{"id":"23038636-25f1-4a41-aad7-fda5dd162a4c","arxiv_id":"2505.07150","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"Per-mille-level CP asymmetries are predicted for Λc+→pπ0, Λc+→pη′, Ξc0→Σ0η and Ξc+→Σ+η from long-distance penguin rescattering in the topological diagram approach.","lead":"This paper predicts that CP violation in several charmed baryon decays reaches the per mille level, about ten times larger than usually expected. It uses flavor symmetry and final-state rescattering to connect the CP-violating penguin amplitudes to measured decay rates and asymmetries.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The tree-to-penguin mapping assumes the fitted W-exchange and hairpin amplitudes E1 and Eh are generated entirely by T/C rescattering; if they contain independent short-distance pieces, the extracted FSR parameters and per-mille CP asymmetries are contaminated.","rationale":"The reader's weakest assumption focuses on the universality of the FSR parameters S−, T−, U− and their extraction from the tree-level fit alone. The concern raised here is sharper: the extraction via Eq. (70) implicitly assumes that the fitted tree-level amplitudes E1 and Eh are entirely generated by s-, t-, and u-channel rescattering of the factorizable T and C vertices, even though the TDA treats E1 and Eh as independent topological amplitudes. Since the same S−, T−, U− then determine all penguin coefficients b_i in Eq. (71), any short-distance component in E1 or Eh directly contaminates the penguin amplitudes and hence the predicted CP asymmetries. This is a load-bearing assumption for the specific headline modes with η/η′, because those asymmetries receive sizable contributions from the hairpin coefficient b1 which inherits this contamination. The concern does not by itself overturn the paper: the FSR-only assignment is an explicit modeling choice, and the concrete test described above could show that the predictions are stable under relaxing it. For that reason the reader's CONDITIONAL verdict remains appropriate; the concern reinforces the condition rather than moving the verdict to ACCEPT or REJECT. It is not identical to the reader's universality concern, so agreement is partial rather than full.","tokens_in":41828,"tokens_out":5450,"duration_ms":60979,"concrete_test":"Re-do the extraction without assuming Eq. (70) holds for all five tree amplitudes. Treat E1 and Eh as independent short-distance amplitudes fixed to their fitted values, and solve Eq. (70) only for T and C (equivalently, for F_V±), setting the FSR-generated parts of E1 and Eh to zero; then recompute b_i from Eq. (71) and the four asymmetries in Eq. (76). If ACP(Λ_c→pπ0), ACP(Λ_c→pη′), ACP(Ξ_c^0→Σ^0η) and ACP(Ξ_c^+→Σ^+η) shift by more than their stated errors, the central claim depends on the assumed FSR-only origin of E1/Eh and the conditional verdict is justified; if the asymmetries stay at the per-mille level, the concern is not load-bearing.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The penguin coefficients b_i are not determined by CP data; they are computed from FSR parameters S−, T−, U− and F_V± that are solved from Eq. (70) using the five fitted TDA tree amplitudes in Table II. However, Eq. (70) is derived from Eqs. (65)-(69), where the weak vertex is restricted to the factorizable external W-emission topologies T and C: the text explicitly says “we have dropped nonfactorizable terms such as E1S, E1A, E3 and Eh” after Eq. (65). In the TDA, E1 and Eh are independent topological amplitudes, and the global fit finds them large (|E1|_S ≈ 2.8 and |Eh|_S ≈ 4.3 in units of 10^-2 GF GeV^2, Table II). The exact inversion of Eq. (70) therefore forces S−, T−, U− to reproduce the entire fitted E1 and Eh, attributing to long-distance rescattering what may in reality be short-distance W-exchange or hairpin dynamics. These same S−, T−, U− enter every b_i in Eq. (71), and b1 is the hairpin penguin that drives the η and η′ asymmetries highlighted in Eq. (76). If E1 or Eh has any component not induced by T/C rescattering, the b_i are miscalibrated, and the per-mille CP asymmetries—especially in Λ_c→pη′, Ξ_c^0→Σ^0η and Ξ_c^+→Σ^+η—may be an artifact of the inversion rather than a robust prediction. The quoted errors in Table IV do not include this model-assignment uncertainty.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper studies CP violation in the two-body weak decays of antitriplet charmed baryons within the topological diagrammatic approach (TDA) and its irreducible SU(3) counterpart. After updating the global fit of the five tree-level TDA amplitudes with six new Belle/Belle-II branching-fraction measurements, the authors project the s-, t-, and u-channel final-state rescattering (FSR) diagrams in Fig. 3 onto tree and penguin topologies, introducing five FSR parameters (F_V^±, S_-, T_-, U_-). Equation (70) converts the fitted tree amplitudes into these FSR parameters, and Eq. (71) then determines the penguin coefficients b_i. The main phenomenological results are the CP asymmetries in Eq. (76): per-mille asymmetries in Λ_c→pπ^0, Λ_c→pη′, Ξ_c^0→Σ^0η and Ξ_c^+→Σ^+η, with the last three attributed to the SU(3)-singlet hairpin penguin b_1.","tokens_in":42265,"tokens_out":10764,"duration_ms":103569,"significance":"The predicted per-mille asymmetries are an order of magnitude above naive short-distance expectations and are testable at LHCb and Belle II; if confirmed, they would indicate that long-distance FSR, rather than short-distance penguins, dominates CP violation in these decays. The paper also provides a useful explicit mapping between TDA and IRA coefficients, includes a u-channel contribution and the hairpin topology beyond earlier work, and gives falsifiable predictions in Eq. (76). However, the numerical predictions inherit strong model assumptions, the fit quality is poor, and there is an internal sign inconsistency, so the significance is conditional on the robustness checks described below.","major_comments":[{"comment":"The extraction of the FSR parameters from the fitted tree amplitudes is an inversion of a model, not a determination from independent data. In Eq. (70) the five fitted tree amplitudes (T, C, C′, E1, Eh) of Table II are used to solve for the five FSR parameters (F_V^+, F_V^-, S_-, T_-, U_-). The text after Eq. (65) explicitly drops the nonfactorizable terms E1S, E1A, E3 and Eh from the weak vertex, so the procedure assumes that the entire fitted W-exchange amplitude E1 and hairpin amplitude Eh are generated by rescattering of T and C. Since Table II gives |E1|_S = 2.79 and |Eh|_S = 4.30 (in units of 10^-2 G_F GeV^2), any short-distance component of E1 or Eh is forced into S_-, T_- and U_- by construction. These parameters enter every b_i in Eq. (71), and b1 drives the η and η′ asymmetries highlighted in Eq. (76). The errors in Table IV do not include this assignment uncertainty. Please provide a robustness test, for example allowing an independent short-distance component in E1/Eh, and show that the per-mille predictions for Λ_c→pη′, Ξ_c^0→Σ^0η and Ξ_c^+→Σ^+η are stable under that relaxation.","section":"Section III.B.2, Eqs. (70)-(71), Table II"},{"comment":"The quality of the underlying global fits is poor, and the central predictions are made only for the better-fitting data subset. Table VI reports χ²/dof = 3.27 in Case I and 3.73-3.75 in Case II, so the tree-level TDA does not describe the data within errors. All CP asymmetries in Eq. (76) are taken from Case I, which excludes the recent Belle measurements of Ξ_c^0→Ξ^0π^0, Ξ^0η and Ξ^0η′ [50]; including these data makes the fit worse. The paper does not report the Case-II CP observables or any stability analysis. Because the penguin coefficients in Eq. (71) are constructed from the fitted tree amplitudes, the poor fit quality and the data-selection dependence must be quantified before the per-mille claim can be evaluated.","section":"Section IV.B, Table VI, Eq. (76)"},{"comment":"The u-channel contribution is retained through the assumption of tensor-coupling dominance with ρ+ = -21, but this assumption is not validated at the level needed for the central predictions. The value ρ+ = -21 is taken from light-cone QCD sum rules, and the only dynamical evidence quoted for the dominance is a single-mode estimate |b/a| ≈ 1.06 for Λ_c^+→pφ (Ref. [47], a private communication). Equation (71) shows that b2, b3 and b4 contain (2ρ++1)U_- and (10ρ++1)U_-; with ρ+ = -21 the small fitted U_- is enhanced by an order of magnitude. The uncertainties of ρ+ and of r_- = 2.5 are not propagated into the errors of Table IV. Please justify the dominance for all channels or propagate the uncertainties; as it stands the error bars in Eq. (76) are likely underestimated.","section":"Section III.B.2, after Eq. (55); Eq. (71); Tables II and IV"},{"comment":"There is an internal sign inconsistency in the headline prediction for Λ_c^+→pη′. Equation (76) quotes A_CP(Λ_c^+→pη′) = (1.4±0.1)×10^-3, while Table IV gives −14.40±1.26 in units of 10^-4, i.e., −(1.44±0.13)×10^-3, with the negative sign. The abstract repeats the positive sign, so this is not an isolated typo. Please correct the sign and verify the corresponding entries in Tables VIII-X and the discussion.","section":"Eq. (76) and Table IV"},{"comment":"The flavor projection of the rescattering amplitudes depends on the choice that the SU(3)-singlet η1 is removed from the intermediate pseudoscalar loop but kept in the emitted meson (Eqs. (58)-(62)). This is a model assumption motivated by the axial anomaly, but it directly affects the hairpin coefficient b1 in Eq. (71), which the paper identifies as the source of the large η and η′ asymmetries. The sensitivity of the predictions to this choice should be tested, for example by repeating the projection with η1 included in P′ or by using a nonet closure relation. Without such a test, the highlighted per-mille asymmetries in the three η/η′ modes are not robust.","section":"Section III.B.2, Eqs. (58)-(62)"}],"minor_comments":[{"comment":"The phrase 'the flavor structure of the these diagrams' contains a duplicated article; the same typo appears in the introduction.","section":"Abstract and Section I"},{"comment":"'In terms of the the decomposition of 3⊗ ¯3⊗ 3' should read 'In terms of the decomposition of 3⊗ ¯3⊗ 3'.","section":"Section II.A, after Eq. (11)"},{"comment":"The sentence 'They are ready extracted from Eq. (70)' should be 'readily extracted', and Ref. [47] has 'privite communication' for 'private communication'.","section":"Section III.B.2, after Eq. (70); Ref. [47]"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is within the journal's scope, and the SU(3)/TDA machinery is competently presented. My main concern for the editor is that the per-mille predictions in Eq. (76) are not robust to the model-inversion step connecting tree-level fits to penguin coefficients, and the paper contains a sign inconsistency in one of its four headline predictions. The poor χ²/dof values reinforce the need for a stability analysis before publication."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things to know. First, this is the most complete attempt to date to get per-mille-level CP asymmetries in charmed baryon decays from long-distance rescattering, adding a u-channel term and a hairpin contribution for η/η′ that were not in He-Liu or the authors' earlier fits. Second, the headline predictions depend on an inversion that the paper does not defend head-on: Eq. (70) uses the fitted W-exchange and hairpin amplitudes E1 and Eh to solve for the rescattering parameters S−, T−, U−, as if E1 and Eh were entirely generated by rescattering of the external-emission topologies T and C. If those amplitudes contain any short-distance piece—and in the TDA they are independent tree-level amplitudes—the penguin coefficients b_i are miscalibrated and the per-mille asymmetries in Λc→pη′, Ξc0→Σ0η, and Ξc+→Σ+η could be an artifact.\n\nCredit where it's due. The flavor decomposition is careful; the TDA and IRA are shown to be equivalent; six new Belle/Belle-II measurements are incorporated; and the comparisons with He-Liu and Jia et al. are explicit and fair. The authors also state their assumptions (tensor-dominance for the u-channel, dropping nonfactorizable terms after Eq. (65)) rather than burying them.\n\nThe soft spots are real but not disqualifying. The global fit has χ²/dof ≈ 3.3–3.7, which is poor; the central CP predictions are shown only for Case I, which excludes the newest Belle data; and the fixed inputs ρ+ = −21 and r− = 2.5 come with uncertainties that never make it into the quoted errors on A_CP. The model-assignment problem above is the biggest issue, and it is addressable: the authors could estimate the short-distance contributions to E1/Eh, or show how the predictions shift when the inversion is relaxed.\n\nWho should read this? Charm-hadron phenomenologists and the LHCb/Belle II theory community. The predictions are testable, and even if the framework needs repair, the paper identifies where the interesting CP asymmetries are likely to show up.\n\nMy recommendation: send it to peer review. A good referee can push for a cleaner treatment of the inversion and for Case II results; the core ideas deserve a serious round.","headline":"Per-mille CP asymmetries in charmed baryons from rescattering—worth engaging, but the tree-to-penguin inversion is the load-bearing assumption that needs scrutiny.","tokens_in":42809,"tokens_out":3531,"would_cite":true,"duration_ms":35428,"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":"Charm-baryon CP violation can reach the per-mille level through final-state rescattering.","keywords":["CP violation","charmed baryons","topological diagrammatic approach","SU(3) flavor symmetry","final-state rescattering","penguin topology","hairpin diagram","per-mille CP asymmetry"],"falsifier":"Measure $A_{CP}(\\Lambda_c^+\\to p\\eta')$ and $A_{CP}(\\Xi_c^0\\to\\Sigma^0\\eta)$ with a precision of a few times $10^{-4}$; the paper predicts $+(1.4\\pm0.1)\\times10^{-3}$ and $+(1.2\\pm0.2)\\times10^{-3}$, so results consistent with zero at that precision would falsify the per-mille enhancement.","tokens_in":41564,"feed_emoji":"🔄","tokens_out":9447,"duration_ms":83195,"temperature":0.7,"pith_summary":"The paper argues that CP violation in two-body hadronic decays of antitriplet charmed baryons can be much larger than the naive $10^{-4}$ expectation, because long-distance penguin amplitudes are generated by final-state rescattering. Working with the topological diagrammatic approach and the irreducible SU(3) approach, it projects $s$-, $t$- and $u$-channel rescattering diagrams onto penguin and tree topologies, introducing one overall parameter per channel ($S_-$, $T_-$, $U_-$). A global fit to branching fractions and Lee-Yang parameters fixes the tree-level amplitudes and the rescattering strengths, which then determine the four penguin coefficients $\\tilde b_{1,2,3,4}$. The paper predicts per-mille CP asymmetries in four singly Cabibbo-suppressed modes, with the $\\eta,\\eta'$ modes receiving sizable contributions from the SU(3)-flavor-singlet hairpin diagram.","feed_headline":"Per-mille CP violation predicted in four charmed-baryon decays","feed_subtitle":"Final-state rescattering turns tiny CKM phases into ~10^-3 asymmetries in pη′, pπ0, and two Ξc eta modes.","key_machinery":"The load-bearing object is the decomposition of final-state rescattering into topological amplitudes. In the topological diagrammatic approach (TDA), decay amplitudes are organized by quark-flow diagrams with five independent tree amplitudes $\\tilde T,\\tilde C,\\tilde C',\\tilde E_1,\\tilde E_h$ and four penguin coefficients $\\tilde b_1,\\dots,\\tilde b_4$; the irreducible SU(3) approach (IRA) supplies the equivalent tensor invariants. The paper assigns one overall parameter to each rescattering channel, $S_-$ for $s$-channel, $T_-$ for $t$-channel and $U_-$ for $u$-channel, and relates all penguin coefficients to the tree amplitudes through Eqs. (70) and (71). The hairpin coefficient $\\tilde b_1$ carries the SU(3)-singlet component of the emitted pseudoscalar and is what drives the enhanced asymmetries in the $\\eta$ and $\\eta'$ modes.","core_discovery":"The central claim is that a set of charmed-baryon decay channels with hadronic final states should exhibit CP asymmetries of order $10^{-3}$, roughly an order of magnitude above the standard short-distance estimate, because the penguin topology receives large long-distance contributions from final-state rescattering. The paper establishes this by decomposing the $s$-, $t$- and $u$-channel rescattering diagrams at the hadron level and showing, through their flavor structure, that they project onto the same topological amplitudes as the penguin diagrams. After fixing the tree-level amplitudes from a global fit and extracting the rescattering strengths $S_-$, $T_-$, $U_-$, the penguin coefficients are obtained and the CP observables computed. Independent TDA and IRA fits give the same predictions within errors; the four modes with per-mille asymmetry are $\\Lambda_c^+\\to p\\pi^0$ with $-(0.8\\pm0.3)\\times10^{-3}$, $\\Lambda_c^+\\to p\\eta'$ with $(1.4\\pm0.1)\\times10^{-3}$, $\\Xi_c^0\\to\\Sigma^0\\eta$ and $\\Xi_c^+\\to\\Sigma^+\\eta$, each with $(1.2\\pm0.2)\\times10^{-3}$.","pith_inferences":["If the per-mille asymmetries are confirmed, the same machinery should produce measurable CP asymmetries in other singly Cabibbo-suppressed channels listed in the paper's tables, so a multi-channel measurement would test the mechanism more stringently than any single mode.","A sharper test than rate asymmetries alone would be a measurement of the strong phase difference $\\delta_P-\\delta_S$ in $\\Lambda_c^+\\to p\\eta'$, because the size and even the sign of the predicted $A_{CP}$ depend on that phase.","One could stress-test the universality assumption by allowing $S_-$, $T_-$, $U_-$ to depend on the quantum numbers of the intermediate resonances; if future data demanded such variation, the pattern of asymmetries across the four predicted modes would change."],"forward_implications":["The four modes listed in Eq. (76) become specific targets for CP-violation searches; measuring their asymmetries at the $10^{-4}$ level would confirm or exclude the per-mille enhancement.","The updated global fits including six new $\\Xi_c^+$ measurements sharpen the predicted branching fractions, Lee-Yang parameters and phase shifts, giving concrete numbers that future data can test.","The U-spin relations such as $A_{CP}(\\Lambda_c^+\\to n\\pi^+)=-A_{CP}(\\Xi_c^+\\to\\Xi^0K^+)$ are predicted to hold in sign, which provides a cross-check of the SU(3) decomposition.","The u-channel contribution is found to be non-negligible because the small $U_-$ is compensated by the large tensor-coupling ratio $\\rho_+$; omitting the u channel, as earlier treatments did, misses part of the penguin amplitude."],"supporting_citations":[{"why":"Supplies the final-state rescattering parameterization with S_- and T_- and the s- and t-channel amplitudes that this work extends with the u channel and the hairpin term.","marker":"[30]"},{"why":"Provides the TDA decay amplitudes and the original global-fit framework used for the tree-level parameters.","marker":"[20]"},{"why":"Provides the updated tree-level fit, the resolution of sign ambiguities in beta and gamma, and the input data before the recent six measurements.","marker":"[22]"},{"why":"Provides the first measurements of beta and gamma for Lambda_c -> Lambda pi, Lambda K used to fix phase shifts and select the S- and P-wave solutions.","marker":"[23]"},{"why":"Provides three new branching-fraction measurements of Xi_c^+ decays added to the global fit.","marker":"[24]"},{"why":"Provides three additional new branching-fraction measurements of singly Cabibbo-suppressed Xi_c^+ decays used as fit inputs.","marker":"[25]"},{"why":"Establishes the observed CP asymmetry difference in charmed meson decays that motivates the large long-distance penguin ansatz.","marker":"[34]"},{"why":"Establishes that the long-distance penguin from final-state rescattering is comparable to the W-exchange topology, the basis for relating penguin coefficients to tree amplitudes.","marker":"[35]"},{"why":"Supplies the numerical vector and tensor baryon couplings used to justify the u-channel tensor dominance.","marker":"[45]"}],"fun_headline_variants":["Rescattering lifts charmed baryon CP violation to 10^-3","Four charmed-baryon modes predicted with per-mille CP asymmetry","Charmed baryon CP asymmetry boosted to per-mille by rescattering","Tiny CKM phases amplified to 10^-3 in charmed baryon decays","Long-distance penguins yield per-mille CP asymmetries in charmed baryons"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The per-mille predictions rest on the assumption that one overall parameter per rescattering channel ($S_-$, $T_-$, $U_-$) is universal across all decay modes and can be extracted from the CP-conserving tree-level fit alone, with the u channel dominated by the tensor coupling of the exchanged vector meson.","fun_headline_variants_meta":{"raw":{"variants":["Rescattering lifts charmed baryon CP violation to 10^-3","Four charmed-baryon modes predicted with per-mille CP asymmetry","Charmed baryon CP asymmetry boosted to per-mille by rescattering","Tiny CKM phases amplified to 10^-3 in charmed baryon decays","Long-distance penguins yield per-mille CP asymmetries in charmed baryons"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001812,"raw_usage":{"total_tokens":7182,"prompt_tokens":1046,"completion_tokens":6136,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":662,"completion_tokens_details":{"reasoning_tokens":6034}},"tokens_in":662,"tokens_out":6136,"duration_ms":39422,"temperature":1.0,"reasoning_tokens":6034,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T22:23:35.234617+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure $A_{CP}(\\Lambda_c^+\\to p\\eta')$ and $A_{CP}(\\Xi_c^0\\to\\Sigma^0\\eta)$ with a precision of a few times $10^{-4}$; the paper predicts $+(1.4\\pm0.1)\\times10^{-3}$ and $+(1.2\\pm0.2)\\times10^{-3}$, so results consistent with zero at that precision would falsify the per-mille enhancement.","supporting_citations":[{"cited_title":"A global analysis of two-body D to VP decays within the framework of flavor symmetry","cited_arxiv_id":"1604.03761","evidence_quote":"Supplies the final-state rescattering parameterization with S_- and T_- and the s- and t-channel amplitudes that this work extends with the u channel and the hairpin term."},{"cited_title":"Quark diagram analysis of charmed baryon decays,","cited_arxiv_id":null,"evidence_quote":"Provides the TDA decay amplitudes and the original global-fit framework used for the tree-level parameters."},{"cited_title":"Two-body charmed baryon decays involving decuplet baryon in the quark-diagram scheme","cited_arxiv_id":"2006.15291","evidence_quote":"Provides three new branching-fraction measurements of Xi_c^+ decays added to the global fit."},{"cited_title":"Search for direct CP violation in D0 -> h- h+ modes using semileptonic B decays","cited_arxiv_id":"1303.2614","evidence_quote":"Supplies the numerical vector and tensor baryon couplings used to justify the u-channel tensor dominance."}],"review_version":1}