{"id":"d9681670-36be-434e-a871-795785be3f70","arxiv_id":"1908.02328","paper_version":2,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"low","formal_verification":"none","parameter_count":3,"one_line_summary":"The c2 coefficient of the charged-lepton energy-squared distribution in any H to H' l nu semileptonic decay is lepton-flavor independent in the SM, and a2/c2 is a universal function of omega.","lead":"This paper derives two new Standard Model predictions for semileptonic decays: the coefficient of the squared charged-lepton energy in the lab-frame spectrum is independent of lepton flavor, and a related ratio of angular and energy coefficients is a universal function. These provide new, model-independent tests of lepton flavor universality in b to c decays such as Lambda_b to Lambda_c, and can distinguish new-physics scenarios that otherwise look identical in total rates.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The SM LFU relations, c2=-4W2 and Eq. (10), appear correct; the vulnerable part is the NP-discrimination claim, which depends on non-public correlation data and on setting the tensor Wilson coefficient to zero.","rationale":"The reader's stated weakest assumption is completeness of the hadron tensor decomposition, specifically the omission of the time-reversal-odd antisymmetric term. That term, if present, would be contracted with the epsilon part of the lepton tensor and would produce an invariant proportional to epsilon(p,q,k',k); in the W rest frame k' and k are back-to-back, so this invariant vanishes after the azimuthal integration implicit in d2Gamma/(domega dE_l) and d2Gamma/(domega dcos theta_l). Thus it does not undermine c2=-4W2 or Eq. (10). The paper's SM derivation is algebraically consistent, and the universal ratio follows straightforwardly from Eqs. (6) and (8). The genuinely load-bearing weakness is the NP illustration: the quantitative statement that c2 or a2 can separate Fits 6 and 7 by more than 5 sigma depends on (i) Wilson-coefficient correlation matrices that are only available through private communication and (ii) setting the tensor Wilson coefficient CT to zero despite its 1 sigma ranges including values up to 0.10. Neither issue affects the SM LFU tests, but both bear directly on the headline claim that a tau c2 measurement can distinguish the otherwise-degenerate NP fits. The appropriate verdict remains conditional, matching the reader's overall assessment, but the condition should be attached to the availability of the correlation data and the size of the neglected tensor effects, not to the hadron-tensor decomposition.","tokens_in":16543,"tokens_out":24442,"duration_ms":261867,"concrete_test":"Recompute Fig. 6 using the full covariance matrices from Ref. [14]/[36] and with CT fixed to its +1 sigma upper values (0.10 for Fit 6 and 0.06 for Fit 7) instead of zero. If the central values of (c2)NP/(c2)SM at omega=1.15 shift by more than the quoted uncertainties or the 68% intervals from the two fits overlap, then the claimed 'more than 5 sigma' discrimination between Fits 6 and 7 is not robust.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central SM predictions are solid: from Eqs. (6) and (8), a2 and c2 are both proportional to W2, and the ratio in Eq. (10) cancels W2 exactly. The T-odd antisymmetric term omitted in footnote 1 would not contribute to the azimuth-integrated d2Gamma/(domega dE_l) or d2Gamma/(domega dcos theta_l) observables, so it is not the load-bearing risk. The load-bearing concern is the quantitative NP-discrimination claim. The effective Hamiltonian in Eq. (17) includes a tensor operator O_T, but the NP formulas in Eqs. (26)-(27) cover only left/right scalar and vector operators. For Fits 6 and 7 the authors set CT to zero, although the fitted values are CT=0.01^{+0.09}_{-0.07} and -0.02^{+0.08}_{-0.07}. A first-order tensor correction to c2 or a2 could shift the ratio (c2)NP/(c2)SM by an amount comparable to the quoted uncertainties (1.40+/-0.04 vs 2.06+/-0.09). The paper checks the effect of dropping CT only on R_Lambda_c, not on c2/a2. In addition, Fig. 6, which yields the claimed >5 sigma separation, relies on Wilson-coefficient correlation matrices obtained by private communication [36]; these correlations are not published, so the quantitative separation cannot be independently reproduced.","agreement_with_reader":"disagree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper develops a general formalism for the double differential semileptonic decay widths d^2Γ/(dω dE_l) and d^2Γ/(dω d cosθ_l) for any H → H' l ν decay, expressing them in terms of hadronic structure functions. Within the Standard Model (SM), the coefficient c2(ω) in the E_l distribution is shown to be proportional to the structure function W2(ω) alone, so it is independent of the charged lepton mass. The authors also derive a universal ratio relating a2(ω) and c2(ω), Eq. (10). They generalize the formalism to include left/right scalar and vector NP operators (setting the tensor coefficient to zero) and apply it to Λ_b → Λ_c l ν using lattice QCD form factors from Ref. [20]. They show that Fits 6 and 7 of Ref. [14], which yield nearly identical R_D, R_D*, and dΓ/dω, predict different values of (c2)_NP/(c2)_SM and claim a separation by more than 5σ.","tokens_in":16921,"tokens_out":6940,"duration_ms":70086,"significance":"The SM relations (c2 = -4W2 and the universal ratio Eq. (10)) are elegant, self-contained, and constitute genuinely new model-independent tests of lepton flavour universality in semileptonic decays. The derivation is transparent and can be checked directly from Eqs. (6) and (8), and the application to Λ_b → Λ_c with modern LQCD form factors provides concrete numerical predictions. However, the advertised NP-discrimination power is conditional: it relies on neglecting the tensor operator and on private correlation matrices for the Wilson coefficients, so the quantitative 5σ claim is not yet fully supported.","major_comments":[{"comment":"The NP predictions for c2 and a2 are obtained after setting the tensor Wilson coefficient C_T to zero, but the fits of Ref. [14] give C_T = 0.01^{+0.09}_{-0.07} (Fit 6) and -0.02^{+0.08}_{-0.07} (Fit 7). The authors only quantify the effect of dropping C_T on R_Λ_c (Fig. 6, bottom panels), not on c2 or a2. Since the separation between Fits 6 and 7 quoted for (c2)_NP/(c2)_SM at ω=1.15 is 1.40 ± 0.04 vs 2.06 ± 0.09, a tensor contribution of order C_T could shift the ratio by an amount comparable to the separation itself. The claim that a measurement of c2 (or a2) would distinguish the two fits requires an estimate of the tensor contribution to these observables.","section":"Sec. III.C, Eqs. (26)-(27) and Fig. 6"},{"comment":"The quantitative statement that the two NP scenarios are separated by more than 5σ is based on Wilson-coefficient correlation matrices obtained by private communication (Ref. [36]), because the correlation matrices are not publicly available from Ref. [14]. This makes the central numerical claim non-reproducible by the reader. The authors should either obtain permission to include the correlation matrices as supplementary material or present the separation as an estimate with the caveat that the uncertainties depend on unpublished correlations.","section":"Fig. 6 and surrounding text"}],"minor_comments":[{"comment":"There is a typo: 'aproximation' should be 'approximation' in the paragraph discussing the flatness of (c2)_NP/(c2)_SM.","section":"Sec. III.C"},{"comment":"The label 'MPJP' is used in the bottom plots but is not defined; it should be identified (presumably as the predictions from Ref. [14], Murgui-Peñuelas-Jung-Pich).","section":"Fig. 6 caption"},{"comment":"The summary sentence 'neither c2 nor a2 are modified by left and right scalar NP terms' should explicitly repeat the C_T = 0 caveat that appears in Sec. III.C, so that the conclusion is self-contained and not overgeneralized.","section":"Sec. IV"}],"recommendation":"major_revision","confidential_remarks":"The reliance on private communication [36] for a key numerical claim is unusual; I would encourage the editor to ask the authors to make the correlation matrices available as supplementary material. The central SM relations are sound, but the NP-discrimination claim needs either a tensor-contribution estimate or a softened presentation."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things to know. First, the paper's main results are the discovery that in the SM the c2 coefficient of the lepton-energy distribution is lepton-flavor independent, and that the ratio a2/c2 (with the kinematic factor) is a universal function for any H→H' semileptonic decay. I checked the derivation; it's a direct consequence of the Lorentz decomposition and the algebra is correct. Second, the paper is honest about what is new: the E_l distribution in the lab frame has not been used this way before, and the universal ratio is not in the earlier literature. This is a genuine, modest but useful contribution.\n\nThe general framework in Sec. II is clean. Eq. (6) and (8) are correct, and Eq. (10) follows by cancelling W2. The T-odd term omitted in footnote 1 would not contribute to the azimuth-integrated double distributions, so that omission is not a problem. The application to Lambda_b using the Detmold et al. LQCD form factors is careful; the error bands come from the published correlation matrix, and the SFs are given for the first time. The observation that fits 6 and 7 of Murgui et al. differ in c2/a2 while giving the same dGamma/domega is interesting and potentially useful.\n\nThe soft spot is the quantitative NP discrimination claim. The authors set the tensor Wilson coefficient C_T to zero, although the fits give it values around 0.01±0.08. They check the effect of dropping C_T only on R_Lambda_c, not on c2/a2. A first-order tensor correction to c2 could shift the ratio by an amount comparable to the quoted uncertainties. The claim of more than 5 sigma separation between Fit 6 and Fit 7 in Fig. 6 also relies on Wilson-coefficient correlation matrices obtained by private communication (Ref. [36]); those correlations are not public, so the quantitative separation cannot be independently reproduced. The authors do flag this, but it means the illustrative NP numbers are not the load-bearing part of the paper.\n\nThe core SM predictions, however, are solid and deserve publication. The paper is for flavor-physics theorists and experimentalists looking for new LFU tests. It deserves a serious referee. I would accept it for review and recommend the authors either make the correlation input public or soften the quantitative claim.","headline":"A clean, algebraically solid pair of new SM LFU observables; the NP-discrimination illustration rests on non-public correlations but the core result stands.","tokens_in":17415,"tokens_out":1878,"would_cite":true,"duration_ms":18666,"reading_group":"yes","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 two Standard Model predictions — a lepton-flavour-independent coefficient c2(ω) and a universal a2/c2 ratio — that turn any semileptonic decay into a lepton-flavour-universality test.","keywords":["lepton flavour universality","semileptonic decays","Lambda_b to Lambda_c","charged lepton energy distribution","structure functions","new physics","b to c transitions","angular distribution"],"falsifier":"Measure d²Γ/(dω dE_τ) for Λ_b→Λ_c τ ν̄ and extract c2(ω) at fixed ω; if it differs from c2(ω) extracted from the electron or muon mode beyond uncertainties, the Standard Model lepton-universality prediction fails. Separately, extract a2(ω) and c2(ω) in a decay such as D→Kℓν and check whether M² a2/[M'²(1−m_ℓ²/q²)c2] equals (ω²−1)/4; a deviation would falsify the five-structure-function decomposition.","tokens_in":16383,"feed_emoji":"⚛️","tokens_out":5494,"duration_ms":55272,"temperature":0.7,"pith_summary":"This paper establishes two Standard Model predictions for any unpolarized semileptonic decay H→H' ℓ ν̄: the coefficient c2(ω) of the E_ℓ² term in the charged-lepton energy distribution is exactly the same for electrons, muons, and taus, and the ratio of a2(ω) (the cosine-squared coefficient in the lepton angular distribution) to c2(ω) reduces to the universal function (ω²−1)/4 after trivial mass factors. Because both predictions hold for any hadron, they turn any measured H→H' decay into a lepton-flavour-universality test that does not rely on hadronic form-factor models. The authors apply the framework to Λ_b→Λ_c using lattice QCD form factors and show that measuring c2 (or a2) in the tau mode would separate two new-physics fits that otherwise agree in R_D, R_D*, R_Λ_c and dΓ/dω. If the predictions fail, that is a model-independent signal of new physics in b→c transitions.","feed_headline":"New lepton-universality test hides in the tau energy spectrum","feed_subtitle":"In the Standard Model, one coefficient of the lepton energy distribution is identical for e, mu, and tau.","key_machinery":"The machinery is the Lorentz decomposition of the unpolarized hadron tensor into five structure functions W1...W5, with the time-reversal-odd antisymmetric term omitted. In the lab-frame lepton energy distribution, the E_ℓ² coefficient is exactly c2 = −4W2; in the W⁻ rest-frame angular distribution, a2 = −(M'²/M²)(ω²−1)(1−m_ℓ²/q²)W2. Because both coefficients share W2, their ratio is universal and form-factor independent, which is what makes c2 and the a2/c2 ratio clean tests of the Standard Model.","core_discovery":"The central claim is that in the Standard Model the doubly differential width d²Γ/(dω dE_ℓ) factorizes kinematically into c0 + c1 E_ℓ/M + c2 E_ℓ²/M², with c2(ω)=−4W2(ω) independent of the charged lepton mass. Since W2 is a hadron structure function, c2 is not predicted to have a particular value, but it is predicted to be identical for e, μ, and τ at every ω. Separately, a2(ω), which controls the cos²θ_ℓ term in the W⁻ rest-frame angular distribution, satisfies M² a2(ω)/[M'²(1−m_ℓ²/q²)c2(ω)] = (ω²−1)/4, a universal relation valid for any H→H' semileptonic decay; the hadron structure function cancels. The paper then shows, within the effective-Hamiltonian scheme of Ref. [14], that left/right scalar new physics leaves both c2 and a2 unchanged, while left/right vector corrections rescale both but leave their ratio intact, so violations of the two Standard Model predictions point to specific Lorentz structures.","pith_inferences":["The same lepton-energy analysis could be applied to B→D(∗)ℓν data already being collected; the c2 equality between light leptons and tau would then become a high-statistics lepton-flavour-universality test complementary to R_D(∗).","Equation (10) could be checked first in light-quark decays such as K→πℓν or D→Kℓν, where backgrounds are smaller, before tau-mode statistics catch up; any violation there would challenge the universal decomposition rather than b→c physics specifically.","A differential measurement of c2(ω) rather than its integral could isolate kinematic regions where scalar new-physics effects are suppressed, sharpening the distinction between vector and scalar explanations.","The helicity decomposition suggests that, combined with e/μ angular data, tau polarisation in the W⁻ frame can be extracted from unpolarized decay distributions, a testable prospect for future high-statistics samples."],"forward_implications":["In any b→c semileptonic decay, the electron and muon modes provide a form-factor-independent Standard Model prediction for c2(ω) in the tau mode; a mismatch is direct evidence of lepton-flavour-universality violation.","The universal a2/c2 ratio turns every measured semileptonic decay — meson or baryon, c→s, c→d, s→u, b→u — into a test of the Standard Model hadron-tensor structure.","If a tau-mode c2 is rescaled relative to e/μ by a constant factor while the a2/c2 ratio still holds, the responsible new physics is a left- or right-handed vector current, not a scalar.","For Λ_b→Λ_c, c2 (or a2) in the tau channel separates the new-physics Fits 6 and 7 of Ref. [14], which otherwise predict the same R_D, R_D*, R_Λ_c, and dΓ/dω.","The coefficients c0, c1, and a1 also show fit-discriminating power, giving additional observables from the same data set."],"supporting_citations":[{"why":"Supplies the effective Hamiltonian with Wilson coefficients CVL, CVR, CSL, CSR and the new-physics Fits 6 and 7 used to show that c2 and a2 distinguish scenarios with identical R_D, R_D*, and dΓ/dω.","marker":"[14]"},{"why":"Provides the lattice QCD form factors, with statistical correlations, used for the numerical Standard Model and new-physics predictions for Λ_b→Λ_c.","marker":"[20]"},{"why":"Supplies the heavy-quark spin-symmetry constraints on the Λ_b→Λ_c form factors that justify treating this baryon decay as a clean b→c probe.","marker":"[19]"},{"why":"Provides the measured muon-mode dΓ/dω spectrum that the lattice QCD form factors are checked against, validating the numerical inputs.","marker":"[16]"},{"why":"Earlier full angular-distribution study for Λ_b→Λ_c(→Λπ)ℓν whose observables the present work complements with the lab-frame charged-lepton energy distribution.","marker":"[23]"},{"why":"Gives masses, lifetimes, and branching-fraction inputs used in the numerical evaluation and in extracting |Vcb| from the Λ_b decay rate.","marker":"[31]"}],"fun_headline_variants":["Lepton-flavor independence of c2: a new SM test","c2 in b→c decays: lepton-universal, new LFU probe","Universal ratio a2/c2 gives new LFU test","SM predicts lepton-universal c2 in semileptonic decays","New LFU test from energy distribution in b→c"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The derivation assumes the hadron tensor for unpolarized H→H' decays is fully captured by the five structure functions of Eq. (4), omitting any time-reversal-odd antisymmetric piece; if spin-dependent or additional Lorentz terms contribute to the E_ℓ² coefficient, the identities c2 = −4W2 and Eq. (10) need not hold.","fun_headline_variants_meta":{"raw":{"variants":["Lepton-flavor independence of c2: a new SM test","c2 in b→c decays: lepton-universal, new LFU probe","Universal ratio a2/c2 gives new LFU test","SM predicts lepton-universal c2 in semileptonic decays","New LFU test from energy distribution in b→c"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000255,"raw_usage":{"total_tokens":1748,"prompt_tokens":1297,"completion_tokens":451,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":913,"completion_tokens_details":{"reasoning_tokens":357}},"tokens_in":913,"tokens_out":451,"duration_ms":4818,"temperature":1.0,"reasoning_tokens":357,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T14:48:36.696103+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure d²Γ/(dω dE_τ) for Λ_b→Λ_c τ ν̄ and extract c2(ω) at fixed ω; if it differs from c2(ω) extracted from the electron or muon mode beyond uncertainties, the Standard Model lepton-universality prediction fails. Separately, extract a2(ω) and c2(ω) in a decay such as D→Kℓν and check whether M² a2/[M'²(1−m_ℓ²/q²)c2] equals (ω²−1)/4; a deviation would falsify the five-structure-function decomposition.","supporting_citations":[{"cited_title":"Blanke, A","cited_arxiv_id":null,"evidence_quote":"Earlier full angular-distribution study for Λ_b→Λ_c(→Λπ)ℓν whose observables the present work complements with the lab-frame charged-lepton energy distribution."},{"cited_title":"Detailed Study of the Decay Lambda_b --> Lambda_c tau {\\bar \\nu}_{\\tau}","cited_arxiv_id":"1804.05592","evidence_quote":"Gives masses, lifetimes, and branching-fraction inputs used in the numerical evaluation and in extracting |Vcb| from the Λ_b decay rate."}],"review_version":1}