Catalog · Beauty · B022

B022 $\mathcal{B}(B^+\to K^+\nu\bar{\nu})$

Invisible rare decay $B+ \to K+ \nu \bar{\nu}$

Status REVIEWED VERIFIED High Code: NO Priority Medium

PDG / equivalent values

Observable	Value	Year	Experiment / source	Provenance
SM BR(B+ $ \to K+ \nu \bar{\nu}$)	5.58e-6 branching fraction	2023	HPQCD2023:B022:sm_prediction	source ↑

Why this constrains the RS scan

This mode probes a $\Delta B=1$ neutral-current transition with missing energy. In RS/anarchic-flavor models it can receive contributions from flavor-changing $b$-$s$ currents coupled to $Z$, KK electroweak gauge bosons, or other neutral invisible states. It is complementary to $\Delta F=2$ $B_s$ mixing because it tests a semileptonic/invisible operator, not a neutral-meson mixing amplitude.

What's changed since the original paper

The CFW 2008 RS-flavor baseline predates the modern $B\to K\nu\bar{\nu}$ program (CsakiFalkowskiWeiler2008:CompositeFlavor). BaBar later set hadronic-tag limits, including $\mathcal{B}(B^+\to K^+\nu\bar{\nu})<3.7\times10^{-5}$ at 90\% CL (BaBar2013:BKstarNuNu). Belle II changed the status of the mode with the 2024 evidence measurement quoted above (BelleII2024:BplusKplusNuNu). On the theory side, modern lattice form factors support the SM prediction quoted above (HPQCD2023:BtoKNuNuSM), and Belle II has released a 2025 model-agnostic likelihood package to reinterpret the measurement under non-SM invisible kinematics or WET coefficient choices (BelleII2025:BKnnLikelihood).

Validity and model dependence

The SM prediction is comparatively clean: there are no charmonium veto regions as in $b\to s\ell^+\ell^-$, and the dominant hadronic input is the $B\to K$ vector form factor. The experimental extraction is less universal: Belle II's headline branching fraction assumes SM kinematics, while invisible new particles can change the $q^2$ spectrum and selection efficiency. A live constraint should therefore use either the published likelihood or a validated reweighting prescription rather than only a one-bin branching-fraction pull.

Code coverage in this repo

NO. Required greps over quarkConstraints/, qcd/, flavorConstraints/, neutrinos/, yukawa/, warpConfig/, solvers/, scanParams/, and tests/ found no $B\to K\nu\bar{\nu}$, $b\to s\nu\bar{\nu}$, or rare invisible decay implementation. The modern phenomenology surface lists only $\epsilon_K$, $K$, $B_d$, $B_s$, and $D^0$ at quarkConstraints/modern/phenomenology.py:23; its note says this is policy-only at quarkConstraints/modern/phenomenology.py:166. The legacy $\Delta F=2$ inputs are at quarkConstraints/deltaf2.py:209, with $B_d$ and $B_s$ mixing evaluators at quarkConstraints/deltaf2.py:903 and quarkConstraints/deltaf2.py:922. The only live lepton-flavor routine seen is $\mu\to e\gamma$ at flavorConstraints/muToEGamma.py:75.

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

Implementation difficulty

HIGH. This would require a new $\Delta B=1$ $b\to s\nu\bar{\nu}$ Hamiltonian, exclusive $B\to K$ form-factor integration, invisible-final-state acceptance treatment, and Belle II likelihood or kinematic-reweighting support. The existing neutral-meson $\Delta F=2$ SLL/SLR/VLL/VRR/LR machinery does not cover this observable.

Reason: A live constraint needs a new $\Delta B = 1$ $b \to s$ $\nu \bar{\nu}$ weak-Hamiltonian normalization, exclusive $B \to K$ form-factor integration, neutrino/invisible final-state treatment, and likely Belle II likelihood or kinematic-reweighting support. The existing $\Delta F = 2$ SLL/SLR/VLL/VRR/LR1/LR2 neutral-meson basis does not compute this mode.

Key references

HFLAV2025Dec:BplusKplusNuNu, PDG2026:BplusKplusNuNu, BelleII2024:BplusKplusNuNu, BelleII2025:BKnnLikelihood, BaBar2013:BKstarNuNu, HPQCD2023:BtoKNuNuSM, and CsakiFalkowskiWeiler2008:CompositeFlavor.

fallback_value_uncertainty BR(B+ -> K+ nu nubar) = (1.38 +- 0.35)e-5

RESOLVED

Match snapshot line 15

L12: <h1>${\cal B}(B^+ \to K^+ \nu \bar{\nu})$</h1>
L13: <p><img src="BR_B+_K+_nu_nubar.png"></p>
L14: <p><table border="1"><tr><th>Experiment</th><th>Measurement [10<sup>-5</sup>]</th><th>$\Delta\chi^2$</th><th>Reference</th><th>Comments</th></tr>
L15: <tr><td><b>Average</b></td><td><b>$1.38 \pm0.35$</b></td><td>5.55</td><td>$p=0.23$ (ndf=4)</td><td></td></tr>
L16: <tr><td><i>PDG</i></td><td><i>$2.30\,^{+0.71}_{-0.64}$</i></td><td></td><td><a href="https://pdglive.lbl.gov/BranchingRatio.action?desig=273&parCode=S041">pdgLive</a></td><td></td></tr>
L17: <tr><td>Belle</td><td>$1.00 \pm0.60$</td><td>0.41</td>
L18: <td><a href="https://inspirehep.net/literature/1512929">Phys.Rev.D <b>96</b>,091101 (2017)</a></td><td>Semileptonic tag. Paper only reports UL. The value reported here is calculated in Ref.~\cite{Belle-II:2023esi}. </td></tr>

fallback_value_uncertainty BR(B+ -> K+ nu nubar) = (2.3 +- 0.71)e-5

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Match 1 of 4 snapshot line 30

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L33: ,   "stat_error_positive": 5.0E-6

Match 2 of 4 snapshot line 32

L29:    "column_name": "VALUE"
L30: ,   "value": 2.3E-5
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L35: ,   "syst_error_positive": 5.0E-6

Match 3 of 4 snapshot line 37

L34: ,   "stat_error_negative": 5.0E-6
L35: ,   "syst_error_positive": 5.0E-6
L36: ,   "syst_error_negative": 4.000000000000001E-6
L37: ,   "value_text": "(2.3 +-0.5+0.5-0.4) E-5"
L38: ,   "used_in_average": true
L39: ,   "used_in_fit": true
L40: ,   "display_value_text": "2.3 +-0.5 +0.5-0.4"

Match 4 of 4 snapshot line 164

L161: , "publication_name": "PR D87 111103"
L162: , "publication_year": 2013
L163: , "doi": "10.1103/PhysRevD.87.111103"
L164: , "inspire_id": "1223991"
L165: , "title": "Search for B --> h^(*) nu nubar with the Full Belle Upsilon(4S) Data Sample"
L166: , "confidence_level": "90.0"
L167: , "technique": "BELL"

fallback_value_uncertainty BR(B+ -> K+ nu nubar) = (2.3 +- 0.5)e-5

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Match 1 of 6 snapshot line 153

L150: 
L151:   <tr class="d-flex">
L152:     <th class="col-2">Abstract</th>
L153:     <td class="col-10">We search for the rare decay $B^{+}\rightarrow K^{+}\nu\bar{\nu}$ in a $362\ \rm{fb}^{-1}$ sample of electron-positron collisions at the $\Upsilon(4S)$ resonance collected with the Belle II detector at the SuperKEKB collider. We use the inclusive properties of the accompanying $B$ meson in $\Upsilon(4S) \to B\kern 0.18em\overline{\kern -0.18em B}{}$ events to suppress background from other decays of the signal $B$ candidate and light-quark pair production. We validate the measurement with an auxiliary analysis based on a conventional hadronic reconstruction of the accompanying $B$ meson. For background suppression, we exploit distinct signal features using machine learning methods tuned with simulated data. The signal-reconstruction efficiency and background suppression are validated through various control channels. The branching fraction is extracted in a maximum likelihood fit. Our inclusive and hadronic analyses yield consistent results for the $B^{+}\rightarrow K^{+}\nu\bar{\nu}$ branching fraction of $\left[2.7\pm 0.5(\mathrm{stat})\pm 0.5(\mathrm{syst})\right] \times 10^{-5}$ and $\left[1.1^{+0.9}_{-0.8}(\mathrm{stat}){}^{+0.8}_{-0.5}(\mathrm{syst})\right] \times 10^{-5}$, respectively. Combining the results, we determine the branching fraction of the decay $B^{+}\rightarrow K^{+}\nu\bar{\nu}$ to be $\left[2.3 \pm 0.5(\mathrm{stat})^{+0.5}_{-0.4}(\mathrm{syst})\right]\times 10^{-5}$, providing the first evidence for this decay at $3.5$ standard deviations. The combined result is $2.7$ standard deviations above the standard model expectation.</td>
L154:   </tr>
L155: 
L156:

Match 2 of 6 snapshot line 198

L195:     author = &quot;Adachi, I. and others&quot;,
L196:     collaboration = &quot;Belle-II&quot;,
L197:     title = &quot;{Evidence for B+{\textrightarrow}K+{\ensuremath{\nu}}{\ensuremath{\nu}}{\textasciimacron} decays}&quot;,
L198:     eprint = &quot;2311.14647&quot;,
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L201:     reportNumber = &quot;Belle II Preprint 2023-017, KEK Preprint 2023-35&quot;,

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L202:     doi = &quot;10.1103/PhysRevD.109.112006&quot;,
L203:     journal = &quot;Phys. Rev. D&quot;,
L204:     volume = &quot;109&quot;,

Match 4 of 6 snapshot line 235

L232:     author = "Adachi, I. and others",
L233:     collaboration = "Belle-II",
L234:     title = "{Evidence for B+{\textrightarrow}K+{\ensuremath{\nu}}{\ensuremath{\nu}}{\textasciimacron} decays}",
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L236:     archivePrefix = "arXiv",
L237:     primaryClass = "hep-ex",
L238:     reportNumber = "Belle II Preprint 2023-017, KEK Preprint 2023-35",

Match 5 of 6 snapshot line 238

L235:     eprint = "2311.14647",
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L239:     doi = "10.1103/PhysRevD.109.112006",
L240:     journal = "Phys. Rev. D",
L241:     volume = "109",

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L262:       <br>
L263:       <span class="text-muted text-sm">latest upload: 2025-03-10</span>
L264:     </span>

fallback_value_uncertainty BR(B+ -> K+ nu nubar) < 3.7e-5 90%

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L11:     <id>http://arxiv.org/abs/1303.7465v2</id>
L12:     <title>Search for B --&gt; K(*) nu nubar and invisible quarkonium decays</title>
L13:     <updated>2013-06-11T18:41:41Z</updated>
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fallback_value_uncertainty SM BR(B+ -> K+ nu nubar) = (5.58 +- 0.37)e-6

RESOLVED

Match snapshot line 67

L64:                         & 4.94(52) & \cite{Du:2015tda}\\
L65:                         & 4.53(64) &\cite{Buras:2021nns}\\
L66:                         & 4.65(62) &\cite{Buras:2022wpw}\\
L67:                         & 5.58(37) & HPQCD '22\\
L68:       \hline
L69:       \hline
L70:     \end{tabular}\caption{Summary of experimental and theoretical results for the branching fraction $\mathcal{B}(B\to K\nu\bar{\nu})$, summed over neutrino flavours. Our results are denoted by `HPQCD '22' and include the long-distance contribution of Eq.~\eqref{eq:nuLD} in the charged $B$ case. Experimental results are given as 90\% confidence limit and marked `Exp.'. In the case of~\cite{Buras:2021nns}, we use $|V_{tb}V_{ts}^*|$ (Table~\ref{tab-SMparams}) to obtain the result.}