{"id":"deba07b4-3608-4fc2-b63e-208a2db5f602","arxiv_id":"2411.09458","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":8.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"New three-particle QCD kernels for the full Weak Effective Theory basis plus a first six-coupling global fit show that the b to c u q puzzle favors four-operator new-physics models over six-operator ones.","lead":"This paper completes the QCD factorization calculation for class-I b to c u q decays in the full new-physics operator basis, and fits up to six effective couplings to current data. The Standard Model alone fails badly, and two families of new-physics solutions emerge, which future measurements can distinguish.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The BSM conclusion depends entirely on assuming QCD power corrections stay at the few-percent level; the paper's own SM+PC' fit shows -20% to -30% corrections absorb the anomaly, so the claim of new physics is conditional on an external prior that is not independently tested.","rationale":"The technical core of the paper—the two-particle NLO kernels, the new three-particle LO kernels, and the LO inclusive width—is presented with cross-checks against known limits and the literature, so I do not see an internal inconsistency there. The reader's weakest-assumption analysis correctly identifies the decisive point: the SM+PC' model in Sec. 5.2.1 already fits the data perfectly with δ ≈ -20% to -30%, and the only reason the authors do not accept it is that such power corrections exceed the estimates of Ref. [21]. That estimate is an external input, not derived in this paper, and no independent calculation is used to rule out the power-correction solution. Because the paper explicitly concedes that the BSM modes are favoured over the SM but not over SM+PC', the argument is honest and internally consistent; the verdict CONDITIONAL is appropriate. The quantitative bounds could also be affected by the Gaussian likelihood approximation, the neglected light-meson uncertainties, and the crude lifetime penalty, but these are secondary to the power-correction prior, which is the single most load-bearing assumption. The proposed LCSR-based re-analysis would directly test whether that assumption survives an independent theoretical input; if it does, the BSM conclusion stands, and if it does not, the phenomenological claim should be weakened. No change to the reader's verdict is needed.","tokens_in":39908,"tokens_out":8084,"duration_ms":86186,"concrete_test":"Use the LCSR computation of non-factorisable corrections in Ref. [27] to build a Gaussian prior for δP and δV (central values, uncertainties, and correlations) and re-run the released EOS analysis for SM+PC' and all WET models. If the SM+PC' posterior still sits at δ ≈ -20% with high probability while the prior is centered near a few percent, the power-correction loophole is closed and the BSM conclusion stands. If the posterior moves to |δ| ≲ 5%, or if K(SM+PC', WET) reverses, the anomaly is compatible with QCD power corrections and the BSM claim should be downgraded.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing step is the interpretation of the SM+PC' result in Sec. 5.2.1. With the two power-correction parameters δP, δV allowed to vary in [-30%, 0] (Eq. 5.9), the fit gives χ² = 1.58 for four observations (p = 45%) and log-evidence 29.12, which is larger than every WET model evidence in Table 4. Thus SM+PC' explains the data at least as well as any four- or six-parameter BSM model. The paper's reason for preferring the BSM interpretation is that the fitted δ values are 'roughly two orders of magnitude' larger than the estimates in Ref. [21]. That estimate is not re-derived or independently tested here; it enters only through the prior in Eq. (5.8). Consequently, the central claim that the data require new physics is exactly as strong as the external assumption that power corrections cannot be as large as -20%. The paper is transparent about this (Sec. 6: 'not over the unconstrained power-correction hypothesis'), which makes the claim internally consistent, but it leaves the decisive premise unverified. Secondary limitations—the Gaussian likelihood in Sec. 5.1.2, fixed LCDA and decay-constant uncertainties in Sec. 5.1.4, and the tree-level one-sided lifetime penalty in Eq. (5.5)—could shift quantitative bounds, but they are not the central hinge; the power-correction prior is.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper presents a WET analysis of the class-I nonleptonic decays \\(\\bar B^0_{(s)}\\to D^{(*)+}_{(s)}P^-\\) with \\(P=\\pi,K\\). The authors recalculate the two-particle hard-scattering kernels at NLO in QCD for the full WET operator basis, confirming the results of Ref. [28]; they then compute, for the first time, the three-particle hard-scattering kernels at LO for the full WET basis. They also derive the two-loop anomalous dimension matrix in the Bern basis and compute the inclusive nonleptonic \\(B\\)-meson decay width at LO in QCD and at leading power in \\(1/m_b\\) for the full \\(qbcu\\) WET sector. These results are implemented in the EOS software and used in a Bayesian analysis of four WET fit models (with four or six simultaneously varied Wilson coefficients), alongside SM, SM+PC, and SM+PC' models. The SM fit is poor (\\(\\chi^2=26.69\\) for 4 d.o.f., \\(p=2\\times10^{-5}\\)), all BSM models are decisively favoured over the SM, and two distinct posterior modes are found in each BSM model. The paper explicitly notes that an unconstrained power-correction model, SM+PC', fits the data with \\(p=45\\%\\) and larger evidence than any WET model, so the BSM preference is conditional on the adopted power-correction prior.","tokens_in":40333,"tokens_out":6412,"duration_ms":63292,"significance":"The theoretical core of the paper is significant and, as far as I can determine, sound: the two-particle NLO kernels reproduce known results and the correct charmless limits, the three-particle kernels are new, and the lifetime calculation at LO for the full WET basis fills a gap in the literature. The paper also ships reproducible code and machine-readable likelihood and form-factor inputs in EOS, which is a clear strength. The phenomenological claim that new physics is required is, however, weaker than the abstract's 'decisively favoured' language suggests, because the paper's own SM+PC' fit—with power corrections of order \\(-20\\%\\) to \\(-30\\%\\)—describes the data at least as well as all BSM models. This is a load-bearing caveat, but the authors are transparent about it in Sec. 6, and the underlying calculations are not circular: the fits use external measurements and the form-factor priors come from independent earlier work.","major_comments":[{"comment":"The SM+PC' fit, with \\(\\delta_P,\\delta_V\\in[-30\\%,0]\\) (Eq. 5.9), yields \\(\\chi^2=1.58\\) with \\(p=45\\%\\) and log-evidence 29.12, which is larger than every WET model evidence in Table 4. The paper's conclusion that BSM is needed is therefore entirely conditional on the prior in Eq. (5.8), which restricts power corrections to the estimates of Ref. [21]; that estimate is not re-derived or independently tested here. The abstract and §5.2.2 nevertheless state that BSM models are 'decisively favoured' over the SM, which is true but potentially misleading without an explicit comparison to SM+PC'. I recommend adding \\(K(\\mathrm{SM+PC'}, \\mathrm{WET\\text{-}i})\\) to Table 4 or a dedicated discussion, and/or exploring a combined fit in which \\(\\delta_P,\\delta_V\\) are treated as nuisance parameters alongside the WET coefficients, so that the power-correction hypothesis competes on equal footing in the model comparison.","section":"§5.2.1 and Table 4"},{"comment":"The claimed SM p-value of \\(2\\times10^{-5}\\) and the associated \\(3.4\\sigma\\) form-factor pull are computed with a multivariate Gaussian approximation to the experimental likelihood, even though Fig. 4 shows that the full likelihood is strongly non-Gaussian in \\(\\mathcal{B}(\\bar B_s\\to D_s\\pi)\\), \\(\\mathcal{B}(\\bar B_s\\to D_s^*\\pi)\\), and \\(f_s/f_d\\). If the full likelihood has heavier tails, both the p-value and the Bayes factors in Table 4 could shift appreciably. Please quantify the effect by evaluating the SM fit and at least the decisive WET-1 versus SM+PC' comparison with the full eight-nuisance-parameter likelihood, or clearly state the size of the systematic shift induced by the Gaussian approximation.","section":"§5.1.2 and Fig. 4"}],"minor_comments":[{"comment":"The quoted Bayes factors \\(K(\\mathrm{WET\\text{-}2B, SM})=1.5\\times10^3\\) and \\(K(\\mathrm{WET\\text{-}1B, SM})=3.4\\times10^5\\) compare a single local mode's evidence with the SM evidence, although Eq. (5.4) defines the global model evidence as the sum of the local evidences; the quoted numbers are therefore conservative lower bounds and should be labelled as such or replaced by global-evidence ratios.","section":"Table 4 and §5.2.2"},{"comment":"The notation \\(O(q^4)\\) in the tensor three-particle matrix element is ambiguous; since the light-meson momentum is on-shell with \\(q^2=m_P^2\\), please restate this as \\(O(m_P^4)\\) for clarity.","section":"Eq. (3.49)"},{"comment":"The assertion that light-meson decay-constant and LCDA uncertainties are 'small' is not quantified; a one-line numerical test, for example varying \\(f_{3P}\\), \\(\\omega_{3P}\\), and the \\(\\alpha_P^i\\) by their quoted uncertainties, would make the sensitivity of the new three-particle kernels more transparent.","section":"§5.1.4"},{"comment":"The distinction between the 'full' and 'approx' likelihoods would be clearer with a legend or labelled contours; the current caption relies on the reader identifying the coloured regions by eye.","section":"Fig. 4"},{"comment":"The statement that providing a p-value is 'not useful' is puzzling for the SM and SM+PC rows, where the number of degrees of freedom is positive; please report p-values for those rows or give a clearer explanation of why they are omitted.","section":"Table 4 caption"}],"recommendation":"major_revision","confidential_remarks":"The authors are honest about the power-correction limitation in Sec. 6, but the abstract and the 'decisively favoured' phrasing in §5.2.2 can be misread as a new-physics discovery claim. I would ask the authors to make the conditional nature of the BSM preference explicit in the abstract and to include the SM+PC' comparison in the main model-comparison table. The use of local-modal evidence for model-level Bayes factors is a correctable presentation issue, and the Gaussian-likelihood approximation should be checked against the full likelihood at least for the decisive comparisons."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The one thing you should know: this paper has real new results, and its BSM claim comes with an honest caveat. The new three-particle hard-scattering kernels for the full 20-operator WET basis and the first LO inclusive nonleptonic width are genuinely novel. The paper is worth reading for those calculations alone.\n\nThe analytic core is solid. They reproduce the two-particle NLO kernels from Ref. [28], check z_c→0 limits against charmless decays, and explain the factor-1/Nc difference from Ref. [10] as a basis choice. That is exactly the kind of cross-check that makes you trust the new results. The phenomenological analysis is transparent: Bayesian fits with the EOS code, released data, documented mode separation, and a clear picture that each BSM model has two modes. The lifetime penalty is crude but honestly described as a volume constraint; the Gaussian approximation to the experimental likelihood is shown in Fig. 4 and acknowledged.\n\nThe real soft spot is the power-correction prior. The SM+PC' fit, with δ_P and δ_V allowed down to −30%, fits the data perfectly and has larger evidence than any BSM model. The authors argue those corrections exceed the Ref. [21] estimates by two orders of magnitude. That argument is reasonable, but it rests on an external estimate, not on anything derived in this paper. The conclusions state this plainly: BSM models are favored over the SM, but not over the unconstrained power-correction hypothesis. So the paper is internally consistent; it just leaves the decisive premise borrowed from elsewhere.\n\nMinor caveat: fixing LCDAs and decay constants likely shifts the quantitative bounds a bit, but that is not the central hinge.\n\nWho this is for: anyone working on class-I nonleptonic B decays, QCDF, or WET constraints. The new kernels will be cited. It deserves a serious referee — I would send it out, and expect the referee to push on the power-correction assumption but not on the core calculations.","headline":"New three-particle kernels and inclusive width are genuine, but the BSM conclusion rests on the power-correction prior — a limitation the authors themselves flag.","tokens_in":40903,"tokens_out":1797,"would_cite":true,"duration_ms":19803,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["81V15","81V05"],"pacs":["13.25.Hw","12.15.Mm","11.30.Hv"],"model":"deepseek-v4-flash","headline":"This paper argues that the Standard Model cannot describe four nonleptonic B-meson decay rates simultaneously, and that a Weak Effective Theory with four new-physics operators accounts for the data with decisive Bayes factors.","keywords":["b to c anti-u q decays","QCD factorization","class-I nonleptonic B decays","weak effective theory","hard-scattering kernels","B-meson lifetime","Bayesian fits","new physics beyond the Standard Model"],"falsifier":"A direct lattice QCD calculation of any of the four branching ratios $\\mathcal{B}(\\bar{B}_s\\to D_s^+\\pi^-)$, $\\mathcal{B}(\\bar{B}_s\\to D_s^{*+}\\pi^-)$, $\\mathcal{B}(\\bar{B}^0\\to D^+K^-)$, or $\\mathcal{B}(\\bar{B}^0\\to D^{*+}K^-)$ that agrees with the Standard Model prediction at the percent level, together with a precision determination of the related $B\\to D^{(*)}$ form factors, would remove the statistical tension and imply that the new-physics fits are an artifact of underestimated power corrections","tokens_in":1561,"feed_emoji":"🔭","tokens_out":2223,"duration_ms":70762,"temperature":0.7,"pith_summary":"The paper studies the class-I nonleptonic decays $\\bar{B}_s^0\\to D_s^{(*)+}\\pi^-$ and $\\bar{B}^0\\to D^{(*)+}K^-$ within the Weak Effective Theory up to dimension six. It provides the first complete set of three-particle hard-scattering kernels at leading order in $\\alpha_s$ for the full operator basis, and the first leading-order calculation of the inclusive nonleptonic $B$-meson width for the full set of $b\\to c\\bar{u}q$ operators. A global Bayesian fit, varying up to six effective couplings simultaneously, finds that the Standard Model alone fails badly: $\\chi^2=26.69$ for four degrees of freedom, corresponding to $p=2\\cdot 10^{-5}$. Every four-operator and six-operator new-physics model is decisively preferred over the Standard Model, with Bayes factors from $1.5\\cdot 10^3$ to $3.4\\cdot 10^5$, and the four-operator models are strongly preferred over the six-operator models. The authors stress that a model with power corrections of order $-20\\%$ to $-30\\%$ also fits perfectly, so the case for new physics hinges on the true size of those corrections.","feed_headline":"Four B-meson decay rates challenge the Standard Model","feed_subtitle":"A global WET fit with up to six couplings is decisively preferred over the SM, but hinges on the size of power corrections.","key_machinery":"The load-bearing object is the QCD-factorization formula for class-I decays, $\\langle Q_i\\rangle = \\sum_j F_j^{B\\to D^{(*)}}(m_P^2)\\int_0^1 du\\, T_{ij}(u,\\mu)\\Phi_P(u,\\mu)+O(\\Lambda_{\\rm QCD}/m_b)$, which separates short-distance physics in the hard-scattering kernels $T_{ij}(u,\\mu)$ from the nonperturbative $B\\to D^{(*)}$ form factors and the light-meson light-cone distribution amplitudes $\\Phi_P(u)$. The paper uses a Fierz-transformed BMU operator basis for the analytic amplitude calculations and the Bern basis for the lifetime and fits, connecting them through a next-to-leading-order basis change that includes evanescent operators. The new three-particle contributions are organized by the twist-3 and twist-4 light-cone distribution amplitudes $\\Phi_{3;P}$ and $\\Phi_{4;P}$, and the inclusive width constraint comes from a tree-level calculation of the cut diagram for $b\\to c\\bar{u}q$ interference.","core_discovery":"The paper establishes the first complete Weak Effective Theory description of the class-I decays $\\bar{B}^0_{(s)}\\to D^{(*)+}_{(s)}P^-$. It recalculates the two-particle hard-scattering kernels at next-to-leading order in $\\alpha_s$ for all twenty operators, confirming the literature, and computes the three-particle ($q\\bar{q}g$) hard-scattering kernels at tree level for the full WET basis for the first time. It also computes the inclusive nonleptonic $B$-meson decay width at leading order in QCD and leading power in $1/m_b$ for the full set of $b\\to c\\bar{u}q$ operators. In the Bayesian analysis, the Standard Model fit yields $\\chi^2=26.69$ for four effective degrees of freedom ($p=2\\cdot10^{-5}$); all four BSM models are decisively favoured over the SM, with Bayes factors ranging from $1.5\\cdot10^3$ to $3.4\\cdot10^5$, and the four-operator models WET-1 and WET-3 are strongly preferred over the six-operator models WET-2 and WET-4. Each BSM model exhibits two well-separated modes, one closer to the SM point and one farther away, and the paper shows that a more precise measurement of $\\mathcal{B}(\\bar{B}_s\\to D_s^+\\pi^-)$ would distinguish them. The paper also notes that allowing power corrections of about $-20\\%$ to $-30\\%$ removes the tension completely, so the new-physics interpretation is conditional on those corrections being small.","pith_inferences":["If independent determinations of the $B\\to D^{(*)}$ form factors or of the power corrections in QCD factorization become precise enough, the ambiguity between the new-physics solution and the large-power-correction solution could be resolved; a power correction near $-20\\%$ would dissolve the puzzle without BSM.","The two-mode structure seen in all four BSM models suggests an approximate discrete symmetry of the likelihood; combining the exclusive data with the lifetime ratio $\\tau(B^+)/\\tau(B^0)$ and the semileptonic CP asymmetry $a_{\\rm sl}^d$ could break this degeneracy and single out one mode.","The same machinery could be extended to a merged ten-operator scenario, allowing the data to decide whether the four-operator or six-operator structure is preferred, and to other class-I decay modes with different CKM factors, adding independent observables to the global fit.","The paper's leading-order inclusive width calculation is a stepping stone: adding $1/m_b$ and $\\alpha_s$ corrections to the lifetime constraint would sharpen the bounds on the $b\\to c\\bar{u}q$ parameter space in future analyses."],"forward_implications":["The complete set of hard-scattering kernels for all twenty WET operators makes class-I nonleptonic decays usable as a general probe of $b\\to c\\bar{u}q$ new physics, not just a test of the two Standard Model operators.","Simultaneously varying up to six Wilson coefficients yields stronger and more realistic bounds on the $qbcu$ sector than previous one- or two-operator scans, and identifies parameter directions that are currently only constrained by the lifetime.","All four BSM models are decisively favoured over the Standard Model, while the four-operator models WET-1 and WET-3 are strongly preferred over the six-operator models WET-2 and WET-4, narrowing the space of plausible new-physics explanations.","A more precise measurement of $\\mathcal{B}(\\bar{B}_s\\to D_s^+\\pi^-)$ would discriminate between the two modes in every BSM model, because all A-mode predictions undershoot the current central value while all B-mode predictions overshoot it.","The lifetime constraint effectively bounds the volume of the WET parameter space, and the paper identifies combinations of Wilson coefficients for which the lifetime is the dominant constraint rather than the exclusive branching ratios."],"supporting_citations":[{"why":"Establishes the QCD factorization formula for class-I decays, on which the whole analysis is built.","marker":"[10]"},{"why":"Provides the estimates of power corrections in the SM that define the SM+PC priors and the size of the tension to be explained.","marker":"[21]"},{"why":"Computes the two-particle hard-scattering kernels for the full WET basis, which the present paper recalculates and extends.","marker":"[28]"},{"why":"Defines the Bern basis of WET operators and the one-loop anomalous dimension matrix used in the lifetime calculation and fits.","marker":"[7]"},{"why":"Provides the BMU operator basis and the two-loop anomalous dimensions, used for the analytic two-particle kernels and the basis change.","marker":"[30]"},{"why":"Provides the convention for the heavy-to-heavy form factors and the B-to-D({*}) form factor inputs used in the analysis.","marker":"[41]"},{"why":"Supplies the correlated B_{s} to D_s^{(*)} form factors that are sampled as nuisance parameters in the fits.","marker":"[72]"},{"why":"Provides the NNLO result for the two-particle hard-scattering kernels that the two-particle NLO check and the SM baseline rely on.","marker":"[39]"}],"fun_headline_variants":["Global WET fit to B decays finds new physics, but with a caveat","B-meson puzzle: Standard Model disfavored by global WET analysis","First complete WET study of B decays hints at beyond Standard Model","B decay puzzle deepens: new physics preferred but power corrections could explain","Six-coupling WET fit to B decays: new modes and a conditional NP signal"],"cache_read_input_tokens":42752,"weakest_assumption_plain":"The conclusion that new physics is needed hinges on the assumption that the power corrections to the QCD-factorization formula for these decays are only a few percent, as estimated in the literature, rather than the large corrections of order minus thirty percent that would make the Standard Model fit perfectly.","fun_headline_variants_meta":{"raw":{"variants":["Global WET fit to B decays finds new physics, but with a caveat","B-meson puzzle: Standard Model disfavored by global WET analysis","First complete WET study of B decays hints at beyond Standard Model","B decay puzzle deepens: new physics preferred but power corrections could explain","Six-coupling WET fit to B decays: new modes and a conditional NP signal"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000773,"raw_usage":{"total_tokens":3509,"prompt_tokens":1120,"completion_tokens":2389,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":736,"completion_tokens_details":{"reasoning_tokens":2288}},"tokens_in":736,"tokens_out":2389,"duration_ms":15995,"temperature":1.0,"reasoning_tokens":2288,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T20:37:47.312533+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A direct lattice QCD calculation of any of the four branching ratios $\\mathcal{B}(\\bar{B}_s\\to D_s^+\\pi^-)$, $\\mathcal{B}(\\bar{B}_s\\to D_s^{*+}\\pi^-)$, $\\mathcal{B}(\\bar{B}^0\\to D^+K^-)$, or $\\mathcal{B}(\\bar{B}^0\\to D^{*+}K^-)$ that agrees with the Standard Model prediction at the percent level, together with a precision determination of the related $B\\to D^{(*)}$ form factors, would remove the statistical tension and imply that the new-physics fits are an artifact of underestimated power corrections","supporting_citations":[],"review_version":1}