Catalog · Beauty · B009

B009 $\mathcal{B}(B^+\to\tau^+\nu_\tau)$

Leptonic $B+ \to \tau^+ \nu_\tau$ branching fraction

Status REVIEWED VERIFIED Medium Code: NO Priority Low

PDG / equivalent values

Observable	Value	Year	Experiment / source	Provenance
HFLAV Rare B decays, End of December 2025 update	1.12 10^-4 branching fraction	2025	HFLAV Rare B decays, End of December 2025 update	source ↑
PDG 2025 REST API, S041.184	1.09 10^-4 branching fraction	2025	PDG 2025 REST API, S041.184	source ↑
UTfit Standard Model Fit results: Summer 2024	0.865 10^-4 branching fraction	2024	UTfit Standard Model Fit results: Summer 2024	source ↑

Why this constrains the RS scan

This channel probes $b\to u\tau\nu$ charged currents. In the SM it is fixed by $f_B |V_{ub}|$, the charged-$B$ lifetime, and the tau mass; therefore it is a clean place where a new charged current can interfere with the SM amplitude. It is directly relevant to charged-Higgs, $W'$, and leptoquark benchmarks. For warped or anarchic-flavor extensions, it is not part of the current quark $\Delta F=2$ lane, but it would test KK charged-gauge-boson or non-minimal charged-scalar effects in the $b$-to-$u$ current and in the tau-neutrino current.

What's changed since the original paper

Relative to the Csaki--Falkowski--Weiler 2008 flavor baseline (cfw2008\_arxiv0804\_1954.txt), the measurement landscape changed substantially. BaBar published semileptonic-tag and hadronic-tag results in 2010 and 2013; Belle followed with hadronic-tag and semileptonic-tag measurements in 2013 and 2015. Belle II added a hadronic-FEI measurement in 2025, which HFLAV includes in the average while noting that the red Belle II input is not part of the PDG average. On the theory/global-fit side, the sidecar records the UTfit Summer 2024 SM prediction, so the comparison is now driven mainly by $|V_{ub}|$ and global-fit conventions rather than by an unavailable leptonic decay constant.

Validity and model dependence

The experimental average is straightforward, but the constraint is model-dependent. It is robust as a charged-current amplitude test; it is not a generic RS bound unless the model supplies a calculable $b\to u\tau\nu$ matching contribution. A charged scalar, $W'$, or leptoquark can interfere constructively or destructively with the SM, so a one-number exclusion requires the operator normalization and neutrino-flavor assumptions. The SM comparison is global-fit dependent through $|V_{ub}|$, even though the leptonic decay constant input itself is now standard.

Code coverage in this repo

NO. I reran the required coverage greps over quarkConstraints/, qcd/, flavorConstraints/, neutrinos/, yukawa/, warpConfig/, solvers/, scanParams/, and tests/. The broad plan greps find the existing neutral $\Delta F=2$ and $\mu\to e\gamma$ surfaces, but no charged-current leptonic-$B$ observable. Targeted searches for $B\string^+ \to \tau$ , B+ --> tau, tau.*nu, b.*->.*u, charged Higgs, leptoquark, and $W'$ returned no code hits. Docs-only catalog-planning rows were not counted as implementation evidence.

Linked evidence (opens GitHub blob at flavor-catalog-website/2026q2):

Implementation difficulty

MEDIUM. The catalog-level formula is simple and uses standard experimental and lattice/CKM inputs, but production use would require a new charged-current observable and model-specific matching for $W'$, charged-scalar, or leptoquark amplitudes. It should not extend the legacy deltaf2.py path; if promoted, it belongs in the modern constraint surface.

Reason: A live constraint would need a new charged-current leptonic-B observable and model matching to W'/charged-scalar/leptoquark-like amplitudes, but the experimental average and SM inputs are standard and no new QCD RG machinery is expected for the catalog-level formula.

Key references

Process-local snapshots before bibliography consolidation: hflav\_dec2025\_btaunu.txt, pdg2025\_btaunu\_api.txt, utfit\_summer2024\_btaunu.txt, belle2013\_arxiv1208\_4678.txt, belle2015\_arxiv1503\_05613.txt, belleii2025\_arxiv2502\_04885.txt, babar2013\_arxiv1207\_0698.txt, babar2010\_arxiv0912\_2453.txt, and cfw2008\_arxiv0804\_1954.txt.

fallback_value_uncertainty = 1.12 +- 0.19 10^-4 branching fraction

RESOLVED

Match snapshot line 10

L7: Observable: ${\cal B}(B^+ \to \tau^+ \nu_{\tau})$.
L8: 
L9: Experiment | Measurement [10^-4] | Delta chi^2 | Reference | Comments
L10: Average | $1.12 \pm0.19$ | 4.25 | $p=0.37$ (ndf=4) | The PDG uncertainty includes a scale factor.
L11: PDG | $1.09\,^{+0.25}_{-0.24}$ | | pdgLive |
L12: Belle | $0.72\,^{+0.27}_{-0.25} \pm0.11$ | 1.88 | Phys.Rev.Lett. 110, 131801 (2013) | Hadronic tagging method.
L13: Belle | $1.25 \pm0.28 \pm0.27$ | 0.11 | Phys.Rev.D 92, 051102 (2015) | Semileptonic tagging method.

fallback_value_uncertainty = 1.09 +- +0.25/-0.24 10^-4 branching fraction

AMBIGUOUS

Match 1 of 2 snapshot line 12

L9: description: B+ --> tau+ nu_tau
L10: section: Semileptonic and leptonic modes
L11: pdg_values:
L12:   value: 1.09376418135583E-4
L13:   error_positive: 2.46801309137533E-5
L14:   error_negative: 2.36425623126656E-5
L15:   value_text: "(1.09+-0.24)E-4"

Match 2 of 2 snapshot line 15

L12:   value: 1.09376418135583E-4
L13:   error_positive: 2.46801309137533E-5
L14:   error_negative: 2.36425623126656E-5
L15:   value_text: "(1.09+-0.24)E-4"
L16:   scale_factor: 1.178431
L17:   type: OUR AVERAGE
L18:

fallback_value_uncertainty = 0.865 +- 0.041 10^-4 branching fraction

AMBIGUOUS

Match 1 of 2 snapshot line 14

L11: Parameter: B(B\rightarrow\tau\nu) \cdot 10^{4}
L12: Input value: 1.06 \pm 0.19
L13: Full fit: 0.872 \pm 0.041
L14: SM Prediction: 0.865 \pm 0.041
L15: Pull: 1.0
L16: 
L17: Interpretation for this catalog entry:

Match 2 of 2 snapshot line 18

L15: Pull: 1.0
L16: 
L17: Interpretation for this catalog entry:
L18: UTfit quotes the B -> tau nu branching fraction in units of 10^-4. The SM prediction used here is therefore (0.865 +- 0.041) x 10^-4.

fallback_value_uncertainty belle2013_arxiv1208_4678 = 0.72 +- +0.27/-0.25 stat, 0.11 syst 10^-4 branching fraction

RESOLVED

Match snapshot line 14

L11: The Belle analysis uses the full Upsilon(4S) data sample containing 772 x 10^6 BBbar pairs. Events are tagged by reconstructing one B meson in hadronic final states, and B- -> tau- nu_tau-bar candidates are detected in the recoil.
L12: 
L13: The abstract reports evidence with a significance of 3.0 standard deviations including systematic errors and measures
L14: B(B- -> tau- nu_tau-bar) = [0.72^{+0.27}_{-0.25}(stat) +/- 0.11(syst)] x 10^-4.

fallback_value_uncertainty belle2015_arxiv1503_05613 = 1.25 +- 0.28 stat, 0.27 syst 10^-4 branching fraction

RESOLVED

Match snapshot line 14

L11: The Belle analysis uses a data sample of 772 x 10^6 BBbar pairs collected at the Y(4S) resonance. The accompanying B meson is reconstructed in a semileptonic decay and the recoiling B candidate is detected in B^+ -> tau^+ nu_tau.
L12: 
L13: The abstract reports
L14: BR(B^+ -> tau^+ nu_tau) = [1.25 +- 0.28 (stat.) +- 0.27 (syst.)] x 10^-4.

fallback_value_uncertainty belleii2025_arxiv2502_04885 = 1.24 +- 0.41 stat, 0.19 syst 10^-4 branching fraction

RESOLVED

Match snapshot line 15

L12: The Belle II analysis uses (387 +- 6) x 10^6 Upsilon(4S) events collected between 2019 and 2022. It reconstructs the accompanying B- meson with hadronic tagging and identifies B^+ -> tau^+ nu_tau candidates in the recoil.
L13: 
L14: The abstract reports evidence at 3.0 standard deviations, including systematic uncertainties, and measures
L15: B(B^+ -> tau^+ nu_tau) = [1.24 +- 0.41 (stat.) +- 0.19 (syst.)] x 10^-4.

fallback_value_uncertainty babar2013_arxiv1207_0698 = 1.83 +- +0.53/-0.49 stat, 0.24 syst 10^-4 branching fraction

RESOLVED

Match snapshot line 14

L11: The BaBar analysis searches for B+ -> tau+ nu using 467.8 x 10^6 BB pairs collected at the Y(4S), with one B- completely reconstructed in hadronic decay modes. Tau+ modes include e+ nu nu, mu+ nu nu, pi+ nu, and rho+ nu.
L12: 
L13: The abstract reports a 3.8 sigma excess including systematic uncertainties and a branching-fraction central value
L14: B(B+ -> tau+ nu) = (1.83^{+0.53}_{-0.49}(stat.) +/- 0.24(syst.)) x 10^-4.

fallback_value_uncertainty babar2010_arxiv0912_2453 = 1.7 +- 0.80 stat, 0.20 syst 10^-4 branching fraction

RESOLVED

Match snapshot line 14

L11: The BaBar analysis searches for B+ -> l+ nu_l in (458.9 +- 5.1) x 10^6 BBbar pairs, using B+B- events where one B meson is reconstructed as B- -> D0 l- nu X.
L12: 
L13: The abstract reports, using the Feldman-Cousins method,
L14: B(B+ -> tau+ nu) = (1.7 +- 0.8 +- 0.2) x 10^-4,
L15: excluding zero at 2.3 sigma.