{"id":"3c5a34e5-d5a2-4a0d-9222-26a582d112e8","arxiv_id":"2505.19758","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"Fitting the Xi_c-Xi_c' mixing angle to the LHCb ratio R=1.41, the author predicts branching fractions (3.2-6.0)% and asymmetry parameters about -0.6 to -0.8 for Xi_cc++ -> Xi_c(')+ pi+, using Schrodinger-equation baryon wave functions.","lead":"A theory paper computes two weak decay modes of the doubly charmed baryon Xi_cc++ in a nonrelativistic quark model that includes Xi_c-Xi_c' mixing. By tuning the mixing angle near -16 degrees it matches the LHCb ratio, then predicts branching fractions of a few percent and negative asymmetry parameters that LHCb and Belle II can test.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Central result depends on a W-exchange pole amplitude that differs by a factor of ~2 and a sign from earlier quark-model calculations; convergence to higher poles is not enough to control this model dependence.","rationale":"The paper's central phenomenological claim is that a large negative Ξ_c-Ξ_c' mixing angle, θ∈(-18.2°,-14.3°), simultaneously explains the LHCb ratio and leads to concrete predictions for branching fractions and asymmetries. The reader correctly identifies the pole-model treatment of the nonfactorizable W-exchange amplitude as the weakest link. My stress-test sharpens this: the decisive object is not only the truncation of higher poles but the reliability of the 1S-pole contribution, which provides about 75% of the total PC amplitude (Table VII). The paper's convergence evidence, based on the 2S and 2P contributions being a few percent of the 1S and 1P terms, does not control the dominant term itself. Table VIII exposes serious model dependence: for Ξ_cc++→Ξ_c+π+, the nonfactorizable PC amplitude Bnf is -35.65 here, while three prior pole-model calculations using different wave functions give +13.6 to +18.91, with opposite sign and much smaller magnitude. If the 1S-pole amplitude were closer to those earlier values, the fitted θ and the branching fractions in Eq. (4.2) would shift substantially, and the 'successful reproduction' of R would change correspondingly. The paper does not explain this discrepancy despite including the comparison table. Therefore, before the quoted predictions can be trusted, the authors should verify that the 1S-pole amplitude is stable under wave-function modeling, for example by recomputing with the same harmonic oscillator wave functions used for the pion, and should bound the truncation error by including 3S and 3P poles. These checks are within reach of the authors' own Gaussian expansion code. Unless they are performed, the central claim is conditional on an uncontrolled model input. The minor numerical inconsistency (abstract and summary say 3.2~4.3%, while Eq. (4.2) says 3.0~4.3%) reinforces the need for a careful revision but is not the load-bearing issue.","tokens_in":21705,"tokens_out":17831,"duration_ms":188182,"concrete_test":"Recompute the pole-model amplitudes of Sec. II.B with the same code but replacing the Gaussian-expansion baryon wave functions with the simple harmonic oscillator wave functions of Refs. [28,29] (the same type used for the pion in Eq. 2.11), and re-derive the ratio R(θ), the fitted θ range, and the branching fractions. If the nonfactorizable amplitude Bnf for Ξ_cc++→Ξ_c+π+ changes sign or by more than 50% relative to Table VIII, or if the fitted θ range shifts by more than its current width of about 4°, the central claim is not robust to the dominant model input.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The ratio R and all derived predictions are controlled by the parity-conserving W-exchange amplitude, whose 1S pole term (Table VII: M_PC,1S = -31.20 for Ξ_c+π+ and -39.55 for Ξ_c'+π+) dominates the total PC amplitude (-41.56 and -50.21). The paper argues that higher poles are negligible because the 2S pole is only about 3% of the 1S pole and the 2P poles are about 4% of the 1P poles (Sec. IV). That argument only bounds the next term in the pole sum; it does not bound the continuum or tail of the sum, and it leaves uncontrolled the dominant 1S contribution itself. The model dependence of that contribution is visible in the paper's own Table VIII: for Ξ_cc++→Ξ_c+π+, the nonfactorizable PC amplitude Bnf is -35.65 in this work, whereas three earlier pole-model calculations [9,10,11] obtain +18.91, +13.6, and +16.8 respectively, i.e., opposite sign and roughly half the magnitude. Since Bnf dominates the total B amplitude (Table VIII), the extracted mixing angle θ∈(-18.2°,-14.3°) and the predicted branching fractions in Eq. (4.2) are highly sensitive to the baryon wave-function input. The paper's claim that solving the Schrödinger equation reduces wave-function uncertainties is not substantiated by this comparison; it actually demonstrates strong model dependence. The missing check is convergence of the pole expansion with additional states (3S, 3P, ...) and stability of the 1S pole amplitude under variation of the Gaussian-basis parameters and the pion size parameter R.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper computes the two-body nonleptonic decays Ξ_cc^{++} → Ξ_c^{(′)+} π^+ in a nonrelativistic quark model, using baryon spatial wave functions obtained by solving the Schrödinger equation with a nonrelativistic potential and a Gaussian expansion method. The weak amplitudes include the factorizable T and C′ diagrams and the nonfactorizable W-exchange diagram treated in a pole model with 1S/2S and 1P/2P intermediate Ξ_cc^+ states. With the Ξ_c−Ξ_c′ mixing angle θ taken in the range (−18.2°, −14.3°), the ratio R = B[Ξ_cc^{++}→Ξ_c^{′+}π^+]/B[Ξ_cc^{++}→Ξ_c^+π^+] is matched to the LHCb value, and the branching fractions and asymmetry parameters are then quoted. The paper also compares its amplitudes with earlier pole-model, CCQM, and LCSR results.","tokens_in":22050,"tokens_out":4951,"duration_ms":51445,"significance":"The calculation is detailed and internally consistent, and the use of Schrödinger-equation wave functions supported by baryon spectroscopy is a methodological strength. If the calculation were robust, the paper would provide a simultaneous extraction of a large negative Ξ_c−Ξ_c′ mixing angle and testable predictions for absolute branching fractions and asymmetry parameters. However, the central 'reproduction' of R is a parameter fit in θ, and the dominant nonfactorizable PC amplitude disagrees in sign and magnitude with earlier pole-model calculations; no systematic uncertainty is propagated from the model inputs. The significance is therefore conditional on additional checks and a reformulated interpretation of the fit.","major_comments":[{"comment":"The ratio R is used as input to fix the mixing angle θ, so the statement that the model 'successfully reproduce[s]' R is circular. Since θ ∈ (−18.2°, −14.3°) is determined by requiring R = 1.41 ± 0.20, the agreement is by construction. The absolute branching fractions and asymmetry parameters should be presented as conditional predictions at the fitted θ, and the theoretical uncertainty in θ from all model inputs should be propagated into the quoted ranges. As written, the only source of the ranges in Eq. (4.2) is the experimental 1σ band on R.","section":"§IV, Fig. 4 and Eq. (4.2)"},{"comment":"The PC nonfactorizable amplitude is dominated by the Ξ_cc^+(1S) pole (e.g., −31.20 versus a total of −41.56 for Ξ_cc^{++}→Ξ_c^+π^+ in Table VII), so the reliability of the central results rests on that single term. The convergence argument in Sec. IV bounds only the next pole (2S ≈ 3% of 1S; 2P ≈ 4% of 1P); it does not bound the continuum or higher excitations. More importantly, Table VIII shows that the nonfactorizable Bnf for Ξ_cc^{++}→Ξ_c^+π^+ is −35.65 in this work, whereas Refs. [9], [10], and [11] obtain +18.91, +13.6, and +16.8, respectively—opposite sign and roughly half the magnitude. The claim that solving the Schrödinger equation 'reduces uncertainties' is not supported by this comparison; it indicates strong model dependence. Please add a stability test of the 1S pole amplitude under variation of the Gaussian-basis parameters and the pion size R, and include further intermediate states (3S, 3P) or a completeness estimate.","section":"§II.B, Table VII and Table VIII"},{"comment":"No systematic uncertainty is propagated from the nonrelativistic potential parameters, the constituent quark masses, fπ, the pion size R, or the pole-model truncation. The ranges quoted in Eq. (4.2) and for α reflect only the experimental θ band. Please provide an uncertainty budget, at minimum by varying the potential parameters in Table IV and R = 0.28 GeV within reasonable ranges, and by checking sensitivity to the Gaussian-basis expansion parameters (r_min, r_max, n_max).","section":"§IV, Table IV and Eq. (4.2)"}],"minor_comments":[{"comment":"The branching fraction for Ξ_cc^{++}→Ξ_c^+π^+ is quoted as (3.0~4.3)% in the body text, but the abstract and summary quote (3.2~4.3)%; please reconcile these numbers.","section":"§IV, Eq. (4.2)"},{"comment":"The columns Afac, Anf, Bfac, Bnf, B, and α are not defined in the table caption or in the text; in particular, the column labeled 'B' mixes the B amplitude with the branching-fraction value, and the label should be clarified.","section":"Table VIII"},{"comment":"There is a typo in 'nonrelativisitc Hamiltonian' near Eq. (3.3); it should read 'nonrelativistic Hamiltonian'.","section":"§III"},{"comment":"The pion size parameter R = 0.28 GeV is taken from Refs. [28,29] without discussing its uncertainty; given that R enters all spatial convolutions, its variation should at least be listed among the model inputs to be varied.","section":"§II.A, Eq. (2.11)"}],"recommendation":"major_revision","confidential_remarks":"The paper is essentially a parameter extraction of the Ξ_c−Ξ_c′ mixing angle from R, not an independent prediction of R; the title and abstract overstate the result. The sign discrepancy of the dominant W-exchange amplitude relative to Refs. [9–11] is a serious concern that should be resolved or explicitly discussed before publication. The requested convergence and stability checks are feasible within the manuscript's scope, so I do not recommend rejection, but the current version is not ready for acceptance."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: the genuinely new thing here is the wave-function input—solving the Schrödinger equation with a nonrelativistic potential instead of using simple Gaussian shapes—and the paper produces new, concrete outputs: branching fractions around 3–6% and asymmetry parameters near −0.8 and −0.6. Those numbers are worth having on the table. But the central claim that the model “reproduces” the LHCb ratio is really a fit: the mixing angle θ is tuned to land on the measured R, and the dominant nonfactorizable amplitude that drives the fit disagrees with earlier pole-model calculations in both sign and magnitude. The paper deserves a serious referee, but it should be read as a model-dependent estimate, not a robust prediction.\n\nWhat the paper does well: the amplitude decomposition is detailed and internally consistent, with explicit spin-flavor matrix elements, tables of pole contributions, and a comparison against prior pole-model, CCQM, and LCSR results. The spectroscopy side is also real work—the potential-model masses are compared to experiment and other quark-model predictions. The abstract and summary state the new numerical predictions clearly, and the paper does not hide the fact that independent lattice and QCD sum-rule analyses prefer a small mixing angle.\n\nThe soft spots are significant. First, the fit-to-data point: after θ is chosen to reproduce R, reporting that agreement as a success is circular. Second, no systematic uncertainties are propagated from the potential parameters, quark masses, pion size parameter, or the pole-model truncation. Third, there is an internal inconsistency in the branching fraction range: the abstract and summary say 3.2–4.3% while Eq. (4.2) says 3.0–4.3%. That needs fixing. Fourth, and most important: Table VIII shows that for Ξ_cc^{++}→Ξ_c^+π^+ the nonfactorizable PC amplitude Bnf is −35.65 in this work, whereas Refs. [9], [10], and [11] get +18.91, +13.6, and +16.8—opposite sign and roughly half the magnitude. The paper argues that higher poles are negligible because the 2S pole is only a few percent of the 1S pole, but that only bounds the next term in the pole sum. It does not control the continuum, nor does it stabilize the dominant 1S contribution itself, which is exactly where the model dependence sits. The claim that solving the Schrödinger equation “reduces uncertainties from baryon wave function choices” is not supported by that comparison; it demonstrates the opposite.\n\nSo who is this for? Hadron phenomenologists working on doubly charmed baryon decays and Ξ_c–Ξ_c′ mixing. They will want to see these numbers and will want the sign discrepancy understood. For a referee, the calculation deserves engagement, not a desk rejection. The path to acceptance is straightforward: propagate uncertainties, check the 3.0/3.2 inconsistency, add a few more poles to test convergence, and reframe the fit honestly. As it stands, I would take the predictions seriously but not as a determination of the mixing angle.","headline":"A legitimate quark-model calculation with new wave-function input and concrete, testable numbers—but the headline agreement with LHCb comes from fitting the mixing angle, and the dominant nonfactorizable amplitude changes sign relative to earlier pole-model results, so the predictions are conditional on the model in a way the paper does not face squarely.","tokens_in":22591,"tokens_out":2618,"would_cite":false,"duration_ms":33273,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["12.39.Jh","13.30.-a","14.20.Lq"],"model":"deepseek-v4-flash","headline":"By combining $\\Xi_c$--$\\Xi_c^\\prime$ mixing with pole-model $W$-exchange amplitudes computed from Schrödinger wave functions, this paper reproduces the LHCb ratio $R=1.41$ and fixes the mixing angle to $\\theta\\in(-18.2^\\circ,-14.3^\\circ)$.","keywords":["doubly charmed baryons","nonleptonic decays","Xi_c-Xi_c' mixing","nonrelativistic quark model","pole model","W-exchange diagram","branching fraction","asymmetry parameter"],"falsifier":"Measure the absolute branching fraction $\\mathcal{B}[\\Xi_{cc}^{++}\\to\\Xi_c^{+}\\pi^+]$ with the quoted lifetime: the allowed mixing window predicts $(3.2\\sim4.3)\\%$, so a value outside this range—or an asymmetry parameter $\\alpha$ far from $-0.80$—would rule out the combined mixing-plus-pole-model explanation.","tokens_in":21482,"feed_emoji":"⚡️","tokens_out":10583,"duration_ms":137180,"temperature":0.7,"pith_summary":"Doubly charmed baryon decays offer a direct test of how nonfactorizable weak amplitudes behave in QCD. The paper tries to show that the measured ratio $R=1.41$ — which factorizable diagrams alone cannot explain — follows naturally when $\\Xi_c$--$\\Xi_c^\\prime$ mixing is combined with $W$-exchange contributions computed through a pole model in a nonrelativistic quark model. If the calculation is right, the same physical mixing angle $\\theta\\in(-18.2^\\circ,-14.3^\\circ)$ fixes absolute branching fractions at the percent level and predicts negative decay-asymmetry parameters, making the scheme testable with the upcoming data.","feed_headline":"A mixing angle reproduces LHCb's 1.41 decay ratio","feed_subtitle":"Pole-model W-exchange plus mixing predicts few-percent branching fractions and negative asymmetries.","key_machinery":"The machinery has two connected parts. First, the physical states $\\Xi_c$ and $\\Xi_c^\\prime$ are written as a rotation of the $\\bar{3}$ and $6$ flavor-spin representations: $|\\Xi_c\\rangle=\\cos\\theta|\\Xi_c^{\\bar{3}}\\rangle+\\sin\\theta|\\Xi_c^{6}\\rangle$, $|\\Xi_c^\\prime\\rangle=-\\sin\\theta|\\Xi_c^{\\bar{3}}\\rangle+\\cos\\theta|\\Xi_c^{6}\\rangle$. Second, the nonfactorizable $W$-exchange amplitude is evaluated with a pole model: intermediate $\\Xi_{cc}^+$ states connect the weak $cd\\to su$ transition to the pion-emission vertex, with $1S$ and $2S$ poles carrying the parity-conserving amplitude and $1P_\\rho,1P_\\lambda,2P_\\rho,2P_\\lambda$ poles carrying the parity-violating one. The baryon spatial wave functions are obtained by solving the nonrelativistic three-quark Schrödinger equation with a linear-plus-Coulomb potential plus spin-dependent terms using the Gaussian expansion method, which turns the pole-model overlaps into concrete numbers.","core_discovery":"The discovery this paper argues for is that the measured ratio $R=\\mathcal{B}[\\Xi_{cc}^{++}\\to\\Xi_c^{\\prime+}\\pi^+]\\big/\\mathcal{B}[\\Xi_{cc}^{++}\\to\\Xi_c^{+}\\pi^+]=1.41\\pm0.17\\pm0.10$ is not a puzzle for the standard weak-decay picture: once $\\Xi_c$--$\\Xi_c^\\prime$ mixing is included and the nonfactorizable $W$-exchange amplitudes are computed in a nonrelativistic quark model with wave functions obtained by solving the Schrödinger equation with a realistic potential, the ratio is reproduced for $\\theta\\in(-18.2^\\circ,-14.3^\\circ)$. In that window the model predicts $\\mathcal{B}[\\Xi_{cc}^{++}\\to\\Xi_c^{+}\\pi^+]=(3.2\\sim4.3)\\%$, $\\mathcal{B}[\\Xi_{cc}^{++}\\to\\Xi_c^{\\prime+}\\pi^+]=(4.2\\sim6.0)\\%$, and asymmetry parameters $\\alpha[\\Xi_{cc}^{++}\\to\\Xi_c^{+}\\pi^+]=(-0.80\\sim-0.81)$, $\\alpha[\\Xi_{cc}^{++}\\to\\Xi_c^{\\prime+}\\pi^+]=(-0.61\\sim-0.62)$.","pith_inferences":["If the large negative mixing window survives, it would put pressure on the small positive mixing angles extracted from lattice QCD and QCD sum rules, suggesting one of the two determinations misses a contribution.","Because the asymmetry parameters are nearly $\\theta$-independent, a future measurement of $\\alpha$ could discriminate between this pole-model scheme and earlier pole-model treatments that give different asymmetries.","The same pole truncation could be tested by adding the next radial excitations ($3S$, $3P$) to the intermediate-state sum; a significant shift in $R$ would indicate that the low-lying pole set is not sufficient.","The method of using potential-model Schrödinger wave functions in weak-decay amplitudes could be extended to other doubly heavy baryon modes, where the nonfactorizable terms are similarly important."],"forward_implications":["The measured $R>1$ is reproduced without new dynamics; the fit selects a sizable negative mixing angle $\\theta\\simeq-16.4^\\circ$.","Absolute branching fractions of both $\\Xi_{cc}^{++}\\to\\Xi_c^{+}\\pi^+$ and $\\Xi_{cc}^{++}\\to\\Xi_c^{\\prime+}\\pi^+$ are predicted at the few-percent level, which can be checked once absolute rates are measured.","The asymmetry parameters are predicted to be close to $-0.8$ and $-0.6$ and almost independent of $\\theta$ in the allowed window, so they provide a sharper test than the ratio itself.","If correct, the approach moves the uncertainty from assumed Gaussian wave functions to spectroscopically constrained Schrödinger wave functions, which can be applied to other doubly charmed baryon decays."],"supporting_citations":[{"why":"Supplies the measured ratio $R=1.41\\pm0.17\\pm0.10$ that the paper reproduces.","marker":"[2]"},{"why":"Introduced the $\\Xi_c$--$\\Xi_c^\\prime$ mixing mechanism that can turn the predicted ratio from below 1 to above 1.","marker":"[6]"},{"why":"Prior pole-model analysis of $\\Xi_{cc}\\to\\Xi_c\\pi$ with mixing; supplies the comparison branching fractions the present work supersedes.","marker":"[10]"},{"why":"Prior quark-model pole calculation of these decays; provides comparative amplitudes, branching fractions, and asymmetry parameters.","marker":"[11]"},{"why":"Supplies the nonrelativistic weak Hamiltonians and pole-model formalism used for the T, C', and E diagrams.","marker":"[28]"},{"why":"Supplies the nonrelativistic potential whose Schrödinger solutions yield the baryon spatial wave functions.","marker":"[47]"},{"why":"Gaussian expansion method used to solve the three-quark Schrödinger equation and expand the wave functions.","marker":"[32]"},{"why":"Provides the PDG masses and lifetime of $\\Xi_{cc}^{++}$ used in the numerical evaluation.","marker":"[58]"}],"fun_headline_variants":["Mixing angle reproduces LHCb's 1.41 ratio for Xi_cc++ decays","Nonrelativistic quark model with mixing matches LHCb ratio","Xi_c–Xi_c' mixing reproduces LHCb's 1.41 decay ratio","Quark model plus mixing predicts Xi_cc++ branching fractions","Mixing angle fits LHCb's Xi_cc++ decay ratio"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The calculation assumes that the nonfactorizable $W$-exchange amplitude is fully captured by the pole model with only a small set of low-lying intermediate $\\Xi_{cc}^+$ states, so any sizable contribution from higher states, continuum, or rescattering would move the extracted mixing angle and the predicted rates.","fun_headline_variants_meta":{"raw":{"variants":["Mixing angle reproduces LHCb's 1.41 ratio for Xi_cc++ decays","Nonrelativistic quark model with mixing matches LHCb ratio","Xi_c–Xi_c' mixing reproduces LHCb's 1.41 decay ratio","Quark model plus mixing predicts Xi_cc++ branching fractions","Mixing angle fits LHCb's Xi_cc++ decay ratio"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000541,"raw_usage":{"total_tokens":2705,"prompt_tokens":1170,"completion_tokens":1535,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":786,"completion_tokens_details":{"reasoning_tokens":1431}},"tokens_in":786,"tokens_out":1535,"duration_ms":12343,"temperature":1.0,"reasoning_tokens":1431,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T14:08:09.056996+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the absolute branching fraction $\\mathcal{B}[\\Xi_{cc}^{++}\\to\\Xi_c^{+}\\pi^+]$ with the quoted lifetime: the allowed mixing window predicts $(3.2\\sim4.3)\\%$, so a value outside this range—or an asymmetry parameter $\\alpha$ far from $-0.80$—would rule out the combined mixing-plus-pole-model explanation.","supporting_citations":[{"cited_title":"Aaij et al","cited_arxiv_id":null,"evidence_quote":"Supplies the measured ratio $R=1.41\\pm0.17\\pm0.10$ that the paper reproduces."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Introduced the $\\Xi_c$--$\\Xi_c^\\prime$ mixing mechanism that can turn the predicted ratio from below 1 to above 1."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Prior pole-model analysis of $\\Xi_{cc}\\to\\Xi_c\\pi$ with mixing; supplies the comparison branching fractions the present work supersedes."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Prior quark-model pole calculation of these decays; provides comparative amplitudes, branching fractions, and asymmetry parameters."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the nonrelativistic weak Hamiltonians and pole-model formalism used for the T, C', and E diagrams."},{"cited_title":"Yoshida, E","cited_arxiv_id":null,"evidence_quote":"Supplies the nonrelativistic potential whose Schrödinger solutions yield the baryon spatial wave functions."},{"cited_title":"Hiyama, Y","cited_arxiv_id":null,"evidence_quote":"Gaussian expansion method used to solve the three-quark Schrödinger equation and expand the wave functions."}],"review_version":1}