryons of different configurations, but that the $\\Lambda_c(2940)$ puzzle needs more than counting rates.","feed_headline":"Charm-baryon yields of 10^6–10^7 expected at EicC and EIC","feed_subtitle":"Rates alone cannot tell Λc(2940) molecule from quark state, but both would be detected in large samples.","key_machinery":"The carrier of the calculation is the t-channel Feynman amplitude for $\\gamma p \\to \\bar{D}^0 \\Lambda_c^{(*)}$, built from effective Lagrangians with nucleon, $D$, and $D^*$ exchange (Fig. 1). The couplings that enter are not all known empirically, so two model schemes supply them: the hadronic-molecule picture, in which $\\Lambda_c(2940)$ and the $(\\bar{D}N)$ states are $S$-wave bound states whose couplings are fixed by the compositeness condition $Z=1-\\Sigma'(m^2)=0$, and the $3P_0$ quark-pair-creation model, which gives the couplings for the three-quark assignments. A monopole form factor with cutoff $\\Lambda_2=2.5$ GeV regulates the off-shell vertices, and the Weizsäcker-Williams equivalent-photon approximation converts the real-photon cross sections into electron-proton yields at the EicC and EIC energies.","core_discovery":"On the paper's own terms, the central discovery is a quantitative yield comparison. For the t-channel process $\\gamma p\\to \\bar{D}^0\\Lambda_c^{(*)}$, treating $\\Lambda_c(2940)$ either as a $D^*N$ molecular state or as the three-quark $\\Lambda_c(1/2^-,2P)$ state changes the photoproduction cross section by less than an order of magnitude over the $5$--$20$ GeV range, with the molecular assumption giving a modest enhancement (Figs. 6 and 7). Converting to electroproduction by the Weizsäcker-Williams method and folding in the integrated luminosities of EicC and EIC, the paper yields $10^6$--$10^7$ events for $\\Lambda_c(2595)$ and $\\Lambda_c(2940)$, and $10^5$ events for the predicted $(\\bar{D}N)$ molecules with isospin $I=0$ and $I=1$. These numbers are presented as evidence that both facilities can meaningfully study charm baryons, while the near-degeneracy of the two $\\Lambda_c(2940)$ models is presented as evidence that photoproduction rates alone are not decisive for its structure.","pith_inferences":["A natural next step, not taken in the paper, is to compute s- and u-channel contributions in the same effective-Lagrangian framework; the near-threshold region ($W$ between 5 and 10 GeV) is where the t-channel approximation is most vulnerable, and an explicit check would show whether the same-order-of-magnitude conclusion survives.","Because the $3P0$ model coupling constants for the excited states were evaluated with the meson off-shell ($p_C^2=0$) and one free parameter $\\gamma$ fixed elsewhere, the quark-model branch of the comparison carries an uncertainty that could be tested against future lattice QCD determinations of the $\\Lambda_c(2940)\\to \\bar{D}N$ coupling.","The same recipe could be applied to bottom counterparts like $\\Lambda_b$ states and $(\\bar{B}N)$ molecules, where the heavier quark mass changes the kinematics and could make the molecular vs quark-model discrimination more visible."],"forward_implications":["$\\Lambda_c(2940)$ production alone will not settle its structure: the molecule and quark-model cross sections stay within the same order of magnitude, so distinguishing them requires other observables such as angular distributions or decay patterns.","After integrated luminosity, EicC and EIC should collect $10^6$--$10^7$ $\\Lambda_c(2595)$ and $\\Lambda_c(2940)$ events, giving large samples for spectroscopy and decay studies.","The $(\\bar{D}N)$ molecules with $I=0$ and $I=1$ should be produced at the $10^5$ level and are within reach of both facilities.","The yield hierarchy is controlled by whether $D$ or $D^*$ exchange dominates: for $\\Lambda_c(2940)$ the $D^*$ exchange pushes production to higher energies, whereas for $(\\bar{D}N)$ the $D$ exchange keeps it at lower energies, explaining the different EicC-vs-EIC ratios."],"supporting_citations":[{"why":"BaBar observation of $\\Lambda_c(2940)$ in the $D^0p$ invariant mass distribution; this is the state the paper tries to model and produce.","marker":"[1]"},{"why":"Provides the $SU(4)$ effective-Lagrangian values $g_{ND\\Lambda_c}=-13.72$ and $g_{ND^*\\Lambda_c}=-5.20$ used for the ground-state couplings.","marker":"[3]"},{"why":"Earlier study of $\\Lambda_c(2940)$ photoproduction as a $J^P=1/2^\\pm$ molecular state, supplying the excited-state couplings $g_{ND\\Lambda^*_c}$ and $g_{ND^*\\Lambda^*_c}$.","marker":"[24]"},{"why":"Predicts the $(\\bar{D}N)$ bound states with masses $m_{I=0}=2804.8$ MeV and $m_{I=1}=2800.2$ MeV that the paper adopts for its molecular-state estimates.","marker":"[28]"},{"why":"Defines the EicC energy and luminosity parameters used to compute integrated yields.","marker":"[25]"},{"why":"Defines the EIC energy and luminosity parameters used to compute integrated yields.","marker":"[26]"},{"why":"The compositeness condition $Z=1-\\Sigma'(m^2)=0$ used to determine the molecular-state coupling constants.","marker":"[39]"},{"why":"Source of the $3P_0$ model parameter $\\gamma=9.83$ fitted to $\\Sigma_c(2520)^{++}\\to\\Lambda_c\\pi^+$, adopted for the quark-model couplings.","marker":"[47]"}],"fun_headline_variants":["Millions of charm baryons expected at EicC and EIC","EicC and EIC could spot 10^5 molecular states","Λc(2940) rates can't reveal its quark vs molecule nature","Large charm yields but Λc(2940) identity ambiguous"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing assumption is that the t-channel meson exchange alone controls the photoproduction cross section, with no s-channel, u-channel, or contact contributions of comparable size; if any of these channels contributes significantly near threshold, the predicted yields for the excited states would shift by an unknown amount.","fun_headline_variants_meta":{"raw":{"variants":["Millions of charm baryons expected at EicC and EIC","EicC and EIC could spot 10^5 molecular states","Λc(2940) rates can't reveal its quark vs molecule nature","Large charm yields but Λc(2940) identity ambiguous"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000894,"raw_usage":{"total_tokens":3876,"prompt_tokens":991,"completion_tokens":2885,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":607,"completion_tokens_details":{"reasoning_tokens":2807}},"tokens_in":607,"tokens_out":2885,"duration_ms":20720,"temperature":1.0,"reasoning_tokens":2807,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T22:38:40.096024+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A measurement of the $\\gamma p\\to \\bar{D}^0\\Lambda_c(2940)$ cross section at a center-of-mass energy around 10 GeV would settle the central estimate: the paper's t-channel model places it in a specific band (the $\\Lambda_2=2.5$ GeV curve in Fig. 7), so a measured value an order of magnitude above or below that band would falsify the yield prediction.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"BaBar observation of $\\Lambda_c(2940)$ in the $D^0p$ invariant mass distribution; this is the state the paper tries to model and produce."},{"cited_title":"Aubert, R","cited_arxiv_id":null,"evidence_quote":"Provides the $SU(4)$ effective-Lagrangian values $g_{ND\\Lambda_c}=-13.72$ and $g_{ND^*\\Lambda_c}=-5.20$ used for the ground-state couplings."},{"cited_title":"Tomasi-Gustafsson, Czech J Phys 55, A179 (2005)","cited_arxiv_id":null,"evidence_quote":"Earlier study of $\\Lambda_c(2940)$ photoproduction as a $J^P=1/2^\\pm$ molecular state, supplying the excited-state couplings $g_{ND\\Lambda^*_c}$ and $g_{ND^*\\Lambda^*_c}$."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines the EIC energy and luminosity parameters used to compute integrated yields."},{"cited_title":"Faessler, T","cited_arxiv_id":null,"evidence_quote":"The compositeness condition $Z=1-\\Sigma'(m^2)=0$ used to determine the molecular-state coupling constants."}],"review_version":1}