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Future LHCb and Belle II fits of B→D(∗)τν decays should share Wilson coefficients and form-factor parameters inside one likelihood, not be averaged after separate fits.

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2026-08-02 16:58 UTC pith:T4JPPE4O

load-bearing objection A useful, honest sensitivity study showing joint likelihood fits beat post-fit sums for b→cτν EFT, but the 'necessary' claim overreaches and the bias demo changes two variables at once. the 3 major comments →

arxiv 2604.00735 v1 pith:T4JPPE4O submitted 2026-04-01 hep-ex

Joint LHCb--Belle II Prospects to Constrain New Physics in Bto D^((*))τν

Johannes Albrecht , Florian Bernlochner , Marco Colonna , Lorenz G\"artner , Abhijit Mathad , Biljana Mitreska , Markus Prim , Ilias Tsaklidis This is my paper
classification hep-ex
keywords B→D(∗)τν decayssemileptonic b→cτν transitionslepton flavour universalityR(D) and R(D*)Wilson coefficientsweak effective theorycombined likelihood fitform-factor systematics
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The persistent hint of new physics in B→D(∗)τν decays will only become interpretable if future LHCb and Belle II measurements are combined in a way that respects their shared theory inputs. This paper argues that combining them inside a single likelihood—where the same Wilson coefficients and the same hadronic form-factor parameters are floated for every channel—reduces model-induced bias and improves sensitivity relative to the common practice of combining separately profiled fits. It demonstrates this with event-by-event reweighting, so that non-standard decay dynamics deform the reconstructed templates coherently without rerunning detector simulation. In projected 2030 and 2040 scenarios, the joint fit tightens constraints on scalar, right-handed vector, and tensor couplings, and a toy example shows that summing independently profiled likelihoods can produce spurious shifts in the inferred couplings when channels use different form-factor parametrisations.

Core claim

The paper establishes that a joint likelihood fit is not merely advantageous but necessary for a well-defined effective-field-theory interpretation of b→cτν data. Sharing a common set of B→D(∗) form-factor parameters across channels and experiments ensures that categories with strong hadronic sensitivity cannot profile away discrepancies using different nuisance directions, which would otherwise masquerade as short-distance effects. The combined sensitivity comes largely from the intersection of degeneracy directions across D and D∗ final states and across different τ decay modes, rather than from any single rate-dominated input. By contrast, a post-fit sum of independently profiled likeliho

What carries the argument

The central mechanism is a single binned likelihood in which every analysis channel shares one vector of Wilson coefficients and one set of hadronic form-factor parameters as common nuisance parameters. Theory dependence enters through event-by-event reweighting: each simulated event carries a weight equal to the ratio of the differential decay rate at the tested parameters to that at the nominal simulation point, so acceptance, resolution, and template shapes deform coherently without regenerating detector simulation. The comparison object is a 'post-fit sum' built by adding independently profiled single-channel likelihoods, which the paper argues need not correspond to any globally consist

Load-bearing premise

The numerical results assume that matching the projected total fractional uncertainty on R(D(∗)) to a single effective Poisson yield reproduces the information content of a future binned likelihood, while the paper explicitly does not model bin-to-bin or channel-to-channel systematic correlations; if those correlations differ from this mapping, the quoted sensitivity gains and the combined-versus-post-fit comparison could change.

What would settle it

Take the full experimental likelihoods (with explicit correlated systematics) for current LHCb and Belle II measurements of R(D) and R(D∗) and perform both a joint fit and a post-fit sum for the same Wilson coefficients. If the post-fit sum yields contours and best-fit points as tight and unbiased as the joint fit for realistic systematics, the claim that a joint likelihood is necessary would be refuted; if the joint fit remains visibly tighter and free of displaced minima, the claim is supported.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Future joint LHCb–Belle II EFT interpretations of B→D(∗)τν should be constructed as one likelihood with shared Wilson coefficients and shared form-factor nuisance parameters, not as averages of independent fits.
  • Channels with strong normalisation handles, such as the muonic normalisation modes, calibrate nuisance directions that would otherwise mask non-standard contributions elsewhere, so sharing form factors gives sensitivity gains beyond simple event-count scaling.
  • Interpreting different channels with different form-factor parametrisations and then summing can produce artificial shifts of the inferred Wilson coefficients; a common parametrisation and a shared nuisance manifold avoids this artefact.
  • With CP-averaged observables alone, imaginary parts of Wilson coefficients remain weakly constrained and carry an approximate Im(C)→−Im(C) ambiguity; CP-odd observables such as CP asymmetries or signed triple-product correlations are needed to break it.
  • Because detector-specific uncertainties are largely uncorrelated between LHCb and Belle II, publishing portable, morphable likelihoods with explicit shared hadronic parameters would let future global combinations proceed without repeating detector simulation.

Where Pith is reading between the lines

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

  • A direct test of the paper's central claim: using the existing LHCb and Belle II likelihoods, a joint fit should yield visibly tighter contours and unbiased best-fit points relative to a post-fit sum; if the two strategies agree for realistic systematics, the 'necessary' part of the claim would weaken.
  • The same shared-nuisance logic should extend to other shared theory inputs beyond the form factors discussed—such as B→D∗∗ feed-down parameters and common background model couplings—where correlated treatment could yield comparable bias reductions.
  • If the effective-yield mapping from total uncertainty to a Poisson rate does not reproduce the bin-to-bin and channel-to-channel correlations of a real systematics-dominated measurement, the quoted contour sizes could be optimistic, although the qualitative comparison between combined and post-fit strategies would remain testable.
  • The morphable-likelihood strategy could be ported to other flavour anomalies where theory inputs are shared across experiments, such as b→sℓℓ or B→Kνν modes, where the same bias arguments would apply.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. This paper presents a sensitivity study of a combined extraction of WET Wilson coefficients in B→D(*)τν decays using simplified LHCb- and Belle II-like template configurations. The authors introduce REDIST, a pyhf/HISTFACTORY-based likelihood that uses HAMMER event-by-event reweighting to propagate changes in Wilson coefficients and form-factor parameters through the detector response. They compare a simultaneous multi-channel, multi-dataset fit with a post-fit sum of independently profiled likelihoods, and claim that the former reduces model-induced biases and improves sensitivity. The paper includes projections for 2030 and 2040 benchmark scenarios and a toy demonstration of bias when different hadronic parameterizations are used in a post-fit combination.

Significance. If the central claims hold, the paper provides a useful and timely argument for future joint LHCb–Belle II EFT fits of b→cτν transitions, and for publishing portable, morphable likelihoods with explicit shared hadronic nuisance parameters. The REDIST architecture is a practical contribution, and the paper is commendably explicit about its simplifications (§5.5). The qualitative message that shared hadronic parameters and Wilson coefficients should be treated in a single likelihood is credible. However, the strongest conclusion that a joint likelihood fit is 'necessary' is not yet supported by the numerical evidence, because the main bias demonstration confounds the combination rule with a change of hadronic model.

major comments (3)
  1. [Section 5.3 (Fig. 5)] The bias demonstration changes two variables at once. The Asimov data use BLPRXP; the post-fit sum interprets the hadronic-τ channels with BGL while the combined fit keeps BLPRXP. Thus the displaced minimum in the post-fit sum may be due entirely to the model mismatch, not to independent profiling. A control in which both combination strategies use the same parameterization (and ideally a second control using BGL for both) is needed to isolate the effect. Without this, the paper does not establish that joint fitting is 'necessary'; it shows that inconsistent hadronic models can bias a post-fit combination.
  2. [Eq. (6) / Section 5.5] The effective-yield calibration is load-bearing because every contour and interval in Section 5 is derived from it. Matching 1/√N_sig to the projected total fractional uncertainty on R(D(*)) folds statistical and systematic components into Poisson counting and assumes the binned template likelihood captures the full correlation structure of future measurements. The paper explicitly declines to model bin-to-bin and channel-to-channel systematic correlations in Section 5.5. I recommend either validating this mapping or presenting the quantitative projections with a clear caveat that the quoted gains and bias magnitudes are conditional on this proxy.
  3. [Section 6 / Abstract] The conclusion that a joint likelihood fit is 'necessary for a well-defined EFT interpretation' exceeds the evidence. The demonstrated advantage is conditional on the effective-yield mapping and on the specific scenario in which the post-fit sum uses an inconsistent hadronic model. If the control suggested above is provided and confirms the advantage, the claim can be restored; otherwise the conclusion should be softened to 'advantageous' or 'strongly preferred'.
minor comments (4)
  1. [Eq. (6)] Typographical: use 1/√N_sig rather than '1pNsig'; more importantly, clarify explicitly that N_sig is an effective constraining power, not a literal event count.
  2. [Fig. 5] The axis label '2 logL' should be 'Δ(2 log L)' to match the text and the usual notation for profile-likelihood differences.
  3. [Section 1] The tool name 'ROOHAMMERMODEL' in the Introduction should be 'RooHammerModel' to match the reference and standard spelling.
  4. [Table 1] The notation 'B0(+)->D−(0)' is confusing; consider using standard charge/conjugate notation (e.g., B→D or B+→D0) consistently.

Circularity Check

1 steps flagged

Bias demonstration in §5.3 is a constructed illustration whose output is the injected parameterization mismatch; the sensitivity projection itself is not circular.

specific steps
  1. other [Section 5.3, Figure 5; conclusion in Section 6]
    "An SM-injected Asimov dataset is generated using the nominal BLPRXP form-factor model [36]. In the interpretation step, the hadronic-τ categories are instead described with a BGL parameterisation [33, 34], while the remaining channels retain BLPRXP. Residual mismodelling that cannot be absorbed by profiling then pulls the best-fit short-distance hypothesis; in this example Re(CVR) provides an efficient lever arm... The post-fit sum inherits the resulting misalignment as an apparent displacement of the combined minimum."

    The toy varies combination rule and hadronic model simultaneously: data are generated with BLPRXP, the post-fit interpretation switches the hadronic-τ channels to BGL, while the combined fit keeps BLPRXP. The post-fit minimum displacement is therefore the direct image of the injected parameterization mismatch, not an independent consequence of separate profiling. Since §5.1 states the two strategies coincide when profiling over an identical nuisance manifold, the missing same-model post-fit control means the conclusion that a joint likelihood is 'necessary' is built into the construction rather than demonstrated. The sensitivity contours and external benchmarks are independent; only the bias/necessity claim is circular.

full rationale

The numerical sensitivity study is largely self-contained: the NP injection point is taken from an external global fit [19], the benchmark uncertainties from Refs. [50,51] enter as inputs through Eq. (6), and the combined-fit contours and intervals are computed from a dedicated binned likelihood with HAMMER reweighting. No fitted parameter is renamed as a prediction, and no load-bearing uniqueness claim is imported from the authors' prior work. The only element that reduces to its own construction is the §5.3 bias toy: it is explicitly labeled an illustration, but the abstract and Section 6 promote it to evidence that sharing form-factor parameters 'reduces model-induced biases' and that a joint fit is 'necessary.' Because the post-fit sum is forced to use a different hadronic parameterization (BGL) while the data and the combined fit use BLPRXP, the observed bias is determined by the setup rather than by the profiling strategy. This makes the 'necessary' claim over-supported, while the central sensitivity projection and the framework description retain independent content, so the circularity is partial rather than total.

Axiom & Free-Parameter Ledger

2 free parameters · 6 axioms · 0 invented entities

The central claim rests on WET assumptions, form-factor parameterisation choices, external precision projections, and the effective-yield calibration of Eq. (6). No new physical entities (particles, forces, dimensions) are postulated. The main free input is the benchmark precision mapping, and the main domain assumptions are about the validity of reweighting and the form-factor models.

free parameters (2)
  • Effective signal yields N_sig per benchmark channel = Not quoted; set via Eq. (6) so that 1/√N_sig equals the projected relative R(D(*)) uncertainties in Table 2 (2.0–4.4% at
    Calibrates all sensitivity contours and intervals; replaces full statistical+systematic projections with Poisson-equivalent sample sizes, which is the weakest quantitative link in the study.
  • Shared form-factor nuisance parameters α (signal BLPRXP; D** feed-down BLR) = External/lattice central values with Gaussian constraints; exact values not given in the paper.
    Profiled in every fit and explicitly shared across channels; the claimed improvement of the combined fit is largely due to how these are treated, so the results depend on their assumed priors.
axioms (6)
  • domain assumption New physics is restricted to the τ sector; e/μ modes are SM-like, and no right-handed neutrinos are introduced (Eq. 1 and footnote 1, Section 2).
    Defines the parameter space of the fit; if right-handed neutrinos or modified e/μ couplings are present, the Wilson-coefficient interpretation changes.
  • ad hoc to paper The Standard Model Wilson coefficient is fixed to its expected value because it is very well constrained by other modes (Section 5.1).
    Avoids scanning a parameter that could absorb NP shifts; reasonable but a priori and not validated in the paper.
  • domain assumption HAMMER event-by-event reweighting of SM-generated fully simulated events correctly propagates NP Wilson-coefficient changes through acceptance, resolution, and reconstructed template shapes (Section 3, Eq. 3).
    Central to the morphing method; if reweighting misses efficiency or mass-window effects, the sensitivity study is optimistic.
  • standard math Asimov datasets and the asymptotic Wilks mapping Δχ²=2.30 give reliable 68% confidence regions for these binned likelihoods (Section 5.1).
    Standard, but requires regularity and sufficient statistics; no ensemble coverage checks are shown.
  • domain assumption BLPRXP is used as the nominal truth form-factor model, and BGL in §5.3 represents a realistic alternative parameterisation mismatch.
    The bias demonstration depends on this choice; with different priors or truncations the induced shift could be smaller or larger.
  • domain assumption Lattice-QCD anchored form-factor normalisations and Gaussian constraints on D** feed-down parameters are valid external inputs (Section 4, Refs. [37,38,42]).
    The fits rely on external determinations rather than deriving them; incorrect constraints would shift the intervals.

pith-pipeline@v1.3.0-alltime-deepseek · 18505 in / 15342 out tokens · 142434 ms · 2026-08-02T16:58:01.131759+00:00 · methodology

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read the original abstract

Semileptonic $b\to c\tau\bar{\nu}_{\tau}$ decays are powerful probes of non-Standard-Model effects within an effective-field-theory (EFT) framework, but fully exploiting them in current and future data demands combinations that maximise sensitivity while controlling biases from Standard-Model-based modelling and from theory inputs that are shared, and therefore correlated, across analyses in different experiments. We present a first sensitivity study of a combined extraction of Wilson coefficients in $\bar{B}\to D^{(*)}\tau\bar{\nu}_{\tau}$ decays using LHCb- and Belle~II-like analysis configurations. Detector simulations for signal and backgrounds are typically generated under Standard Model assumptions; if non-SM contributions are present, this can bias the fitted Wilson coefficients. In addition, hadronic inputs such as form-factor parameters of signal and background components are common across analyses, requiring a consistent treatment of fully correlated effects in combinations. To avoid repeating large-scale detector simulation for each EFT hypothesis, we use event-by-event reweighting to map simulated samples to arbitrary combinations of Wilson coefficients. We then compare a simultaneous fit across multiple $\bar{B}\to D^{(*)}\tau\bar{\nu}_{\tau}$ channels and datasets with a combination based on post-fit averages. Sharing Wilson coefficients and common form-factor parameters in the simultaneous fit reduces model-induced biases and improves sensitivity relative to independent fits, providing a robust and scalable strategy for precision EFT constraints in $b\to c\tau\bar{\nu}_{\tau}$ transitions using forthcoming LHCb and Belle~II datasets.

Figures

Figures reproduced from arXiv: 2604.00735 by Abhijit Mathad, Biljana Mitreska, Florian Bernlochner, Ilias Tsaklidis, Johannes Albrecht, Lorenz G\"artner, Marco Colonna, Markus Prim.

Figure 1
Figure 1. Figure 1: Distributions of the reconstructed squared momentum [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: LHCb-like template projections arranged by channel (rows) and observable (columns). For [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Belle II-like template projections arranged by category (rows) and [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: 68% confidence regions in the complex planes of (top) CSL , (middle) CVR , and (bottom) CT for the 2030 benchmark. The star indicates the injected point; the SM point at (0,0) is shown for reference in the NP-injected case [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: illustrates this with a toy example. An SM￾injected Asimov dataset is generated using the nominal BL￾PRXP form-factor model [36]. In the interpretation step, the hadronic-τ categories are instead described with a BGL pa￾rameterisation [33, 34], while the remaining channels retain BLPRXP. Residual mismodelling that cannot be absorbed by profiling then pulls the best-fit short-distance hypothesis; in this ex… view at source ↗
Figure 6
Figure 6. Figure 6: Projected combined-fit 68% confidence regions for the 2030 (orange) and 2040 (teal) benchmark scenarios in the complex planes of (left) CSL , (middle) CVR , and (right) CT . The star indicates the injected point; the SM point at (0,0) is shown for orientation in the NP-injected case [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗

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Forward citations

Cited by 1 Pith paper

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Reference graph

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