{"id":"1e8dfa32-78be-4cad-b022-263e7f94cd23","arxiv_id":"2411.15857","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"QCD sum rules are used to obtain all ten Lambda_c to p form factors, which then yield branching fractions and angular observables for Lambda_c and Xi_c rare decays, plus an exploratory new physics scan.","lead":"Researchers derived a complete set of QCD sum rule form factors for the rare charm baryon decay Lambda_c to a proton plus a lepton pair, and used them to predict branching fractions and angular observables, including estimates for Xi_c decays. A generalist might care because rare charm decays are a clean but unexplored place to look for new particles, and this paper maps out what experiments should see under the Standard Model and under new physics scenarios.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The form-factor derivation rests on an unshown QCDSR Borel-window/OPE-convergence check: Section 3.1 states the 40% pole and <30% <qqbar>^2 criteria, but only f1 is displayed in Fig. 1, with no RPC curves or Borel-window values for the ten form factors.","rationale":"The central claim is that the ten QCD sum-rule form factors provide a complete and reliable hadronic description of Lambda_c -> p, so every subsequent branching fraction and angular observable inherits the validity of Section 3.1. The paper explicitly states the two standard reliability criteria for the truncated OPE, but never demonstrates them for the full set of form factors. This is not a stylistic omission: the same framework is shown by the authors themselves to fail for Lambda_b -> n, where the <qqbar>^2 condensate dominates (Fig. 1), and the only counter-evidence offered for Lambda_c is a single curve for f1. The Borel parameters are reduced by Eq. (16) to one free variable, yet the chosen window, the RPC values, and the per-form-factor condensate breakdown are not quoted. Without these, a reader cannot verify that the q^2 points used in the z-series fit come from a region where quark-hadron duality and OPE truncation are controlled. The g2(0) discrepancy with lattice QCD in Table 1 strengthens the concern: either the lattice and sum-rule conventions differ, or one of the sum rules fails the stated criteria, and the paper does not provide enough information to decide. I would keep the reader's CONDITIONAL verdict: the calculation is coherent and the comparison table is useful, but the central form-factor claim should not be accepted as final until the Borel-window and OPE-convergence evidence is supplied for all ten form factors.","tokens_in":18571,"tokens_out":13941,"duration_ms":134787,"concrete_test":"Independently implement the three-point OPE spectral densities for the ten form-factor Lorentz structures using the inputs in Eq. (15), reproduce Table 1, and plot RPC_Lambda_c, RPC_p, and R_{<qqbar>^2} versus tau_2^2 at q^2=0 and q^2=-0.4 GeV^2 for each form factor. Accept the QCDSR input only if an acceptable Borel window, ideally a common window, satisfies RPC>40% and R_{<qqbar>^2}<30% for all ten; if any form factor (especially f3, g2, or gT1) fails, the z-series fit is not justified and the form-factor set must be revised.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section 3.1 defines the pole-contribution ratios RPC_Lambda_c and RPC_p in Eqs. (17)-(18) and the OPE-convergence criterion R_{<qqbar>^2}<30%, then proceeds directly to Table 1 without showing the Borel window or these curves for any form factor. Figure 1 displays only f1 for the <qqbar>^2 fraction; the text's only justification that the Lambda_c channel is safe is the contrast with Lambda_b -> n, where the same method is acknowledged to fail (Fig. 1 and Ref. [81]). Since the z-series input points are taken from q^2 in [-0.4, 0.4] GeV^2, convergence must hold at every fitted point, not just at q^2=0, and for all ten Lorentz structures. A symptom of the missing check is Table 1: g2(0) = -0.25 +/- 0.02 versus LQCD 0.003 +/- 0.052, a disagreement not mentioned in the paper's exception list; without per-form-factor RPC/condensate plots one cannot tell whether this is a convention difference or a failed sum rule. If even one form factor fails the stated criteria, the complete-set claim and every downstream branching fraction and NP observable inherit an uncontrolled systematic error.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper derives, within the QCD sum-rule framework, a complete set of ten form factors for the transition Λc → p (f1,f2,f3,g1,g2,g3,fT1,fT2,gT1,gT2). The form factors are computed at q^2 = 0 and in a small spacelike interval q^2 ∈ [−0.4,0.4] GeV^2, then extrapolated to the full physical region using a z-series parametrization. These form factors are used to compute branching fractions for Λc → p e+e− and Λc → p μ+μ−, both with and without long-distance vector-resonance contributions, as well as angular observables (AFB and FL). Flavor-symmetry relations are used to estimate branching fractions for Ξc decays. The paper also studies the sensitivity of the observables to new physics in the Wilson coefficients C7 and C10.","tokens_in":21,"tokens_out":4087,"duration_ms":99954,"significance":"If the form-factor set is correct, this would be a useful ingredient for charm-baryon rare-decay phenomenology, complementing lattice QCD and quark-model results. The paper has several positive features: the QCD sum-rule framework is standard, the comparison with existing LQCD and RQM predictions is informative, and the z-series formalism is appropriate in spirit. The no-resonance branching fractions are genuine predictions and correctly respect the LHCb upper limit on Λc → pμ+μ−. The angular observables proposed as new-physics diagnostics, especially the vanishing SM AFB, are well motivated. However, the central claim of a complete and reliable form-factor set is not fully supported by the evidence presented: the Borel-window/OPE-convergence checks are not shown for most form factors, one form factor disagrees sharply with lattice QCD without being discussed, and the z-series fits have very large slope uncertainties. The resonance-included branching fractions are also normalized to the same data they are meant to predict, which weakens their significance. These issues are reparable, but they need to be addressed before the paper can be accepted.","major_comments":[{"comment":"The paper states two criteria for choosing the Borel window: the pole contribution must exceed 40% and the ⟨qq̄⟩^2 condensate contribution must remain below 30%. However, only the second criterion is displayed, and only for the single form factor f1. No RPC curves or Borel-window values are shown for the other nine form factors, and Fig. 1 shows only the ⟨qq̄⟩^2 fraction for f1. Since the fits in Table 2 use points in q^2 ∈ [−0.4,0.4] GeV^2, convergence must hold at each fitted point and for each Lorentz structure. Without these checks, the claim of a complete and reliable set of form factors is unsupported.","section":"Sec. 3.1, Eqs. (17)–(18) and Fig. 1"},{"comment":"The value g2(0) = −0.25 ± 0.02 disagrees with lattice QCD, g2(0) = 0.003 ± 0.052 [46], by approximately 5σ, yet the paper's list of form factors with reasonable agreement (f3, fT1, gT1) does not include g2. This discrepancy is either a sign/convention error or a sign that the sum rule fails for the g2 structure. The authors need to investigate and either correct the calculation or explain the discrepancy, because g2 enters the helicity amplitudes in Eq. (29) and affects the branching fractions and FL.","section":"Table 1"},{"comment":"The z-series fits have extremely large slope uncertainties (for example, f1: a1 = −0.36 ± 4.44; gT1: a1 = −23.25 ± 16.28), despite the fits being performed over the narrow interval [−0.4,0.4] GeV^2. Using these fits to extrapolate to q^2 ≈ 1.8 GeV^2, the entire physical range, is uncontrolled. The paper should either justify that a single slope parameter suffices, add constraints from the endpoint behavior, or provide error bands that faithfully propagate the slope uncertainties into the branching fractions.","section":"Sec. 3.1, Eq. (19) and Table 2"},{"comment":"The resonance couplings aω and aφ are determined from Eq. (26), which equates the contribution from C9^R alone to the measured Br(Λc → pV)Br(V → μ+μ−). Consequently, the resonance-included branching fraction for Λc → pμ+μ− in Table 3 is essentially the experimental input reflected back and is not an independent prediction. The agreement with the LHCb limit in Fig. 3 is therefore not a test of the calculation. The paper should clearly separate genuine predictions (no-resonance rates and off-resonance bins) from input-normalized estimates, and the new-physics analysis in Sec. 3.3, which uses C9 = C9^R, should be framed accordingly.","section":"Sec. 3.2, Eqs. (25)–(28) and Table 3"}],"minor_comments":[{"comment":"There are several typographical and grammatical issues, e.g., \"exhibit an heavily dependence\" in the Introduction and \"the the four-vector\" near Eq. (1). The abstract and text should be carefully proofread.","section":"Abstract and Introduction"},{"comment":"The caption writes \"the √q2 region\" in a way that is hard to read; it should say \"the region of sqrt(q^2) excluding ±40 MeV intervals around mω and mφ\" for clarity.","section":"Fig. 3 caption"},{"comment":"The text says the symbol points in Fig. 2 denote the fitted points, but the figure appears to show only central curves; the caption should clarify what the points and error bands represent, especially given the large a1 uncertainties.","section":"Fig. 2 and Table 2"},{"comment":"The Xi_c predictions in Table 3 rely on U-spin symmetry and on adopting aω from Λc → p; this should be stated as an order-of-magnitude estimate rather than a precise prediction, and the large systematic uncertainty from the symmetry assumption should be acknowledged in the discussion.","section":"Sec. 3.2, Flavor-symmetry relations"},{"comment":"Ref. [75] is used both as a source of input parameters and as a comparison for LCSR form factors; the text should be explicit about which quantities are taken from which reference to avoid ambiguity.","section":"References"}],"recommendation":"major_revision","confidential_remarks":"The paper addresses a timely topic and contains useful material, but the missing convergence checks and the unaddressed g2 discrepancy are load-bearing for the claim of a complete form-factor set. The resonance-normalization issue is conceptually less severe but should be clarified. I believe these points can be fixed in a revision, provided the authors can demonstrate OPE convergence for all ten form factors and resolve or explain the lattice discrepancy. If the g2 discrepancy cannot be resolved, the claim of a complete and reliable form-factor set would need to be substantially weakened."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is a real calculation, not a toy, but it is being sold as more predictive than it is. The genuinely new piece is the three-point QCDSR evaluation of all ten Lambda_c -> p FCNC form factors at q^2=0, the z-series extrapolation to the physical region, and the rough U-spin relations for Xi_c decays. That is a useful alternative to lattice QCD and the quark models, and the q^2=0 values for f1, g1, f2, g2 line up reasonably with existing LCSR and lattice numbers. The authors are also honest that the same method fails for Lambda_b -> n; the contrast is informative and the formalism itself looks standard.\n\nThe soft spots are serious but not all equal. First, the Borel-window and OPE-convergence criteria in Sec. 3.1 are stated but not shown. The text gives the 40% pole and 30% <qqbar>^2 criteria, yet only f1 is displayed in Fig. 1, and there are no RPC curves or Borel windows for the other nine structures. Given that Table 1 shows g2(0) = -0.25 +/- 0.02 versus lattice 0.003 +/- 0.052, this is not a cosmetic omission; one wants to know whether g2 is a failed sum rule or a convention difference. The stress-test note is right about this.\n\nSecond, the resonance-included branching fractions in Table 3 are calibrated, not predicted. Eq. (26) fixes a_omega and a_phi from measured Br(Lambda_c -> p V) Br(V -> mu+mu-). The resonant part then dominates, so the agreement with other groups in Table 3 mostly means the fit reproduces the input. The paper should say that plainly.\n\nThird, the non-resonant rate is 2.4e-13 for mu+mu-, roughly two orders below the lattice number 4.1e-11 and also below the relativistic quark model's 2.8e-12. The authors attribute the spread to Wilson coefficient choice, but a 100x gap is hard to explain by C9 variation alone, and the z-series slopes in Table 2 carry huge uncertainties (f1 a1 = -0.36 +/- 4.44), so the extrapolated form factors have more slack than the quoted central values suggest.\n\nThere are smaller issues: no numerical comparison with Ref. [42], which did a related QCDSR study of Lambda_c -> p FCNC, and the NP section is over-sold. The rates are resonance-dominated and short-distance physics is far below current sensitivity, so statements that new physics \"may be testified\" in these modes need more careful hedging.\n\nWho gets value: people working on charm FCNC phenomenology who want an independent QCDSR form-factor set and a map of existing approaches. I would cite it as a cross-check, not as a primary input. It deserves a serious referee, but the report should ask for the missing Borel-window plots, an explicit discussion of the lattice discrepancy, and a cleaner separation between calibrated resonance rates and genuine predictions. With those changes it could become a reliable reference.","headline":"A legitimate new QCD sum-rule calculation of the complete Lambda_c -> p form-factor set, but the resonance-dominated rates are calibrated to data, the no-resonance rate is two orders below lattice, and the Borel-window checks are missing for most form factors.","tokens_in":19471,"tokens_out":2870,"would_cite":true,"duration_ms":27460,"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":"This paper derives all ten form factors for the rare Lambda_c -> p l+l- decay from QCD sum rules, turning it into a new-physics test.","keywords":["rare charm baryon decays","Lambda_c -> p l+l-","QCD sum rules","baryonic form factors","flavor-changing neutral currents","angular observables","new physics","Xi_c decays"],"falsifier":"A direct check would be to plot, for each of the ten form factors, the pole-contribution ratio and the relative $\\langle \\bar q q\\rangle^2$ contribution across the Borel window; any form factor violating the stated 40%/30% criteria would break the extraction. An independent lattice QCD computation of $g_2(0)$ would also settle the issue, since the paper's value $-0.25\\pm0.02$ differs sharply from the existing lattice estimate near zero.","tokens_in":18348,"feed_emoji":"⚛️","tokens_out":11462,"duration_ms":93964,"temperature":0.7,"pith_summary":"This paper tries to establish that the rare baryon decay $\\Lambda_c \\to p \\ell^+\\ell^-$ can be described from first principles well enough to act as a new-physics probe. It derives the complete set of ten form factors for the $\\Lambda_c \\to p$ transition in the large-recoil region using QCD sum rules, then extends them to the full kinematic range with a $z$-series parametrization. With these form factors it computes branching fractions for $\\Lambda_c \\to p e^+e^-$ and $\\Lambda_c \\to p \\mu^+\\mu^-$, and for related $\\Xi_c$ modes through flavor-symmetry relations. The key phenomenological payoff is that the lepton forward-backward asymmetry is predicted to be exactly zero in the Standard Model, so any measured nonzero value would indicate new physics, while the fraction of longitudinally polarized dileptons would acquire visible resonance peaks only under new-physics effects.","feed_headline":"Ten form factors make rare Lambda_c decays a new-physics probe","feed_subtitle":"A zero forward-backward asymmetry in the Standard Model makes any measured signal a clean sign of new particles.","key_machinery":"The load-bearing machinery is the three-point QCD sum rule. Two interpolating currents with the quark content of $\\Lambda_c$ and the proton are contracted with a weak transition current, and the resulting correlation function is evaluated both phenomenologically, through hadronic states and decay constants $\\lambda_{\\Lambda_c},\\lambda_p$, and in QCD, through an operator-product expansion truncated at dimension six that includes quark, gluon, mixed, and four-quark condensates. Matching the two representations by quark-hadron duality and a double Borel transform yields the form factors; the extraction is kept only in a Borel window where the ground-state pole contribution exceeds 40% and the highest-dimension condensate stays below 30%. The $z$-series parametrization then carries the ten form factors from the large-recoil region to the full physical $q^2$ range, and helicity amplitudes built from the form factors produce the differential width and the angular observables $A_{FB}$ and $F_L$. A useful internal identity is $f_{T2}(0)=g_{T2}(0)$, which emerges from the sum rules and matches the covariant quark-model result.","core_discovery":"The central claim is that a first-principles QCD-sum-rule calculation yields a complete hadronic description of $\\Lambda_c \\to p$: the ten form factors $f_1,f_2,f_3,f_{T1},f_{T2},g_1,g_2,g_3,g_{T1},g_{T2}$ at $q^2=0$, extrapolated across the physical region by a $z$-series fit. From these the paper predicts the differential and total branching fractions for $\\Lambda_c \\to p e^+e^-$ and $\\Lambda_c \\to p \\mu^+\\mu^-$ with and without long-distance $\\rho,\\omega,\\phi$ resonance contributions, and shows that the no-resonance rate lies below the present experimental upper limit. It also finds $A_{FB}=0$ throughout the physical range in the Standard Model, $F_L=1/3$ at both kinematic endpoints, and uses U-spin relations to estimate $\\Xi_c \\to (\\Sigma,\\Lambda)\\ell^+\\ell^-$ branching fractions. These results are offered as concrete tests: a nonzero forward-backward asymmetry, or resonance structure in $F_L$ absent in the Standard Model, would signal new physics in $c \\to u \\ell^+\\ell^-$ transitions.","pith_inferences":["Our inference: because the same sum rules fail their convergence test for $\\Lambda_b\\to n$, where the $\\langle\\bar q q\\rangle^2$ contribution reaches 50-90%, the method should not be expected to transfer directly to $b$-baryon decays; a light-cone or heavy-quark-effective-theory formulation would be needed there.","Our inference: a first measurement of $\\Xi_c^+\\to\\Sigma^+\\mu^+\\mu^-$ could validate the U-spin-extended form factors more cheaply than $\\Lambda_c$ decays, since the predicted rate sits in a range future datasets might reach.","Our inference: the roughly 60% uncertainty attributed to the charm-scale choice implies that improved Wilson coefficients, not just better form factors, are the limiting input for precision tests of $c\\to u\\ell^+\\ell^-$ transitions.","Our inference: the endpoint identity $F_L=1/3$ is a parameter-free prediction that a future angular analysis can test immediately; a measured deviation would point to new physics or to missing Standard Model contributions."],"forward_implications":["The predicted no-resonance branching fractions for $\\Lambda_c \\to p e^+e^-$ and $\\Lambda_c \\to p \\mu^+\\mu^-$, $(3.2\\pm2.3)\\times10^{-13}$ and $(2.4\\pm1.8)\\times10^{-13}$, sit below the current experimental upper limit and can be tested with more data.","$A_{FB}$ is predicted to vanish across the full $q^2$ range in the Standard Model, so any nonzero measurement is a clean new-physics signal.","$F_L$ takes the parameter-free endpoint values $1/3$ at $q^2=4m_\\ell^2$ and at $q^2=(M_{\\Lambda_c}-M_p)^2$, independent of the form-factor uncertainties.","Under new physics, $F_L$ acquires resonance peaks at the $\\rho,\\omega,\\phi$ poles that are absent in the Standard Model, providing a distinguishing signature.","U-spin relations extend the $\\Lambda_c\\to p$ form factors to six $\\Xi_c$ rare modes, for example predicting ${\\rm Br}(\\Xi_c^+\\to\\Sigma^+\\mu^+\\mu^-)=(5.2\\pm3.7)\\times10^{-13}$ without resonance contributions."],"supporting_citations":[{"why":"supplies the form-factor decomposition and helicity-amplitude expressions used to construct the decay observables.","marker":"[36]"},{"why":"earlier relativistic quark model calculation of Lambda_c -> p l+l- used as a comparison for form factors and branching fractions.","marker":"[38]"},{"why":"provides the helicity-amplitude framework and the f_{T2}=g_{T2} identity the analysis relies on.","marker":"[39]"},{"why":"lattice QCD form factors and phenomenological results that this work compares against, including a divergent g2(0) value.","marker":"[46]"},{"why":"the experimental upper limit used to gauge whether the predicted no-resonance branching fraction is accessible.","marker":"[27]"},{"why":"defines the c -> u effective Hamiltonian and Wilson coefficients the branching-fraction calculation is based on.","marker":"[29]"},{"why":"supplies the vector-resonance model and the new-physics constraints on C7 and C10 used in the angular-observable analysis.","marker":"[32]"},{"why":"two-point sum rules with the same interpolating currents that provide the decay constants and threshold parameters in Eq. (15).","marker":"[75]"},{"why":"introduces the z-series parametrization used to extrapolate the form factors across the full physical range.","marker":"[83]"},{"why":"documents the nonconvergence of three-point QCD sum rules in b-quark decays, motivating the condensate-convergence criterion adopted here.","marker":"[81]"}],"fun_headline_variants":["Rare charmed baryon decays: zero asymmetry flags new physics","Ten form factors predict clean new-physics probe in Λc decays","Zero forward-backward asymmetry: clean signature of new physics","QCD sum rules reveal rare Λc decays as new-physics test","New physics detectable in Λc rare decays via zero asymmetry"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The calculation assumes that in the chosen Borel window for $\\Lambda_c \\to p$ the truncated operator-product expansion converges and ground-state baryons, not excited states, dominate the sum rule; the paper sets these criteria as a pole contribution above 40 percent and a dimension-six condensate below 30 percent, and it reports that the same criteria fail for $\\Lambda_b \\to n$. If either condition fails for any of the ten form factors, the extracted form factors and the observables built from them would not be reliable.","fun_headline_variants_meta":{"raw":{"variants":["Rare charmed baryon decays: zero asymmetry flags new physics","Ten form factors predict clean new-physics probe in Λc decays","Zero forward-backward asymmetry: clean signature of new physics","QCD sum rules reveal rare Λc decays as new-physics test","New physics detectable in Λc rare decays via zero asymmetry"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00068,"raw_usage":{"total_tokens":3106,"prompt_tokens":976,"completion_tokens":2130,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":592,"completion_tokens_details":{"reasoning_tokens":2042}},"tokens_in":592,"tokens_out":2130,"duration_ms":15859,"temperature":1.0,"reasoning_tokens":2042,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T13:50:51.373244+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A direct check would be to plot, for each of the ten form factors, the pole-contribution ratio and the relative $\\langle \\bar q q\\rangle^2$ contribution across the Borel window; any form factor violating the stated 40%/30% criteria would break the extraction. An independent lattice QCD computation of $g_2(0)$ would also settle the issue, since the paper's value $-0.25\\pm0.02$ differs sharply from the existing lattice estimate near zero.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"supplies the form-factor decomposition and helicity-amplitude expressions used to construct the decay observables."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"earlier relativistic quark model calculation of Lambda_c -> p l+l- used as a comparison for form factors and branching fractions."},{"cited_title":"Gutsche, M","cited_arxiv_id":null,"evidence_quote":"provides the helicity-amplitude framework and the f_{T2}=g_{T2} identity the analysis relies on."},{"cited_title":"Meinel, Λ c → N form factors from lattice QCD and phenomenology of Λ c → nℓ+νℓ and Λc → pµ+µ− decays, Phys","cited_arxiv_id":null,"evidence_quote":"lattice QCD form factors and phenomenological results that this work compares against, including a divergent g2(0) value."},{"cited_title":"Aaij et al., Search for the rare decay of charmed baryon Λ c into the pµ+µ− final state, Phys","cited_arxiv_id":null,"evidence_quote":"the experimental upper limit used to gauge whether the predicted no-resonance branching fraction is accessible."},{"cited_title":"de Boer and G","cited_arxiv_id":null,"evidence_quote":"defines the c -> u effective Hamiltonian and Wilson coefficients the branching-fraction calculation is based on."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"supplies the vector-resonance model and the new-physics constraints on C7 and C10 used in the angular-observable analysis."},{"cited_title":"Khodjamirian, C","cited_arxiv_id":null,"evidence_quote":"two-point sum rules with the same interpolating currents that provide the decay constants and threshold parameters in Eq. (15)."},{"cited_title":"Bourrely, I","cited_arxiv_id":null,"evidence_quote":"introduces the z-series parametrization used to extrapolate the form factors across the full physical range."},{"cited_title":"Ball and V","cited_arxiv_id":null,"evidence_quote":"documents the nonconvergence of three-point QCD sum rules in b-quark decays, motivating the condensate-convergence criterion adopted here."}],"review_version":1}