{"id":"c0317dce-2930-4118-95f3-ead6dbbef598","arxiv_id":"2504.15789","paper_version":2,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"Using a color-magnetic interaction model anchored to P_c(4312), the authors predict three stable doubly-charmed pentaquarks below their strong decay thresholds.","lead":"A quark model calculation predicts three stable doubly-charmed pentaquark states, particles made of two charm quarks plus three light quarks. If found at LHCb, they would be the first observation of a pentaquark with two charm quarks and would test the color-magnetic interaction model.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Stability margins are smaller than the model's own internal spread: the adopted ccnn nbar mass (3714 MeV) is only 45 MeV below Xi_cc pi, while the same paper's alternative formula estimates range from 3603 to 3865 MeV.","rationale":"The reader's verdict (CONDITIONAL) is appropriate. Our stress-test pass found the same broad vulnerability but located it more precisely. The paper is self-consistent as a model calculation and provides a large amount of numerical detail, which is genuinely useful. However, the central stability prediction is a threshold comparison with margins of 45, 112, and 210 MeV for the three states, and the paper nowhere quantifies the uncertainty of its chosen mass formula. Table II alone shows that alternative formulae within the same model produce a 262 MeV spread for the most fragile state and place the Sigma_c D-threshold estimate only 7 MeV below threshold. Since Eq. (5) is selected as 'the theoretical predictions' without an uncertainty estimate, the conclusion that these states are stable is conditional on the reference-scale choice and on the CMI parameter extraction. The reader's weakest_assumption identifies the P_c(4312) J^P assignment; we partially agree, because that assignment is one way the scale can shift, but the concern is broader: even granting the reference assignment, the internal formula spread shows the margin is within the model's noise. The concrete Monte Carlo sensitivity check would settle whether the stability claim survives a realistic range of parameter choices. If it does not, the paper should be accepted only with the stability claim downgraded to a model-dependent prediction requiring experimental search.","tokens_in":48993,"tokens_out":12512,"duration_ms":123824,"concrete_test":"Monte Carlo sensitivity test: vary the input C_ij and Delta_sn within the fit spread obtained from the conventional-hadron extractions in Refs [82,85] (e.g., ±20% for C_ij and ±15 MeV for Delta_sn), and independently vary (E_CMI)_Pc(4312) by the spread of the compact-pentaquark fits in Refs [80,81]; recompute the three ground-state masses and their allowed S-wave thresholds. The stability claim survives only if the fraction of samples with all three masses below threshold is close to 1; in particular, report separately the fraction for the ccnn nbar state, whose margin is 45 MeV.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Load-bearing concern: the central 'three stable pentaquarks' claim is not robust to the model's internal uncertainty, independent of external debate about P_c(4312). For the most fragile predicted state, the lowest I(J^P)=1/2(1/2^-) ccnn nbar with I_nn=0, Table II lists four masses from the paper's own formulae: 3714.2 MeV (Eq. (5), adopted), 3751.6 MeV (Eq. (3) with Sigma_c D), 3603.0 MeV (Eq. (3) with Xi_cc pi), and 3865.2 MeV (Eq. (2) upper limit). The Xi_cc pi threshold is 3758.9 MeV, so the adopted mass is bound by only 44.7 MeV; the Sigma_c D-threshold estimate is bound by only 7.3 MeV, and the upper-limit estimate is 106.3 MeV above threshold. The spread among the paper's own estimates (~262 MeV) dwarfs the 45 MeV binding margin. The paper states in Sec. IV that effective masses and couplings extracted from conventional hadrons 'may introduce uncertainties' but gives no error bars and no quantitative criterion for preferring Eq. (5) over the alternatives. A +45 MeV shift in the scale parameter mtilde (from the assumed P_c(4312) 3/2^- compact assignment, from C_ij fits, or from Delta_sn) would make the headline state unbound; shifts of +112 and +210 MeV would destroy the other two stability claims. The reader's reference-assignment concern is one route to such a shift, but the deeper issue is that the model's mass-scale uncertainty is comparable to the claimed binding energies.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript applies a color-magnetic interaction (CMI) mass-splitting model to S-wave compact ccqq\\bar q (q=u,d,s) pentaquark states. It uses three mass formulae: the original effective-quark-mass formula Eq. (2), the meson-baryon threshold formula Eq. (3), and a reference-pentaquark formula Eq. (5) that fixes the overall scale by assuming P_psi(4312)^+ is a compact hidden-charm pentaquark with I(J^P)=1/2(3/2^-), giving m_tilde_penta=4382.6 MeV. The paper computes CMI matrices, eigenvalues, eigenvectors, and masses for eight flavor/isospin cases, and estimates two-body rearrangement decay widths using a constant decay Hamiltonian C extracted from the measured P_c(4312) width. The central results are three ground states predicted to be stable: the lowest I(J^P)=1/2(1/2^-) ccnn\\bar n with I_nn=0 at 3714.2 MeV, the lowest 0(1/2^-) ccnn\\bar s at 4004.7 MeV, and the lowest 0(1/2^-) ccns\\bar n at 3898.7 MeV, each below its lowest S-wave rearrangement threshold.","tokens_in":49399,"tokens_out":7500,"duration_ms":66489,"significance":"If substantiated, the prediction of stable doubly-charmed pentaquarks in the compact picture is a sharp and testable outcome that would distinguish compact multiquark configurations from molecular interpretations and could motivate targeted searches at LHCb and future facilities. The paper's strengths are the explicit spin-color bases, CMI matrices, and detailed decay tables, which make the calculation reproducible, and the systematic comparison with alternative mass estimates from Eqs. (2) and (3) and with earlier literature. However, the stability claim is currently supported only at the level of central values: the model's own internal spread is comparable to the binding margins, and no uncertainties are propagated to any mass or width. The paper is therefore of interest, but the headline conclusion requires substantial qualification before it can be accepted as a prediction of stable states.","major_comments":[{"comment":"The headline stable state, the lowest I(J^P)=1/2(1/2^-) ccnn\\bar n with I_nn=0, is listed at 3714.2 MeV, only 44.7 MeV below the Xi_cc pi threshold (3758.9 MeV). The same quantum state is estimated within the paper's own alternative formulae at 3751.6 MeV (Eq. (3) with the Sigma_c D threshold), 3603.0 MeV (Eq. (3) with the Xi_cc pi threshold), and 3865.2 MeV (Eq. (2) upper limit). The spread among these estimates is about 262 MeV, and one of them lies 106 MeV above the threshold. Since the paper provides no quantitative criterion for preferring Eq. (5) over these alternatives and no uncertainty estimate, the central 'stable' claim is not robust to the model's internal uncertainty.","section":"Table II / Sec. III.B"},{"comment":"The scale m_tilde_penta=4382.6 MeV is obtained by subtracting the calculated CMI eigenvalue of P_psi(4312)^+ (assumed to be a compact state with I(J^P)=1/2(3/2^-)) from its measured mass. This assumption is adopted from Refs. [80,81] and is not independently established in the present paper. A shift of only +45 MeV in m_tilde_penta would move the adopted ccnn\\bar n mass above the Xi_cc pi threshold, and shifts of about +112 and +210 MeV would undermine the other two stability claims. The paper should state the shift in the scale needed to destroy each prediction and discuss the evidence for the assumed quantum numbers, or it should present the predictions with an explicit caveat that they are conditional on this assignment.","section":"Sec. II.A, Eq. (4); Sec. IV"},{"comment":"All input couplings C_ij, the mass gap Delta_sn=90.6 MeV, and the reference scale are quoted without propagated uncertainties, and no error bars are given for any predicted mass or width. Section IV concedes that parameters extracted from conventional hadrons 'may introduce uncertainties,' but the central conclusion concerns binding energies of 45, 111, and 210 MeV, which are exactly the quantities most sensitive to these parameter shifts. A quantitative uncertainty analysis, or at minimum a sensitivity scan over the extracted C_ij, Delta_sn, and m_tilde_penta, is needed to support the claim that these states are stable.","section":"Sec. III.A and Sec. IV"},{"comment":"The paper defines stability only with respect to S-wave two-body rearrangement channels, as stated in Sec. II.C ('we consider just the two-body S-wave strong decays'). The ground states may in principle decay through D-wave or three-body channels, and no calculation or argument is provided that these are negligible. The conclusion should therefore be phrased as 'stable against S-wave two-body rearrangement decays within the model,' rather than the unqualified 'stable' used in the abstract and Sec. IV.","section":"Sec. II.C and Sec. IV"}],"minor_comments":[{"comment":"In the paragraph discussing the wave-function compositions, 'propotions' should be 'proportions.'","section":"Sec. IV"},{"comment":"In the ccns\\bar s, J^P=1/2^- block, the partial-width entry '(19,2,-)' appears to be a typo for '(19.2,-)'.","section":"Table IX"},{"comment":"The abstract says the paper concentrates on 'mass differences relative to P_psi^N(4312)^+', but the results are presented as absolute masses; rewording the abstract to say the scale is fixed by the assumed P_c(4312) mass would be clearer.","section":"Abstract"},{"comment":"The threshold lines in the eight panels are not all labeled with their numerical values; given that the stability margins are only 45-210 MeV, labeling the relevant thresholds directly in the figure would help the reader assess the claim.","section":"Fig. 1"}],"recommendation":"major_revision","confidential_remarks":"This is a straightforward application of the authors' existing CMI framework; its potential contribution is the specific three-stable-state prediction. The main concern is that the stability claim is not yet quantitatively supported: the model's own internal estimates straddle the relevant threshold, and the reference scale is fixed by an assumption from the authors' previous papers. I would like to see either a propagated uncertainty analysis and a sharpened wording ('stable against S-wave rearrangement within the model') or a reduction of the central claim to a central-value prediction. The P_c(4312) compact 3/2^- assignment should be flagged as an assumption in the abstract and conclusions, not only in Sec. IV."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"This is a workmanlike extension of the authors' CMI mass-splitting model to doubly-charmed pentaquarks, with a systematic spectrum and rearrangement-decay calculation and three concrete stability predictions. That is genuinely useful: it gives experimentalists specific states to search for and is a legitimate new result within the authors' program.\n\nThe mechanics are fine. The CMI matrices are fully tabulated, the wave functions respect the Pauli principle, and the decay calc is transparent. The comparison with other model predictions (QCD sum rules, quark potential models, chiral EFT) is fair, and the citation pattern is thorough. The paper also flags its own limitations in Sec. IV, which is honest.\n\nThe soft spots are real, and one is load-bearing. First, there are no propagated uncertainties anywhere; every predicted mass is a bare central value. Second, the entire scale is set by assuming P_c(4312) is a compact I(J^P)=1/2(3/2^-) pentaquark, which is not independently established and is, if anything, in tension with the molecule interpretation. Third—and this is the sharper problem—the model's own alternative mass formulae give a spread of 3603–3865 MeV for the lowest ccnn nbar state, while the Xi_cc pi threshold is 3759 MeV. The adopted mass is bound by only 45 MeV; the Sigma_c D-threshold estimate is bound by 7 MeV; the upper-limit estimate is 106 MeV above threshold. The 'stable' claim depends on choosing Eq. (5) and on a scale that can shift by far less than the internal spread. The paper acknowledges the couplings may introduce uncertainties but gives no quantitative criterion for preferring Eq. (5). That is not a robust prediction.\n\nI would not call the paper incoherent—it is a legitimately constructed model calculation and may well be right about some of these states. But the stability claim, as presented, is conditional rather than firm. The paper deserves a serious referee, even though the referee should push hard for an explicit uncertainty band on each mass—from the spread of the formulae and from reasonable variations in the scale parameter—and a more careful defense of the P_c(4312) assignment. Without that, the headline conclusion is too fragile.\n\nIf you work on doubly-charmed pentaquark searches, cite this for the spectrum and for the candidate list, but treat the stabilities as model-dependent suggestions.","headline":"A careful CMI-model study of doubly-charmed pentaquarks whose headline stability claim is undercut by the model's own internal spread of mass estimates.","tokens_in":49909,"tokens_out":2861,"would_cite":true,"duration_ms":27876,"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":"Three doubly-charmed pentaquarks predicted stable","keywords":["doubly-charmed pentaquarks","compact multiquark states","color-magnetic interaction","mass splitting model","Pψ(4312)","strong decays","quark rearrangement","exotic hadron spectroscopy"],"falsifier":"Measure the quantum numbers of $P_\\psi^N(4312)^+$: if it is found to have $J^P=1/2^-$ or a molecular rather than compact structure, the reference scale $\\tilde{m}_{\\rm penta}$ would change enough to lift the predicted ground states above their thresholds. Independently, a lattice QCD calculation of the $I(J^P)=\\frac{1}{2}(\\frac{1}{2}^-)$ $ccnn\\bar{n}$ ($I_{nn}=0$) ground state that comes out above the $\\Xi_{cc}\\pi$ threshold would directly falsify the stability claim.","tokens_in":48780,"feed_emoji":"⚛️","tokens_out":8035,"duration_ms":67343,"temperature":0.7,"pith_summary":"The paper aims to show that the lightest doubly-charmed pentaquark states with quark content $ccqq\\bar{q}$ $(q=u,d,s)$ should exist as compact five-quark hadrons, provided the observed $P_\\psi^N(4312)^+$ is itself a compact hidden-charm pentaquark with quantum numbers $I(J^P)=\\frac{1}{2}(\\frac{3}{2}^-)$. Working only with mass differences relative to that reference state removes the largest uncertainty in usual color-magnetic interaction estimates. The calculation places three ground states below every allowed $S$-wave two-body threshold: the $I(J^P)=\\frac{1}{2}(\\frac{1}{2}^-)$ $ccnn\\bar{n}$ ($I_{nn}=0$) at about $3714$ MeV, the $0(\\frac{1}{2}^-)$ $ccnn\\bar{s}$ at about $4005$ MeV, and the $0(\\frac{1}{2}^-)$ $ccns\\bar{n}$ at about $3899$ MeV. If correct, these are stable doubly-charmed pentaquarks that experiments could search for in $\\Xi_{cc}\\pi$, $\\Xi_{cc}K$, and $\\Xi_{cc}\\bar{K}$ spectra. The paper also gives a first rearrangement-decay estimate of the widths of the unstable states.","feed_headline":"Three doubly-charmed pentaquarks predicted stable","feed_subtitle":"Anchored to Pψ(4312)+, a mass-splitting model puts all three ground states below S-wave decay thresholds.","key_machinery":"The central object is the modified color-magnetic interaction mass formula $M=\\tilde{m}_{\\rm penta}+E_{\\rm CMI}+\\sum n_{ij}\\Delta_{ij}$, where $\\tilde{m}_{\\rm penta}=M_{P_\\psi^N(4312)^+}-(E_{\\rm CMI})_{P_\\psi^N(4312)^+}=4382.6$ MeV replaces the uncertain sum of effective quark masses and $\\Delta_{ij}$ are quark-mass gaps such as $\\Delta_{sn}=90.6$ MeV. The $E_{\\rm CMI}$ eigenvalues come from diagonalizing the spin-color Hamiltonian in the ten base vectors built from $(cc)(qq)\\bar{q}$ color couplings; the same bases feed the rearrangement-decay overlaps. This construction is what transfers the scale from a single measured pentaquark to all $ccqq\\bar{q}$ systems while keeping the calculation parameter-light.","core_discovery":"On the paper's own terms, adopting $P_\\psi^N(4312)^+$ as a compact reference pentaquark with $I(J^P)=\\frac{1}{2}(\\frac{3}{2}^-)$ fixes a single scale $\\tilde{m}_{\\rm penta}=4382.6$ MeV, and all doubly-charmed pentaquark masses follow from color-magnetic energy splittings plus quark-mass gaps. The three predicted stable ground states are the lowest $I(J^P)=\\frac{1}{2}(\\frac{1}{2}^-)$ $ccnn\\bar{n}$ with $I_{nn}=0$ at $3714.2$ MeV (about $45$ MeV below $\\Xi_{cc}\\pi$), the lowest $0(\\frac{1}{2}^-)$ $ccnn\\bar{s}$ at $4004.7$ MeV (about $111$ MeV below $\\Xi_{cc}K$), and the lowest $0(\\frac{1}{2}^-)$ $ccns\\bar{n}$ at $3898.7$ MeV (about $210$ MeV below $\\Xi_{cc}\\bar{K}$). In all three, the color-antitriplet $cc$ diquark component dominates and the light $qq\\bar{q}$ cluster is mostly spin $1/2$, so they resemble a $\\Xi_{cc}$ baryon in which the $n$ quark is replaced by a compact triquark. The decay widths computed with a constant rearrangement Hamiltonian indicate that every other $S$-wave state has at least one open channel, while the stable ones have none.","pith_inferences":["If the spin-parity of $P_\\psi^N(4312)^+$ were instead $J^P=1/2^-$ (the molecule assignment), the reference eigenvalue changes and the whole doubly-charmed spectrum shifts almost rigidly; the $45$ MeV margin of the lightest state could disappear, so the stability prediction is a direct test of that quantum-number assignment.","The model's pattern suggests a targeted experimental search: look for a narrow peak just below the $\\Xi_{cc}\\pi$ threshold in prompt or $b$-hadron decays, and for analogues near $\\Xi_{cc}K$ and $\\Xi_{cc}\\bar{K}$; any observed doubly-charmed pentaquark above these thresholds would disfavor the compact picture.","Because the stable states are essentially $\\Xi_{cc}$-like cores with a tightly bound $\\bar{q}qq$ triquark, lattice QCD calculations of the $ccqq\\bar{q}$ ground state with these quantum numbers could settle whether the compact configuration is bound without relying on the CMI scale assumption.","The near degeneracy of $\\rho$ and $\\omega$ in the decay tables means isospin partners of the same state have nearly equal widths into $\\Omega_{cc}^{(*)} \\rho$ and $\\Omega_{cc}^{(*)} \\omega$; precise width ratios in future data could help confirm the underlying flavor wave functions."],"forward_implications":["The lowest $ccnn\\bar{n}$ state at $3714$ MeV should be a stable or very narrow pentaquark, since all $S$-wave rearrangement channels are closed by about $45$ MeV.","The lowest $ccnn\\bar{s}$ at $4005$ MeV lies about $111$ MeV below $\\Xi_{cc}K$, so it cannot decay strongly into that or any other $S$-wave two-body channel.","The lowest $ccns\\bar{n}$ at $3899$ MeV is about $210$ MeV below $\\Xi_{cc}\\bar{K}$, making it the most deeply bound of the three predicted stable states.","The second-lowest $I_{nn}=0$ $3/2^-$ $ccnn\\bar{n}$ state cannot decay in $S$-wave but may decay through $D$-wave, so it should appear as a narrow near-threshold structure.","For all eight flavor-isospin systems, predicted masses are tens of MeV lower than previous threshold-anchored CMI estimates, and the $ccss\\bar{s}$ masses drop by about $150$ MeV."],"supporting_citations":[{"why":"Supplies the experimentally observed $P_\\psi^N(4312)^+$ whose measured mass anchors the reference scale in Eq. (4).","marker":"[25]"},{"why":"Introduces the third mass formula with $P_\\psi^N(4312)$ as reference and gives the $J^P=3/2^-$ assignment used to fix $\\tilde{m}_{\\rm penta}$.","marker":"[81]"},{"why":"Argues $P_\\psi^N(4312)^+$ is best described as a compact pentaquark with $I(J^P)=1/2(3/2^-)$, the load-bearing structural input.","marker":"[80]"},{"why":"Provides the spin-color bases and CMI matrices for $ccqq\\bar{q}$ states that the present spectrum diagonalization inherits.","marker":"[42]"},{"why":"Gives the extraction procedure for the $C_{ij}$ couplings used in the CMI Hamiltonian.","marker":"[82]"},{"why":"Supplies the quark-mass gap $\\Delta_{sn}=90.6$ MeV used to shift strange-quark systems.","marker":"[83]"},{"why":"Supplies the measured hadron masses used for thresholds, phase-space factors, and the reference pentaquark mass.","marker":"[88]"}],"fun_headline_variants":["Mass-splitting model predicts three stable pentaquarks","Three stable doubly-charmed pentaquarks from Pψ(4312)+","Doubly-charmed pentaquark trio predicted stable by model","Model finds three stable doubly-charmed pentaquarks"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The whole calculation stands or falls on the assumption that the observed $P_\\psi^N(4312)^+$ particle is a compact five-quark state with spin-parity $3/2^-$; if that turns out wrong, every predicted mass shifts by roughly the same amount and the 10 to 210 MeV stability margins could change sign.","fun_headline_variants_meta":{"raw":{"variants":["Mass-splitting model predicts three stable pentaquarks","Three stable doubly-charmed pentaquarks from Pψ(4312)+","Doubly-charmed pentaquark trio predicted stable by model","Model finds three stable doubly-charmed pentaquarks"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00039,"raw_usage":{"total_tokens":2108,"prompt_tokens":1055,"completion_tokens":1053,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":671,"completion_tokens_details":{"reasoning_tokens":978}},"tokens_in":671,"tokens_out":1053,"duration_ms":8950,"temperature":1.0,"reasoning_tokens":978,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T11:16:55.867054+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the quantum numbers of $P_\\psi^N(4312)^+$: if it is found to have $J^P=1/2^-$ or a molecular rather than compact structure, the reference scale $\\tilde{m}_{\\rm penta}$ would change enough to lift the predicted ground states above their thresholds. Independently, a lattice QCD calculation of the $I(J^P)=\\frac{1}{2}(\\frac{1}{2}^-)$ $ccnn\\bar{n}$ ($I_{nn}=0$) ground state that comes out above the $\\Xi_{cc}\\pi$ threshold would directly falsify the stability claim.","supporting_citations":[],"review_version":1}