$\mathcal{B}(B\rightarrow\tau\nu)$ measurement with the hadronic FEI at Belle~II

Giovanni Gaudino

REVIEW 3 major objections 5 minor 15 references

$\mathcal{B}(B\rightarrow\tau\nu)$ measurement with the hadronic FEI at Belle~II

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read The Belle II experiment reports 3.0σ evidence for $B^+\to\tau^+\nu_\tau$ with branching fraction $[1.24 \pm 0.41 \pm 0.19]\times10^{-4}$, a new input to the $|V_{ub}|$ determination and new-physics constraints.

desk verdict A readable Moriond summary of the Belle II hadronic-tag B→tau nu result, but the quoted 3-sigma evidence is not supported by the note's own numbers and all substance lives in the full paper. read the letter →

arxiv 2506.03000 v1 pith:R27O3WWQ submitted 2025-06-03 hep-ex

Giovanni Gaudino This is my paper

classification hep-ex

keywords B→τνbranchingfractionhadronictaggingFullEventInterpretationBelleIICKMmatrixelement|Vub|two-dimensionalfitchargedHiggsUpsilon(4S)

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Using $365.4\,\mathrm{fb}^{-1}$ of $\Upsilon(4S)$ data from the Belle II detector, this paper reports evidence at $3.0\sigma$ for the purely leptonic decay $B^+\to\tau^+\nu_\tau$, with measured branching fraction $\mathcal{B}(B^+\to\tau^+\nu_\tau) = [1.24 \pm 0.41\,(\mathrm{stat.}) \pm 0.19\,(\mathrm{syst.})]\times10^{-4}$. The claim matters because this decay is a theoretically clean Standard Model probe: given the lattice-QCD decay constant, it determines the CKM element $|V_{ub}|$ without the hadronic uncertainties of semileptonic decays, and it is directly sensitive to charged-Higgs or other new-physics contributions that can change the rate by up to a factor of four. The paper frames the result as a new experimental input to both the $|V_{ub}|$ determination and new-physics constraints.

What carries the argument

The analysis tags one $B$ meson fully in hadronic decays via the Full Event Interpretation algorithm, then looks for the $\tau$ in the recoil. To separate signal from background it builds a two-dimensional binned probability density function of $E_{\rm extra}^{\rm ECL}$, the calorimeter energy not belonging to the reconstructed final state, and $M^2_{\rm miss}$, the missing-mass squared of the event: signal events populate low $E_{\rm extra}^{\rm ECL}$ and large $M^2_{\rm miss}$, backgrounds the opposite. The PDFs are taken from simulation, corrected bin-by-bin by data-driven reweighting of the photon multiplicity $n_{\gamma\,\mathrm{extra}}$ and validated in sidebands; a simultaneous fit over the four $\tau$ modes floats one common branching fraction and four background yields, with signal yields fixed through $n_{s,k}=2n_{B^+B^-}\epsilon_k\,\mathcal{B}(B^+\to\tau^+\nu_\tau)$.

What would settle it

Apply the identical two-dimensional fit to a high-statistics control decay with a known branching fraction, such as $B^+\to D^0\ell^+\nu_\ell$ reconstructed with the same hadronic tag, and compare the fitted yield with the world average; a significant discrepancy would show that the simulated correlation of the two fit variables is not reliable in the signal region.

Watch

Extended reading notes

Core claim

The central claim is that Belle II, in $365\,\mathrm{fb}^{-1}$ of data, has found evidence for $B^+\to\tau^+\nu_\tau$: $94 \pm 31$ signal events in a simultaneous fit to four $\tau^+$ decay channels ($e^+\nu_e\bar\nu_\tau$, $\mu^+\nu_\mu\bar\nu_\tau$, $\pi^+\bar\nu_\tau$, $\rho^+\bar\nu_\tau$), corresponding to the branching fraction quoted above, with significance $3.0\sigma$ including all systematics. The measurement is presented as a preliminary result; under the Standard Model it translates into $|V_{ub}| = [4.41^{+0.74}_{-0.89}]\times10^{-3}$.

Load-bearing premise

The whole measurement rests on the assumption that the simulated two-dimensional pattern of extra calorimeter energy versus missing mass squared is correct in the signal region after a simple photon-count reweighting; if the pattern is wrong, the fitted signal yield is biased.

Editorial extensions

If this is right

A correct measurement gives a $|V_{ub}|$ determination that is theoretically cleaner than semileptonic $B\to X_u\ell\nu$ decays, with a different experimental systematic budget.
The result adds a new point to the world average for $\mathcal{B}(B\to\tau\nu)$, alongside earlier hadronic-tag measurements from BaBar and Belle.
It sharpens constraints on charged-Higgs models, which can modify $\mathcal{B}(B\to\tau\nu)$ by up to a factor of four.
The demonstrated two-dimensional fit technique provides a template for future Belle II $\tau$ analyses, where larger data and simulation samples will reduce both uncertainties.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Combining this hadronic-tag result with Belle II's semileptonic-tag $B\to\tau\nu$ measurement, which has uncorrelated tag-side systematics, should give a tighter combined branching fraction; the paper does not perform that combination.
Since limited simulation statistics is the largest systematic (13.3%), generating larger simulated samples or using data-driven templates from control channels could cut the total uncertainty before more collision data arrive.
A testable extension is to apply the same tagging and fit chain to $B^+\to\mu^+\nu_\mu$; the ratio of the two branching fractions would isolate lepton-flavor-universality violation from tag-side systematics.
If the central value persists with more data, it pulls the world average above the Standard Model expectation from exclusive $|V_{ub}|$, strengthening the case for a charged-Higgs or similar scalar contribution.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

This note is a Moriond conference summary of the Belle II hadronic-tag B→tau nu measurement already reported in arXiv:2502.04885. There are no new numbers or methods here. The branching fraction, the tagging technique, the fit setup, and the systematic list are all taken from that earlier paper. As a one-page overview it is clear and honest—it explicitly says the full analysis is in Ref. [1] and does not pretend to be more than it is.

What the paper does well: it collects the essential numbers in one place and compares them with previous Belle and BaBar results and with SM expectations. The measurement itself is a serious experimental result: 365 fb^-1 of Belle II data, hadronic FEI tagging, four tau decay modes, sideband validations, and a reasonably complete systematic breakdown. The central value, [1.24 ± 0.41 ± 0.19] x 10^-4, is consistent with the world average and with the SM. That is all real and worth saying.

Now the soft spots. First, the note is not self-contained. Every validation, control plot, and systematic derivation is deferred to Ref. [1]. That is acceptable for a conference note, but it means the arXiv posting alone contains no evidence a referee could check. Second, and more concerning, the significance claim looks internally inconsistent. The abstract and Section 4 say "evidence at 3.0 standard deviations, including systematic uncertainties," but the quoted uncertainties combine to about 1.24/0.45 ≈ 2.8 sigma. The text says they convolved the likelihood profile with a Gaussian of width equal to the total systematic and obtained 3.0 sigma. That is not impossible if the profile is non-parabolic, but the note gives no profile and no explanation for why adding a 15.5% systematic does not degrade the significance. As written, the claim lacks internal support. A reader cannot verify it from this note alone; they would have to consult the full paper or ask the authors for more detail.

There is also a minor labeling issue: calling 3.0σ "evidence" is a bit generous by HEP convention (5σ is discovery, 3σ is borderline), but that is not a serious flaw.

Who is this for? Someone who wants a quick summary of a Belle II result without reading the long paper. That has some utility. But as a standalone submitted paper, it would not be worth referee time because all the substance is elsewhere and the central claim is not backed by the numbers shown. The full analysis in arXiv:2502.04885 is the work that deserves careful review. For this note, my recommendation is: do not send it to peer review as a primary publication. Treat it as a proceedings contribution and point the reader to the full paper.

Referee Report

3 major / 5 minor

Summary. The paper reports a measurement of the branching fraction of B+ → τ+ντ using 365 fb^-1 of Belle II data collected with a hadronic tagging method. A simultaneous two-dimensional fit to E_extra^ECL and M^2_miss in four τ decay channels yields B(B+ → τ+ντ) = [1.24 ± 0.41(stat) ± 0.19(syst)] × 10^-4, with a claimed significance of 3.0σ including systematic uncertainties. The paper is a short conference-style note that defers all fit validation, control plots, and systematic derivations to a separate full analysis, Ref. [1].

Significance. If correct, this measurement provides a new experimental input to the B→τν world average and to determinations of |Vub|, with implications for testing the Standard Model and constraining new physics. The analysis uses a large Belle II data sample and a well-established hadronic tagging technique, and the branching fraction is consistent with previous measurements. The significance and the comparison with SM predictions are the main physics results. However, the brevity of the paper and its reliance on Ref. [1] limit the independent verifiability of the central claim, and there is a potential inconsistency in the reported significance that needs to be resolved.

major comments (3)

[Sec. 4, Eq. (3)] The claimed significance of 3.0σ including systematic uncertainties is not consistent with the quoted branching fraction and uncertainties. Combining the statistical and systematic uncertainties in quadrature gives sqrt(0.41^2 + 0.19^2) = 0.45 × 10^-4, which yields a significance of 1.24/0.45 ≈ 2.7σ against the null hypothesis. The text states that the significance is obtained by convolving the likelihood profile with a Gaussian of width equal to the total systematic uncertainty (15.5%), but for a near-Gaussian likelihood such a convolution should degrade the significance to approximately 2.7σ, not maintain it at 3.0σ. The authors must either correct the reported significance, specify more precisely which systematic uncertainty was used in the convolution (for example, whether normalization-only uncertainties were excluded), or demonstrate that the likelihood profile is sufficiently non-Gaussian to account for the difference. This is a load-bearing point because the abstract and conclusions explicitly claim evidence at 3.0σ.
[Secs. 2 and 3] The paper defers all fit validation, control-sample checks, and systematic derivations to Ref. [1]. The present text does not show the two-dimensional PDF shapes, the sideband validation of E_extra^ECL and M^2_miss, or the fit quality, so the central measurement cannot be independently assessed from the information provided. If this manuscript is intended as a standalone publication, the authors should include the key validation figures and a summary of the fit results; if it is a conference summary of Ref. [1], the paper should explicitly state that status and explain which results are new or preliminary. As written, the supporting evidence for the quoted branching fraction and significance is not contained in the manuscript.
[Sec. 4] The description of the systematic uncertainty propagation is incomplete. For example, the 13.3% uncertainty from limited simulation statistics is estimated by fluctuating the bin contents of the two-dimensional PDFs 200 times, but it is not stated whether these fluctuations are applied coherently across the four tau modes or how they are correlated with the background yields. Similarly, the 5.5% uncertainty from the n_gamma_extra reweighting is assessed with 100 sets of correction factors, but the correlation among the modes is not described. These details are necessary to judge whether the total systematic uncertainty of 15.5% is robust; the current text refers to Ref. [1] for the full description, which is not sufficient for a standalone measurement.

minor comments (5)

[Abstract] The phrase "We presented at Moriond EW 2025" should likely be "We present" for a report of ongoing work, or "We presented" if this is a historical account; please align the tense with the intended publication format.
[Sec. 1] In the text, the number of BB pairs is written as "387 ± 6 × 10^6", which is ambiguous; it should be "(387 ± 6) × 10^6".
[Sec. 4] The test statistic is defined as −2 log(L/L0), which is non-positive under the signal hypothesis; the description of the p-value as the fraction of fits yielding a test statistic "smaller than that observed" is correct for this convention if smaller means more negative, but it may confuse readers. Please clarify the sign convention or use a more standard definition such as q0 = −2 ln(L0/L).
[Sec. 2.1] The correction factors for the tagging efficiency range from 0.6 to 1.1, which is a large correction (up to 40%). A brief comment on why such a large correction is needed and how the control samples constrain it would be useful.
[Fig. 1] The caption refers to yellow and green bands, but the figure as rendered in the arXiv is likely in grayscale; consider using distinct patterns or adding explicit labels to the bands.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the branching-fraction measurement is extracted from a data fit with independent inputs, not defined into itself.

full rationale

This is an experimental measurement paper, not a derivation that assumes its own conclusion. The branching fraction B(B+ -> tau+ nu_tau) is extracted via a simultaneous two-dimensional fit to E_extra_ECL and M^2_miss, with signal yields derived from Eq. (2) using the number of BB pairs, the B+B- fraction f_+-, per-mode efficiencies from simulation, and the floated branching fraction. No equation defines the measured quantity in terms of itself, and no fitted parameter is later renamed as a prediction. The comparison to previous measurements and to SM predictions in Fig. 1 and Eq. (4) is external validation, not an input. The quoted significance procedure convolves the likelihood with a systematic-width Gaussian and uses background-only pseudo-experiments; even if the resulting 3.0 sigma is internally questionable given the quoted uncertainties, that is a statistical-consistency issue, not circular reasoning. The dependence on the companion paper (Ref. 1) and on Belle II calibration notes is normal experimental referencing, and none of these references supplies the target result as an assumption. Therefore the circularity score is 0.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The measurement relies on the fidelity of the Belle II simulation after data-driven corrections and on external inputs: number of Upsilon(4S), f_+-, f_B (for |Vub|). No new entities are postulated.

free parameters (3)

Background yields nb,k per tau mode = Fit results not quoted
Four floating parameters in the simultaneous fit over e, mu, pi, rho modes (Section 3). They are necessary to separate signal from background and are determined from the data.
Hadronic FEI tag efficiency correction factors = 0.6 to 1.1 per Btag mode
Data-driven corrections from B→Xℓν and B→D(*)π control samples (Section 2.1), applied to simulated tag efficiencies. They affect the expected signal yield via Eq. (2).
nγextra multiplicity reweighting factors = 0.8 to 1.2
Bin-by-bin corrections to the photon multiplicity distribution (Section 2.1), used to build the fit PDFs.

assumptions (4)

domain assumption The Belle II detector simulation accurately models the shapes of E_extra_ECL and M^2_miss for signal and backgrounds after data-driven corrections.
The fit PDFs are constructed from simulation (Section 3); only efficiency and multiplicity corrections are applied. Inaccuracy in the simulated correlation would bias the fitted branching fraction.
domain assumption The number of B+B- pairs is given by n_B+B- = n_Y(4S) f_+-, with f_+- from Ref. [4].
Used in Eq. (2) to convert the branching fraction to signal yields. The value f_+- = 0.5113 with uncertainties is an external input.
domain assumption The background composition (continuum, tau+tau-, BB) is correctly modeled by Monte Carlo simulation.
Backgrounds are constrained by off-resonance data and control samples (Section 1), but their shapes are from simulation.
domain assumption The lattice QCD value f_B = 190.0 ± 1.3 MeV from FLAG [3] is correct.
Used only for the |Vub| extraction in Eq. (4), not for the main measurement. Included for completeness.

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Cite this review

Pith. "Pith review of $\mathcal{B}(B\rightarrow\tau\nu)$ measurement with the hadronic FEI at Belle~II." pith.science (2026). https://pith.science/paper/R27O3WWQ

@misc{pith2026250603000,
  author       = {Pith},
  title        = {Pith review of: $\mathcalB(B\rightarrow\tau\nu)$ measurement with the hadronic FEI at Belle~II},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/R27O3WWQ}},
  note         = {Machine review of arXiv:2506.03000}
}

abstract

We presented at Moriond EW 2025 a measurement of the branching fraction of $B\to\tau\nu$ decays using $(387\pm 6) \times 10^6$ $\Upsilon (4S)$ collected between 2019 and 2022 with the Belle~II detector at the SuperKEKB $e^+e^-$ collider. We reconstruct the accompanying $B^-$ meson using the hadronic tagging method, while $B\to\tau\nu$ candidates are identified in the recoil. We find evidence for $B\to\tau\nu$ decays at 3.0 standard deviations, including systematic uncertainties. The measured branching fraction is $\mathcal{B}(B\rightarrow\tau\nu) = [1.24 \pm 0.41~\text{(stat.)} \pm 0.19~\text{(syst.)}] \times 10^{-4}$

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Reference graph

Works this paper leans on

15 extracted references · 9 canonical work pages

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

[1] [1]

Measurement of B+ → τ +ντ branching fraction with a hadronic tagging method at Belle II

I. Adachi et al. [Belle II Collaboration], “Measurement of B+ → τ +ντ branching fraction with a hadronic tagging method at Belle II”, arXiv:2502.04885 [hep-ex]

work page arXiv

[2] [2]

Review of Particle Physics

S. Navas et al. [Particle Data Group], “Review of Particle Physics”, Phys. Rev. D 110, no.3, 030001 (2024), doi:10.1103/PhysRevD.110.030001

doi:10.1103/physrevd.110.030001 2024

[3] [3]

FLAG Review 2024

Y. Aoki et al. , “FLAG Review 2024”, arXiv:2411.04268 [hep-lat]

arXiv 2024

[4] [4]

Averages of b-hadron, c-hadron, and τ -lepton properties as of 2023,

Sw. Banerjee et al., “Averages of b-hadron, c-hadron, and τ -lepton properties as of 2023,” arXiv:2411.18639 [hep-ex]

arXiv 2023

[5] [5]

Charged-Higgs phenomenology in the aligned two-Higgs- doublet model

M. Jung, A. Pich and P. Tuz´ on, “Charged-Higgs phenomenology in the aligned two-Higgs- doublet model”, JHEP 11, 003 (2010), doi:10.1007/JHEP11(2010)003

work page doi:10.1007/jhep11(2010)003 2010

[6] [6]

Explaining B → Dτ ν, B → D∗τ νand B → τ νin a 2HDM of type III

A. Crivellin, C. Greub and A. Kokulu, “Explaining B → Dτ ν, B → D∗τ νand B → τ νin a 2HDM of type III”, Phys. Rev. D 86, 054014 (2012), doi:10.1103/PhysRevD.86.054014

work page doi:10.1103/physrevd.86.054014 2012

[7] [7]

Update of the global electroweak fit and constraints on two-Higgs-doublet models

J. Haller et al., “Update of the global electroweak fit and constraints on two-Higgs-doublet models”, Eur. Phys. J. C 78, no.8, 675 (2018), doi:10.1140/epjc/s10052-018-6131-3

doi:10.1140/epjc/s10052-018-6131-3 2018

[8] [8]

Evidence of B+ → τ +ν decays with hadronic B tags

J. P. Lees et al. [BABA RCollaboration], “Evidence of B+ → τ +ν decays with hadronic B tags”, Phys. Rev. D 88, 031102 (2013), doi:10.1103/PhysRevD.88.031102

work page doi:10.1103/physrevd.88.031102 2013