{"id":"d0f7bcb5-4e23-484b-8c5c-15ef9a772e1c","arxiv_id":"1909.01213","paper_version":3,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":7,"one_line_summary":"A three-point QCD sum-rule calculation of B_c to D^(*) form factors supports a new |Vub| extraction channel and predicts lepton universality ratios R_c(D^0) = 0.64 +/- 0.05 and R_c(D*) = 0.55 +/- 0.05.","lead":"The authors calculate how often the B_c meson decays into D or D* mesons plus a lepton and a neutrino, using QCD sum rules for the decay form factors. They argue these rare decays give a new way to measure the quark mixing parameter |Vub| and to test whether different lepton species behave identically.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The 7.5% |Vub| uncertainty omits the self-admitted 20-30% z-series truncation error; until this is propagated, the central quantitative claim is unsupported.","rationale":"The paper is a serious QCD sum rule calculation with useful cross-checks: the Bc→J/ψ form factors agree with lattice HPQCD results (Fig. 12), the Bc→D form factors roughly match quark-model predictions (Fig. 4), and the authors explicitly discuss correlation effects, Borel windows, and non-perturbative contributions. The central claim, however, is a quantitative uncertainty estimate: competitive |Vub| extraction at 7.5% theoretical precision. That estimate requires the full decay width ζD0, which includes a substantial high-q^2 region obtained by linear z-extrapolation. The paper itself admits in Appendix B.1 that the truncation error from this linear extrapolation is 20-30% and is not included in the uncertainties. The same appendix also notes that the J/ψ and Bs fits carry the same omission, so the normalized ratio |Vub|/|Vcb| is affected as well, and Sec. 3.2 adds a further 10% correlation uncertainty that is not shown in Fig. 11. This is not a disagreement with an external consensus; it is an internal gap between the stated error budget and the quoted precision. The reader's verdict of CONDITIONAL already identifies this as the key weakness, and the proposed check would determine whether the 7.5% claim survives once the admitted truncation and correlation errors are propagated. No verdict change is needed beyond the reader's conditionality.","tokens_in":39650,"tokens_out":3775,"duration_ms":35432,"concrete_test":"Re-evaluate Eq. (3.15) including the truncation error: refit the Bc→D form factors with quadratic and cubic BCL terms b2, b3 using the covariances in Appendix B.2 and unitarity bounds, take the spread in ζD0 relative to the linear fit as an additional systematic, and add the 10% correlation uncertainty from Sec. 2.2 to the low-q^2 bins. If the total relative error on ζD0 exceeds 15%, the quoted 7.5% |Vub| uncertainty is not supported; if it remains below 15%, the concern is answered.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central quantitative claim, ζD0 = (2.0 ± 0.3) × 10^-3 eV leading to a 7.5% theoretical uncertainty on |Vub| (Sec. 3.2, Eq. 3.15), depends on form factors extrapolated with a linear BCL z-fit from q^2 ≤ 10 GeV^2 to q^2_max ≈ 19.4 GeV^2. Appendix B.1 states explicitly that these uncertainties 'do not include the truncation error, which is always of the order of 20-30% in our calculations, since we extrapolate only linearly in z(q^2)'. Since Table 9 shows roughly 40% of the integrated rate lies above 10 GeV^2, a 20-30% error on high-q^2 form factors propagates into ζD0. Combining that with the quoted 15% (0.3/2.0) width error can plausibly push the |Vub| error above 7.5%. Moreover, Sec. 2.1 says that including higher orders in z changes the central f_+(q^2_max) by 'at most ~10%', while Appendix B.1 quotes 20-30%; the text never reconciles these numbers or propagates either into Table 5 or Eq. (3.15). The ratio |Vub|/|Vcb| is also presented in Fig. 11 without the additional 10% correlation uncertainty that Sec. 3.2 says should be assigned, so 'significantly reduced theoretical uncertainty' is not demonstrated.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper computes the B_c → D^0 and B_c → D^* semileptonic form factors in the framework of three-point QCD sum rules in the range 0 ≤ q^2 ≤ 10 GeV^2, extrapolates them to q^2_max with BCL and BGL z-expansions, and uses the results to predict branching fractions, the LFU ratios R_c(D^0) and R_c(D^*), angular observables, and binned decay-rate distributions. Based on ζ_{D^0} = (2.0 ± 0.3) × 10^{-3} eV, the authors claim that |V_{ub}| can be extracted from B_c → D^0 μ ν with 7.5% theoretical uncertainty, and that normalizing to B_c → J/ψ μ ν provides a determination of |V_{ub}|/|V_{cb}| with reduced theoretical uncertainty. They also examine |V_{ub}|/|V_{cs}| via the B_c → B_s zero-recoil ratio and obtain R_FF = 0.8 ± 0.3.","tokens_in":40079,"tokens_out":8346,"duration_ms":85310,"significance":"If the headline uncertainty claims hold, the paper would add a new, independent exclusive channel to the inclusive-exclusive |V_{ub}| puzzle, which is valuable for flavor physics. The work is careful in several respects: Borel plateaus are checked, continuum contributions are kept below 50%, lattice decay constants anchor the effective thresholds, the B_c → J/ψ form factors are compared with HPQCD lattice results with good agreement, and a dedicated section examines correlations among pseudo-data points. The tabulated BCL coefficients, covariance matrices, and binned Δζ_{D^0} and R_{D^0J/ψ} distributions are useful for future LHCb analyses. However, the central quantitative claims rest on an unpropagated systematic error and on an inconsistency between the 10% and 20–30% truncation estimates; until these are reconciled and propagated, the 7.5% and 'significantly reduced' statements are not established.","major_comments":[{"comment":"The headline 7.5% theoretical uncertainty on |V_{ub}| is not supported by the error budget as presented. Appendix B.1 states that the quoted form-factor uncertainties 'do not include the truncation error, which is always of the order of 20-30% in our calculations, since we extrapolate only linearly in z(q^2)', while Sec. 2.1 says that including higher orders in z changes the central value of f_+(q^2_max) by at most ~10% and that this change 'always stays inside the uncertainties of the linear z fit.' These two statements are inconsistent, and neither is propagated into Table 5 or Eq. (3.15). Since approximately 40% of the integrated rate lies above q^2 = 10 GeV^2 (Table 9), a 20–30% error on the extrapolated form factors in that region cannot be neglected in a 7.5% claim. The manuscript must either include this systematic error in the quoted uncertainty or base the central claim on the q^2 ≤ 10 GeV^2 partial rate, where the extrapolation is not needed.","section":"Sec. 2.1, App. B.1, Eq. (3.15), Table 9"},{"comment":"The claim that normalizing B_c → D^0 μ ν to B_c → J/ψ μ ν yields a |V_{ub}|/|V_{cb}| determination with significantly reduced theoretical uncertainty is not demonstrated. The text following Fig. 11 says that, in line with Sec. 2.2, 'one should assign a further 10% uncertainty to |V_{ub}|/|V_{cb}| not shown in the plot.' The figure and the surrounding discussion present the ratio as a prediction without this additional uncertainty, and no error budget for R_{D^0J/ψ} is provided in which the cancellation of hadronic uncertainties is quantified. Please show the version of Fig. 11 that includes the 10% correlation uncertainty and state explicitly whether the claimed reduction in theoretical uncertainty survives.","section":"Sec. 3.2, Fig. 11"},{"comment":"The 3ptSR calculation is performed at leading order in α_s, and all higher-order and higher-dimension corrections are assumed to be absorbed into effective thresholds s0^{eff} calibrated from two-point sum rules against lattice decay constants. This is a reasonable strategy, but for the three-point correlators it is an uncontrolled assumption because the threshold modification is not validated at q^2 > 0. The authors acknowledge this implicitly by calling it a 'hope' in Sec. 2, yet the 7.5% uncertainty contains no explicit component for this systematic effect. I request a sensitivity study in which s0^{eff} for the B_c and D channels is varied by ±10–20% (larger than the two-point fitting uncertainty) and the resulting changes in ζ_{D^0} and R_{D^0J/ψ} are reported. If the sensitivity is small, the statement should be made quantitative; if not, the error budget must incorporate it.","section":"Sec. 2, Table 1, Eqs. (2.9)-(2.10)"}],"minor_comments":[{"comment":"The chi-square definition in Eq. (2.25) has [σ^2_{Fi}(q^2_j)]^2 in the denominator. Unless this is intentional, a conventional chi-square divides by the variance, not by the variance squared; please correct the typo or clarify the definition.","section":"Eq. (2.25)"},{"comment":"The Jacobian-based covariance estimate is not fully specified: which six parameters enter the matrix P in Eq. (2.28), and are the derivatives in J analytic or numerical? This matters because the 'extra 10%' uncertainty used in Sec. 3.2 is derived from this procedure.","section":"Sec. 2.2, Eqs. (2.26)-(2.29)"},{"comment":"The choice of t^* is motivated in the text, but since t^* is not the lowest physical threshold, the sensitivity of the BCL coefficients and of the extrapolated f_+(q^2_max) to the choice t^* = (m_B(∗)+m_π)^2 should be quantified, even if that choice produces less stable pole behavior.","section":"Sec. 2.1, Table 4"},{"comment":"Several integrated angular observables have very large uncertainties (for example F_L^{D*,τ} = 0.4 ± 0.3). The statement that these observables are 'relatively independent of the hadronic form factors' would be more persuasive if a form-factor variation study were shown, or if the sentence were restricted to the observables for which the uncertainty is actually small.","section":"Sec. 3.1, Table 6"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is an honest and careful QCDSR calculation, and the comparison with lattice data for B_c → J/ψ is encouraging. The main issue is that the headline precision claims are not backed by the paper's own error estimates. I recommend major revision and ask for a revised error budget that propagates the truncation and correlation uncertainties; if those propagated uncertainties push the |V_{ub}| theory error well above 10%, the wording of the abstract, Sec. 3.2, and the conclusion must be adjusted accordingly."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Here's the short version: this is a careful three-point QCD sum rule calculation of B_c->D(*) form factors, and the first serious analysis of |Vub| extraction from B_c->D0 mu nu in the LHCb Upgrade II context. But the headline number—a 7.5% theoretical uncertainty on |Vub|—is not supported once you account for the paper's own statements about z-series truncation. The paper deserves a referee, but the central quantitative claim needs to be reworked.\n\nWhat's new and what's good: The form factors are new. The authors include non-local condensates, calibrate effective thresholds to lattice decay constants, and perform Borel plateau checks. They compare their B_c->J/psi form factors to HPQCD lattice results and find good agreement, which is a strong sanity check. They also devote a whole section to correlations among pseudo-data points, which is rare in sum rule papers. The predictions for R_c(D0)=0.64±0.05 and R_c(D*)=0.55±0.05 will be useful if LHCb can measure them.\n\nThe soft spots: The 7.5% error on |Vub| is derived from ζ_D0 = (2.0±0.3)e-3 eV. But Appendix B.1 explicitly says that the uncertainties 'do not include the truncation error, which is always of the order of 20-30%' because the extrapolation is linear in z. Table 9 shows roughly 40% of the integrated rate sits above 10 GeV^2, exactly where the extrapolation is doing the work. So the 7.5% understates the theory error by a factor that could be three or four. There's also an inconsistency: Sec. 2.1 says higher-order z terms change f+ by at most ~10%, while Appendix B.1 says 20-30%. The paper never reconciles these numbers. And the |Vub|/|Vcb| ratio in Fig. 11 is presented without the additional 10% correlation uncertainty that the text says should be assigned. These are not fatal in the sense that the qualitative conclusion—B_c->D could be a competitive new channel—may still survive, but the quantitative claims as stated are unreliable.\n\nWho this is for: anyone working on semileptonic B_c decays, CKM determinations, or LFU. It deserves serious peer review, with major revision requiring the authors to propagate the truncation and correlation errors into all headline numbers and to fix the internal inconsistency. If they do that, the paper could be a useful contribution.","headline":"New B_c->D(*) form factors and an interesting |Vub| extraction proposal, but the 7.5% uncertainty claim omits the paper's own admitted 20-30% z-series truncation error.","tokens_in":40625,"tokens_out":3770,"would_cite":true,"duration_ms":32763,"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":"Semileptonic $B_c\\to D^{(*)}\\ell\\nu$ decays can provide a competitive determination of the CKM element $|V_{ub}|$ with 7.5% theoretical uncertainty, and normalizing to $B_c\\to J/\\psi\\,\\mu\\bar{\\nu}_\\mu$ offers a low-uncertainty ratio…","keywords":["B_c meson decays","CKM matrix |Vub|","QCD sum rules","lepton flavour universality","semileptonic decays","B_c to D form factors","z-series parametrization","LHCb Upgrade II"],"falsifier":"Measure the differential rate $d\\Gamma(B_c\\to D^0\\mu\\bar{\\nu}_\\mu)/dq^2$ in the low-$q^2$ bins tabulated in the paper; if the extracted $|V_{ub}|$ from different $q^2$ bins disagrees by more than the quoted errors, or if the measured ratio to $B_c\\to J/\\psi$ falls outside the predicted band, the sum-rule form factors are falsified. A direct lattice computation of the $B_c\\to D$ form factors would also settle the extrapolation question.","tokens_in":39364,"feed_emoji":"⚛️","tokens_out":7474,"duration_ms":68163,"temperature":0.7,"pith_summary":"This paper shows that semileptonic $B_c \\to D^{(*)} \\ell \\nu$ decays, once measured at the planned LHC upgrade, can become a new exclusive probe of the CKM element $|V_{ub}|$. Using three-point QCD sum rules to calculate the $B_c \\to D$ and $B_c \\to D^*$ form factors, the authors find that the $B_c \\to D^0 \\mu \\bar{\\nu}_\\mu$ decay rate determines $|V_{ub}|$ with a 7.5 percent theoretical uncertainty. Normalizing this rate to $B_c \\to J/\\psi\\,\\mu \\bar{\\nu}_\\mu$ gives the ratio $|V_{ub}|/|V_{cb}|$ with strongly reduced hadronic uncertainty, which is easier to measure. The same form factors yield branching-ratio predictions, $q^2$ distributions, angular observables, and lepton-flavour-universality ratios $R_c(D^0)=0.64\\pm0.05$ and $R_c(D^*)=0.55\\pm0.05$ that future data can test.","feed_headline":"B_c to D decays could fix |Vub| at 7.5 percent","feed_subtitle":"Normalizing to B_c to J/psi cuts the hadronic error, adding a new test of the inclusive-exclusive |Vub| gap.","key_machinery":"The load-bearing object is the set of $B_c\\to D^{(*)}$ form factors ($f_+, f_0$ for $D$, and $V, A_1, A_2, A_0$ for $D^*$) computed from three-point QCD sum rules at $q^2\\le 10$ GeV$^2$ and extrapolated to the full kinematic range with a linear BCL $z$-series, checked against BGL parametrization. These form factors convert a measured $B_c\\to D^{(*)}\\ell\\nu$ rate into $|V_{ub}|$; their uncertainties, largely from effective thresholds calibrated to lattice decay constants, set the 7.5% error in $|V_{ub}|$ from the $D^0$ mode and the roughly 20% error from the $D^*$ mode. For the ratio $|V_{ub}|/|V_{cb}|$, the same machinery is applied to $B_c\\to J/\\psi$ form factors that reproduce lattice results, so the hadronic uncertainties largely cancel.","core_discovery":"The central discovery is that the $B_c \\to D^0 \\mu \\bar{\\nu}_\\mu$ channel is a viable exclusive route to $|V_{ub}|$ once the $B_c \\to D^{(*)}$ form factors are computed with the three-point sum-rule method. The paper derives $\\zeta_{D^0} = (2.0\\pm0.3)\\times 10^{-3}$ eV for the reduced decay width and $\\zeta_{D^*} = (5\\pm2)\\times 10^{-3}$ eV, implying a 7.5% theoretical error for the $D^0$ channel and 20% for the $D^*$ channel. By dividing by the $B_c\\to J/\\psi\\,\\mu\\bar{\\nu}_\\mu$ width, the ratio $|V_{ub}|/|V_{cb}|$ can be extracted with form-factor uncertainties largely cancelling, which is the most practical route for the expected dataset of roughly 30,000 reconstructed $B_c\\to D^0\\ell\\nu$ events. The paper also establishes that non-perturbative condensate contributions to the sum rules are numerically negligible and that the form factors obey heavy-quark spin symmetry relations, validating the ratio to $B_c\\to B_s$ for a future $|V_{ub}|/|V_{cs}|$ determination.","pith_inferences":["One extension not drawn in the paper: an explicit $\\mathcal{O}(\\alpha_s)$ correction to the three-point sum rule would replace the effective-threshold calibration and likely reduce the quoted 7.5% uncertainty below its current value.","If lattice QCD later computes $B_c\\to D^{(*)}$ form factors, the effective-threshold calibration used here can be checked directly, and a lattice-driven $|V_{ub}|$ from this channel would provide an independent handle on the inclusive-exclusive $|V_{ub}|$ puzzle.","The integrated ratios $R_c(D^0)$ and $R_c(D^*)$ are relatively form-factor-independent, but their $q^2$ distributions carry sharper discriminating power between the competing form-factor models listed in the paper.","The zero-recoil ratio $B_c\\to D^0$ over $B_c\\to B_s$ could become a practical $|V_{ub}|/|V_{cs}|$ measurement if lattice input supplies the high-$q^2$ extrapolation that the sum rules cannot provide."],"forward_implications":["A measurement of $B_c \\to D^0 \\mu \\bar{\\nu}_\\mu$ at the LHCb Upgrade II would determine $|V_{ub}|$ with about 7.5% theory error, rivalling the $B\\to\\pi$ exclusive determination.","The ratio $B(B_c\\to D^0\\mu\\bar{\\nu}_\\mu)/B(B_c\\to J/\\psi\\,\\mu\\bar{\\nu}_\\mu)$ gives $|V_{ub}|/|V_{cb}|$ with reduced hadronic uncertainty, and the provided binned tables allow direct comparison to future data.","The predicted lepton-flavour-universality ratios $R_c(D^0)=0.64\\pm0.05$ and $R_c(D^*)=0.55\\pm0.05$ provide a new $B_c$-based test of lepton-flavour universality.","The $B_c\\to D^*\\mu\\bar{\\nu}_\\mu$ channel is less suited for $|V_{ub}|$ extraction due to its 20% uncertainty but remains useful as a cross-check.","The $q^2$ distributions and angular observables supplied in the paper give future experiments a direct way to test the Standard Model predictions for these decays."],"supporting_citations":[{"why":"Supplies the projected LHCb Upgrade II sample of about 30,000 reconstructed $B_c\\to D^0\\ell\\nu$ decays that motivates the measurement.","marker":"[15]"},{"why":"Previous three-point sum-rule calculation of $B_c\\to J/\\psi,\\eta_c$ form factors used as the methodological baseline and for the normalization decay.","marker":"[18]"},{"why":"Establishes the three-point QCD sum-rule method that is the paper's central computational tool.","marker":"[20]"},{"why":"Discusses the validity and limitations of the three-point sum-rule approach, which the authors follow when estimating uncertainties.","marker":"[25]"},{"why":"Provides the BCL $z$-series parametrization used to extrapolate the sum-rule form factors from low $q^2$ to the full kinematic range.","marker":"[57]"},{"why":"Lattice calculation of $B_c\\to J/\\psi$ form factors that the sum-rule computation reproduces and that enters the $|V_{ub}|/|V_{cb}|$ ratio.","marker":"[64]"},{"why":"Heavy-quark spin symmetry argument for the $B_c\\to D^0$ over $B_c\\to B_s$ zero-recoil ratio used to propose a future $|V_{ub}|/|V_{cs}|$ extraction.","marker":"[65]"}],"fun_headline_variants":["B_c to D mu nu pins |Vub| to 7.5%","Ratio with J/psi slashes |Vub| error in B_c to D","B_c to D decays: 7.5% |Vub| plus LFU probe","Sum-rule form factors unlock |Vub| from B_c to D"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The central assumption is that the leading-order three-point sum-rule form factors, with effective thresholds calibrated to lattice decay constants, remain accurate after a linear $z$-series extrapolation from $q^2\\le 10$ GeV$^2$ to the full kinematic range, so that the stated 20-30% truncation error can be left out of the quoted uncertainty budget.","fun_headline_variants_meta":{"raw":{"variants":["B_c to D mu nu pins |Vub| to 7.5%","Ratio with J/psi slashes |Vub| error in B_c to D","B_c to D decays: 7.5% |Vub| plus LFU probe","Sum-rule form factors unlock |Vub| from B_c to D"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000988,"raw_usage":{"total_tokens":4332,"prompt_tokens":1234,"completion_tokens":3098,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":850,"completion_tokens_details":{"reasoning_tokens":3007}},"tokens_in":850,"tokens_out":3098,"duration_ms":23581,"temperature":1.0,"reasoning_tokens":3007,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T05:24:40.017703+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the differential rate $d\\Gamma(B_c\\to D^0\\mu\\bar{\\nu}_\\mu)/dq^2$ in the low-$q^2$ bins tabulated in the paper; if the extracted $|V_{ub}|$ from different $q^2$ bins disagrees by more than the quoted errors, or if the measured ratio to $B_c\\to J/\\psi$ falls outside the predicted band, the sum-rule form factors are falsified. A direct lattice computation of the $B_c\\to D$ form factors would also settle the extrapolation question.","supporting_citations":[{"cited_title":"Sum rules for light quarks in quantum chromodynamics","cited_arxiv_id":null,"evidence_quote":"Establishes the three-point QCD sum-rule method that is the paper's central computational tool."},{"cited_title":"$B_c$ decays from highly improved staggered quarks and NRQCD","cited_arxiv_id":"1611.01987","evidence_quote":"Lattice calculation of $B_c\\to J/\\psi$ form factors that the sum-rule computation reproduces and that enters the $|V_{ub}|/|V_{cb}|$ ratio."}],"review_version":1}