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arxiv: 2606.22215 · v1 · pith:LMXV6TQ6new · submitted 2026-06-20 · ✦ hep-ex

Accelerating Discovery: Model-Agnostic Likelihoods for the Reinterpretation of Particle Physics Results and their Application to the Belle II B⁺to K⁺νbar{ν} Measurement

Lorenz G\"artner This is my paper

Pith reviewed 2026-06-26 10:44 UTC · model grok-4.3

classification ✦ hep-ex
keywords reinterpretationmodel-agnostic likelihoodsparticle physicsBelle IIB to K nu nubarreweighting methodnew physics constraintsopen science
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The pith

Reweighting joint distributions by theory prediction ratios produces model-agnostic likelihoods from existing particle physics results.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper presents a method for reinterpreting particle physics experimental results under alternative theoretical models without performing a full reanalysis. It works by reweighting the joint distribution of reconstruction and kinematic variables using the ratio of predictions from the new model to the original hypothesis. This produces updated templates that maintain all correlations and systematic uncertainties. The approach is validated and applied to the Belle II measurement of B+ to K+ nu nubar, which shows a 2.7 sigma tension with the Standard Model, to constrain new physics parameters in effective theories and search for light particles. Releasing these likelihoods publicly allows theorists to quickly test their models against the data.

Core claim

The central discovery is a reinterpretation technique that starts from a histogram-based likelihood and reweights the joint distribution of reconstruction and kinematic variables according to the ratio of theoretical predictions of alternative to null hypotheses, thereby generating updated templates for any theoretical model while preserving correlations and systematic uncertainties, as shown in its application to the Belle II B+ to K+ nu nubar measurement for both Weak Effective Theory constraints and light new physics searches.

What carries the argument

The reweighting of the joint distribution of reconstruction and kinematic variables according to the ratio of theoretical predictions of alternative to null hypotheses, which generates updated templates from an existing histogram-based likelihood.

If this is right

  • Any theoretical model can have updated templates produced from the original data.
  • Correlations between variables and systematic uncertainties remain preserved in the reweighted distributions.
  • The method enables constraints on Wilson coefficients in Weak Effective Theory from the Belle II result.
  • A search for light new physics in two-body decays B+ to K+ X can be performed using the same likelihoods.
  • Public release of the model-agnostic likelihoods makes experimental data more accessible for theoretical validation.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • This approach could be extended to other collider experiments to speed up model testing across the field.
  • The distributable likelihoods might encourage more experiments to release similar tools, increasing the reuse of data.
  • By reducing computational demands, it allows exploration of a wider range of theoretical parameters than previously feasible.
  • Potential applications include rapid checks of models against multiple datasets simultaneously.

Load-bearing premise

Reweighting the joint distribution by the ratio of theoretical predictions updates the likelihood accurately for alternative hypotheses without needing corrections for differences in acceptance or efficiency between models.

What would settle it

Performing a full reanalysis for an alternative model where efficiency or acceptance varies significantly from the original and comparing the resulting limits or templates to those from the reweighting method would falsify the claim if they disagree substantially.

Figures

Figures reproduced from arXiv: 2606.22215 by Lorenz G\"artner.

Figure 2
Figure 2. Figure 2 [PITH_FULL_IMAGE:figures/full_fig_p028_2.png] view at source ↗
Figure 2.1
Figure 2.1. Figure 2.1: Feynman diagrams for the b → sνν¯ transition. The left diagram is the penguin diagram, while the right diagram is the box diagram. The W bosons are exchanged in both diagrams, while the Z 0 boson is only exchanged in the penguin diagram. The neutrino νl can be any of the three active neutrinos, νe, νµ, or ντ . 14 [PITH_FULL_IMAGE:figures/full_fig_p028_2_1.png] view at source ↗
Figure 2
Figure 2. Figure 2 [PITH_FULL_IMAGE:figures/full_fig_p035_2.png] view at source ↗
Figure 2.2
Figure 2.2. Figure 2.2: Illustration of the variety of shapes of the [PITH_FULL_IMAGE:figures/full_fig_p036_2_2.png] view at source ↗
Figure 2
Figure 2. Figure 2 [PITH_FULL_IMAGE:figures/full_fig_p037_2.png] view at source ↗
Figure 2.3
Figure 2.3. Figure 2.3: Illustration of the variety of shapes of the [PITH_FULL_IMAGE:figures/full_fig_p038_2_3.png] view at source ↗
Figure 3.1
Figure 3.1. Figure 3.1: A schematic view of the SuperKEKB collider complex. Electron and positron [PITH_FULL_IMAGE:figures/full_fig_p043_3_1.png] view at source ↗
Figure 3
Figure 3. Figure 3 [PITH_FULL_IMAGE:figures/full_fig_p043_3.png] view at source ↗
Figure 3.2
Figure 3.2. Figure 3.2: A technical design drawing of the Belle II detector [ [PITH_FULL_IMAGE:figures/full_fig_p044_3_2.png] view at source ↗
Figure 4.1
Figure 4.1. Figure 4.1: This figure illustrates two types of modifiers in [PITH_FULL_IMAGE:figures/full_fig_p067_4_1.png] view at source ↗
Figure 4
Figure 4. Figure 4 [PITH_FULL_IMAGE:figures/full_fig_p067_4.png] view at source ↗
Figure 4
Figure 4. Figure 4 [PITH_FULL_IMAGE:figures/full_fig_p069_4.png] view at source ↗
Figure 4.2
Figure 4.2. Figure 4.2: Expected yields of the custom modifier example for three different parameter [PITH_FULL_IMAGE:figures/full_fig_p070_4_2.png] view at source ↗
Figure 5
Figure 5. Figure 5 [PITH_FULL_IMAGE:figures/full_fig_p074_5.png] view at source ↗
Figure 5.1
Figure 5.1. Figure 5.1: The PDFs of the test statistic, given two different hypotheses. The cho￾sen value of α = 0.05 defines tcut, which separates the rejection region (right) from the acceptance region (left). The integrals of the shaded regions correspond to α and β, re￾spectively. Any hypothesis test involves two types of errors: rejecting H0 when it is true (Type I error, probability α), and failing to reject H0 when H1 is… view at source ↗
Figure 5
Figure 5. Figure 5 [PITH_FULL_IMAGE:figures/full_fig_p075_5.png] view at source ↗
Figure 5.2
Figure 5.2. Figure 5.2: The PDFs of the test statistic, given two different hypotheses. The chosen value of α = 0.05 defines tcut, which separates the rejection region from the acceptance region. The observed value of the test statistic tobs defines the lower bound of the inte￾gration for the P-value. some model. The alternative hypothesis H1 describes the case where background only is observed (H1 = b). A P-value can be define… view at source ↗
Figure 5
Figure 5. Figure 5 [PITH_FULL_IMAGE:figures/full_fig_p084_5.png] view at source ↗
Figure 5.3
Figure 5.3. Figure 5.3: Neyman construction of confidence intervals. The confidence interval is con [PITH_FULL_IMAGE:figures/full_fig_p085_5_3.png] view at source ↗
Figure 2
Figure 2. Figure 2 [PITH_FULL_IMAGE:figures/full_fig_p097_2.png] view at source ↗
Figure 7
Figure 7. Figure 7 [PITH_FULL_IMAGE:figures/full_fig_p100_7.png] view at source ↗
Figure 7.1
Figure 7.1. Figure 7.1: The null histogram yields, reweighted to the benchmark point in [PITH_FULL_IMAGE:figures/full_fig_p100_7_1.png] view at source ↗
Figure 7
Figure 7. Figure 7 [PITH_FULL_IMAGE:figures/full_fig_p101_7.png] view at source ↗
Figure 7.2
Figure 7.2. Figure 7.2: Both the null/ [PITH_FULL_IMAGE:figures/full_fig_p101_7_2.png] view at source ↗
Figure 7.3
Figure 7.3. Figure 7.3: The bin-integrated null/SM (blue) and alternative/BSM (red) predictions for the differential branching ratio dB(B → Kνν¯)/dq2 . tions of Wilson coefficients. Hence, each linear combination is represented as a positive real-valued number. Their prior is chosen as the uncorrelated product of uniform distri￾butions with support 5 < |CVL + CVR| < 20, 0 < |CSL + CSR| < 15, 0 < |CTL| < 15. (7.13) These ranges … view at source ↗
Figure 7.4
Figure 7.4. Figure 7.4: The null joint number density, showing the 8 bins of the reconstruction variable [PITH_FULL_IMAGE:figures/full_fig_p103_7_4.png] view at source ↗
Figure 7
Figure 7. Figure 7 [PITH_FULL_IMAGE:figures/full_fig_p103_7.png] view at source ↗
Figure 7
Figure 7. Figure 7 [PITH_FULL_IMAGE:figures/full_fig_p104_7.png] view at source ↗
Figure 7.5
Figure 7.5. Figure 7.5: The marginalized posterior distributions, obtained by [PITH_FULL_IMAGE:figures/full_fig_p105_7_5.png] view at source ↗
Figure 2
Figure 2. Figure 2 [PITH_FULL_IMAGE:figures/full_fig_p106_2.png] view at source ↗
Figure 7
Figure 7. Figure 7 [PITH_FULL_IMAGE:figures/full_fig_p107_7.png] view at source ↗
Figure 7.6
Figure 7.6. Figure 7.6: Both the null/SM (blue lines) and alternative/BSM (red lines) B → K∗ νν¯ datasets, according to the pure theoretical prediction, after detector resolution smearing and efficiency correction. 93 [PITH_FULL_IMAGE:figures/full_fig_p107_7_6.png] view at source ↗
Figure 7
Figure 7. Figure 7 [PITH_FULL_IMAGE:figures/full_fig_p109_7.png] view at source ↗
Figure 7.7
Figure 7.7. Figure 7.7: The marginal posterior distributions, obtained by [PITH_FULL_IMAGE:figures/full_fig_p110_7_7.png] view at source ↗
Figure 7
Figure 7. Figure 7 [PITH_FULL_IMAGE:figures/full_fig_p111_7.png] view at source ↗
Figure 7.8
Figure 7.8. Figure 7.8: The comparison of the posterior distribution resulting from a model with only [PITH_FULL_IMAGE:figures/full_fig_p112_7_8.png] view at source ↗
Figure 8.1
Figure 8.1. Figure 8.1: The signal-selection efficiencies for the [PITH_FULL_IMAGE:figures/full_fig_p119_8_1.png] view at source ↗
Figure 8.2
Figure 8.2. Figure 8.2: The best-fit yields of the ITA analysis as a function of η(BDT2) × q 2 rec. The off-resonance fit is shown on the left, the on-resonance fit on the right. Pull distributions are shown in the lower panels. Figure taken from Reference [2] [PITH_FULL_IMAGE:figures/full_fig_p120_8_2.png] view at source ↗
Figure 8.3
Figure 8.3. Figure 8.3: The best-fit projection of the ITA analysis onto the q 2 rec variable. Pull distri￾butions are shown in the lower panels. Figure taken from Reference [2]. 106 [PITH_FULL_IMAGE:figures/full_fig_p120_8_3.png] view at source ↗
Figure 8.4
Figure 8.4. Figure 8.4: The best-fit yields of the HTA analysis as a function of η(BDTh). Pull distributions are shown in the lower panels. Figure taken from Reference [2]. The ITA and HTA likelihoods were combined into one likelihood, accounting for the correlations between the systematic uncertainties in the two methods (for details, see section XIV of Reference [2]). The combined likelihood includes 231 nuisance parameters χ… view at source ↗
Figure 8
Figure 8. Figure 8 [PITH_FULL_IMAGE:figures/full_fig_p122_8.png] view at source ↗
Figure 8.5
Figure 8.5. Figure 8.5: The ITA (top) and HTA (bottom) binned joint number densities. The hori￾zontal axis corresponds to the generated q 2 . The vertical axis represents the binning used in the B+ → K+νν¯ analysis [2]. The heatmap shows the weighted signal events. 110 [PITH_FULL_IMAGE:figures/full_fig_p124_8_5.png] view at source ↗
Figure 9
Figure 9. Figure 9 [PITH_FULL_IMAGE:figures/full_fig_p128_9.png] view at source ↗
Figure 9.1
Figure 9.1. Figure 9.1: The marginalized posterior for the Wilson coefficients in [PITH_FULL_IMAGE:figures/full_fig_p129_9_1.png] view at source ↗
Figure 9.2
Figure 9.2. Figure 9.2: Observed and predicted best-fit yields in the [PITH_FULL_IMAGE:figures/full_fig_p130_9_2.png] view at source ↗
Figure 2
Figure 2. Figure 2 [PITH_FULL_IMAGE:figures/full_fig_p132_2.png] view at source ↗
Figure 9
Figure 9. Figure 9 [PITH_FULL_IMAGE:figures/full_fig_p133_9.png] view at source ↗
Figure 9.3
Figure 9.3. Figure 9.3: The marginalized posterior for the Wilson coefficients in [PITH_FULL_IMAGE:figures/full_fig_p134_9_3.png] view at source ↗
Figure 9
Figure 9. Figure 9 [PITH_FULL_IMAGE:figures/full_fig_p135_9.png] view at source ↗
Figure 9.4
Figure 9.4. Figure 9.4: The distribution of the goodness-of-fit test statistic for the [PITH_FULL_IMAGE:figures/full_fig_p136_9_4.png] view at source ↗
Figure 9
Figure 9. Figure 9 [PITH_FULL_IMAGE:figures/full_fig_p138_9.png] view at source ↗
Figure 9.5
Figure 9.5. Figure 9.5: Distribution of the test statistic for the [PITH_FULL_IMAGE:figures/full_fig_p139_9_5.png] view at source ↗
Figure 9.6
Figure 9.6. Figure 9.6: Distribution of the test statistic for the unconstrained [PITH_FULL_IMAGE:figures/full_fig_p139_9_6.png] view at source ↗
Figure 2
Figure 2. Figure 2 [PITH_FULL_IMAGE:figures/full_fig_p140_2.png] view at source ↗
Figure 8
Figure 8. Figure 8 [PITH_FULL_IMAGE:figures/full_fig_p141_8.png] view at source ↗
Figure 10.1
Figure 10.1. Figure 10.1: The predicted differential branching ratio from [PITH_FULL_IMAGE:figures/full_fig_p143_10_1.png] view at source ↗
Figure 10
Figure 10. Figure 10 [PITH_FULL_IMAGE:figures/full_fig_p143_10.png] view at source ↗
Figure 10.2
Figure 10.2. Figure 10.2: Comparison of bin-integrated distributions for the null hypothesis (blue, [PITH_FULL_IMAGE:figures/full_fig_p144_10_2.png] view at source ↗
Figure 10.3
Figure 10.3. Figure 10.3: Marginalized posterior distributions for the [PITH_FULL_IMAGE:figures/full_fig_p146_10_3.png] view at source ↗
Figure 9
Figure 9. Figure 9 [PITH_FULL_IMAGE:figures/full_fig_p147_9.png] view at source ↗
Figure 8
Figure 8. Figure 8 [PITH_FULL_IMAGE:figures/full_fig_p147_8.png] view at source ↗
Figure 10.4
Figure 10.4. Figure 10.4: Observed and predicted best-fit yields in the [PITH_FULL_IMAGE:figures/full_fig_p148_10_4.png] view at source ↗
Figure 10
Figure 10. Figure 10 [PITH_FULL_IMAGE:figures/full_fig_p150_10.png] view at source ↗
Figure 8
Figure 8. Figure 8 [PITH_FULL_IMAGE:figures/full_fig_p150_8.png] view at source ↗
Figure 10.5
Figure 10.5. Figure 10.5: Frequentist 95% confidence-level upper limit on [PITH_FULL_IMAGE:figures/full_fig_p151_10_5.png] view at source ↗
Figure 10
Figure 10. Figure 10 [PITH_FULL_IMAGE:figures/full_fig_p152_10.png] view at source ↗
Figure 10.6
Figure 10.6. Figure 10.6: The distribution of the goodness-of-fit test statistic for the [PITH_FULL_IMAGE:figures/full_fig_p153_10_6.png] view at source ↗
Figure 10
Figure 10. Figure 10 [PITH_FULL_IMAGE:figures/full_fig_p155_10.png] view at source ↗
Figure 10.7
Figure 10.7. Figure 10.7: Distribution of the test statistic for the [PITH_FULL_IMAGE:figures/full_fig_p156_10_7.png] view at source ↗
Figure 11
Figure 11. Figure 11 [PITH_FULL_IMAGE:figures/full_fig_p160_11.png] view at source ↗
Figure 11.1
Figure 11.1. Figure 11.1: The B → Kνν¯ SM differential branching ratio (left) and f+ form factor (right), based on the hadronic parameters from Reference [42] (labelled as BGNS:2014) and from References [45, 46] (labelled as HPQCD+FLAG). The bands represent the uncertainty in the hadronic parameters. The signal MC for the B0 → K∗0 νν¯ and B+ → K∗+νν¯ channels is based on the hadronic parameters from Reference [48]. In this case,… view at source ↗
Figure 11.2
Figure 11.2. Figure 11.2: The B → K∗ νν¯ SM differential branching ratio (left) and A1, A12, V form fac￾tors (right), based on the hadronic parameters from Reference [48] (labelled as BSZ:2015) and from References [130, 131] (labelled as GRvDV:2021+HLMW:2015). The bands repre￾sent the uncertainty in the hadronic parameters. |VtbV ∗ ts| = 0.039 ± 0.001 from exclusive modes [10, 43, 45]. Theoretical uncertainties arise from two ma… view at source ↗
Figure 11
Figure 11. Figure 11 [PITH_FULL_IMAGE:figures/full_fig_p164_11.png] view at source ↗
Figure 11
Figure 11. Figure 11 [PITH_FULL_IMAGE:figures/full_fig_p165_11.png] view at source ↗
Figure 11
Figure 11. Figure 11 [PITH_FULL_IMAGE:figures/full_fig_p166_11.png] view at source ↗
Figure 11
Figure 11. Figure 11 [PITH_FULL_IMAGE:figures/full_fig_p167_11.png] view at source ↗
Figure 11.3
Figure 11.3. Figure 11.3: Signal efficiency as a function of q 2 and cos θ for all channels, determined from the signal region selection. The cos θ distributions are provided for vector mesons only. 155 [PITH_FULL_IMAGE:figures/full_fig_p169_11_3.png] view at source ↗
Figure 11.4
Figure 11.4. Figure 11.4: Post fit distribution from the Asimov fit of the [PITH_FULL_IMAGE:figures/full_fig_p170_11_4.png] view at source ↗
Figure 11.5
Figure 11.5. Figure 11.5: Post fit distribution from the Asimov fit of the [PITH_FULL_IMAGE:figures/full_fig_p171_11_5.png] view at source ↗
Figure 11.6
Figure 11.6. Figure 11.6: Profiled likelihood scan of the Asimov fit for the four signal channels. [PITH_FULL_IMAGE:figures/full_fig_p172_11_6.png] view at source ↗
Figure 11.7
Figure 11.7. Figure 11.7: Correlation matrix of the uncorrelated model resulting from the Asimov fit. [PITH_FULL_IMAGE:figures/full_fig_p173_11_7.png] view at source ↗
Figure 11.8
Figure 11.8. Figure 11.8: Correlation matrix of the isospin correlated model resulting from the Asimov [PITH_FULL_IMAGE:figures/full_fig_p174_11_8.png] view at source ↗
Figure 11.9
Figure 11.9. Figure 11.9: Profiled likelihood scans for the pseudoscalar [PITH_FULL_IMAGE:figures/full_fig_p175_11_9.png] view at source ↗
Figure 11.10
Figure 11.10. Figure 11.10: Correlation matrix of the fully correlated model resulting from the Asimov [PITH_FULL_IMAGE:figures/full_fig_p176_11_10.png] view at source ↗
Figure 11.11
Figure 11.11. Figure 11.11: Profiled likelihood scan for the fully correlated signal strength across all [PITH_FULL_IMAGE:figures/full_fig_p177_11_11.png] view at source ↗
Figure 9
Figure 9. Figure 9 [PITH_FULL_IMAGE:figures/full_fig_p213_9.png] view at source ↗
Figure 9
Figure 9. Figure 9 [PITH_FULL_IMAGE:figures/full_fig_p214_9.png] view at source ↗
Figure 9
Figure 9. Figure 9 [PITH_FULL_IMAGE:figures/full_fig_p215_9.png] view at source ↗
Figure 8
Figure 8. Figure 8 [PITH_FULL_IMAGE:figures/full_fig_p217_8.png] view at source ↗
Figure 10
Figure 10. Figure 10 [PITH_FULL_IMAGE:figures/full_fig_p221_10.png] view at source ↗
Figure 10
Figure 10. Figure 10 [PITH_FULL_IMAGE:figures/full_fig_p222_10.png] view at source ↗
Figure 10
Figure 10. Figure 10 [PITH_FULL_IMAGE:figures/full_fig_p223_10.png] view at source ↗
Figure 10
Figure 10. Figure 10 [PITH_FULL_IMAGE:figures/full_fig_p224_10.png] view at source ↗
Figure 10
Figure 10. Figure 10 [PITH_FULL_IMAGE:figures/full_fig_p225_10.png] view at source ↗
read the original abstract

Experimental results in high-energy physics are inherently hypothesis-dependent, as collider analyses are designed to test specific theoretical frameworks. The proliferation of theoretical models creates a mismatch between the pace of theory development and experimental validation, motivating the reinterpretation of existing results in terms of alternative hypotheses. Existing strategies face limitations: full reanalysis requires enormous computational resources and experimental expertise, while simplified methods sacrifice accuracy by neglecting kinematic variations and systematic uncertainties. This thesis develops, validates, and applies a novel reinterpretation method that preserves statistical rigour while dramatically reducing computational requirements, enabling rapid inference on alternative theoretical parameters through distributable likelihoods. The method reweights the joint distribution of reconstruction and kinematic variables according to the ratio of theoretical predictions of alternative to null hypotheses. Starting from a histogram-based likelihood, this produces updated templates for any theoretical model while preserving correlations and systematic uncertainties. The method is validated through examples and applied to the Belle II $B^+ \to K^+ \nu\bar{\nu}$ measurement ($2.7\sigma$ tension with the Standard Model). Two analyses are presented: a Weak Effective Theory reinterpretation constraining Wilson coefficients, and a light new physics search via ${B^+ \to K^+ X}$ two-body decays. The public release of the resulting model-agnostic likelihoods establishes an important precedent for open science in experimental particle physics. By facilitating rapid theoretical validation, this approach democratizes experimental data access, enhances scientific return on investments, and advances FAIR Data principles in high-energy physics.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The paper claims to develop a reinterpretation method that starts from a histogram-based likelihood and reweights the joint distribution of reconstruction and kinematic variables by the ratio of theoretical predictions (alternative to null hypothesis). This produces updated templates for arbitrary models while preserving correlations and systematic uncertainties. The method is validated on examples and applied to the Belle II B+ → K+ νν̄ measurement (2.7σ SM tension), yielding a Weak Effective Theory analysis constraining Wilson coefficients and a search for light new physics in B+ → K+ X two-body decays. The resulting model-agnostic likelihoods are released publicly to enable rapid theoretical reinterpretation.

Significance. If the central claim holds, the approach would substantially lower the barrier to reinterpretation of experimental results by avoiding full reanalyses, while maintaining statistical rigour. The public release of the likelihoods is a concrete strength that advances open science and FAIR principles in HEP. The application to an existing measurement with observed tension demonstrates immediate utility for both EFT and BSM searches.

major comments (1)
  1. [Abstract] Abstract and method description: the central claim that reweighting the joint distribution by the ratio of theoretical predictions produces accurate updated templates for any model rests on the assumption that these predictions already incorporate all model-dependent differences in acceptance, efficiency, and detector response. The manuscript does not specify whether the theoretical predictions are evaluated at generator level or with full, model-specific simulation; if the former, kinematics-dependent efficiency variations between models would remain uncorrected and the reweighting would be insufficient.
minor comments (2)
  1. The term 'distributable likelihoods' is used in the abstract but not defined or distinguished from standard histogram likelihoods; a brief clarification of the precise output format would aid readers.
  2. Validation examples are mentioned but no quantitative metrics (e.g., pull distributions or coverage tests) are referenced in the abstract; adding a short summary of these metrics in the main text would strengthen the validation section.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their positive evaluation of the work's significance and for the constructive comment on the abstract and method. We address the point below and will revise the manuscript to improve clarity.

read point-by-point responses

  1. Referee: [Abstract] Abstract and method description: the central claim that reweighting the joint distribution by the ratio of theoretical predictions produces accurate updated templates for any model rests on the assumption that these predictions already incorporate all model-dependent differences in acceptance, efficiency, and detector response. The manuscript does not specify whether the theoretical predictions are evaluated at generator level or with full, model-specific simulation; if the former, kinematics-dependent efficiency variations between models would remain uncorrected and the reweighting would be insufficient.

    Authors: We agree that the manuscript does not explicitly state the level at which the theoretical predictions are evaluated. In the method, the ratio is formed from generator-level predictions for the alternative and null hypotheses, with reweighting applied directly to the joint distribution of reconstructed and kinematic variables obtained from the original analysis. This preserves the detector response encoded in the original templates but assumes that efficiency and acceptance variations between models are either negligible or already captured in the ratio for the observables considered. The referee is correct that this assumption requires clarification, particularly for models with substantially different kinematics. We will revise the abstract, method section, and discussion to explicitly note that predictions are generator-level, state the assumption regarding efficiency, and add a limitations paragraph describing the regime of validity (small efficiency variations) and when full simulation would be needed instead. revision: yes

Circularity Check

0 steps flagged

No circularity; method uses independent external theory inputs

full rationale

The paper's central procedure reweights joint distributions of reconstruction and kinematic variables by the ratio of theoretical predictions (alternative/null hypotheses) to produce updated templates. This step is defined in terms of external theoretical predictions, not quantities fitted from the Belle II data or self-referential definitions. No load-bearing steps reduce by construction to inputs via self-citation, fitted parameters renamed as predictions, or ansatz smuggling. The derivation chain remains independent of the target result and relies on external benchmarks for the theory ratios.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available; no explicit free parameters, axioms, or invented entities are described in sufficient detail to populate the ledger.

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