Catalog · Kaon · K004

K004 $K^+ \to \pi^+ \nu\bar{\nu}$

Charged rare kaon decay $K+ \to \pi^+ \nu \bar{\nu}$

Status REVIEWED VERIFIED Medium Code: NO Priority Medium

PDG / equivalent values

Observable	Value	Year	Experiment / source	Provenance
NA62 preliminary 2026 Moriond contribution	9.6 dimensionless branching fraction	2026	NA62 preliminary 2026 Moriond contribution	source ↑
NA62 Collaboration, JHEP 02 (2025) 191	13.0 dimensionless branching fraction	2025	NA62 Collaboration, JHEP 02 (2025) 191	source ↑
Buras and Venturini, arXiv:2203.10099	8.60 dimensionless branching fraction	2022	Buras and Venturini, arXiv:2203.10099	source ↑
Brod, Gorbahn, and Stamou, arXiv:2105.02868	7.73 dimensionless branching fraction	2021	Brod, Gorbahn, and Stamou, arXiv:2105.02868	source ↑

Why this constrains the RS scan

Anarchic warped models can generate misaligned $s$-$d$ neutral currents through KK gauge exchange, $Z$-coupling shifts, or related electroweak matching effects. Unlike the current quark lane's $\DeltaFtwo$ kaon observables, this is a $\Delta F=1$ semileptonic process. It therefore tests whether the model has controlled short-distance neutral currents beyond the four-quark $K$-mixing sector. The charged mode is especially useful because it is theoretically clean, uses a hadronic matrix element tied to semileptonic kaon data, and can interfere with the SM amplitude rather than only setting an incoherent upper bound.

What's changed since the original paper

The CFW-era RS discussion used $\DeltaFtwo$ flavor bounds as the central pressure point, quoting a generic RS KK-gluon mass scale of about $21$ TeV and a composite pseudo-Goldstone scenario scale of about $33$ TeV. Since that era, NA62 reported the published observation in 2025 and a newer 2026 preliminary combination with better-than-$20\%$ precision. On the theory side, post-2008 SM updates have sharpened the short-distance prediction and exposed the role of CKM-input choices: Brod--Gorbahn--Stamou quote $7.73(61)\times10^{-11}$, while Buras--Venturini quote $(8.60\pm0.42)\times10^{-11}$ using a strategy designed to avoid the direct $|V_{cb}|$ and $|V_{ub}|$ tensions.

Validity and model dependence

As an experimental branching-ratio constraint this mode is clean, but its use inside an RS scan is model-dependent. A production constraint needs Wilson coefficients for $(\bar{s}\gamma_\mu P_{L,R}d)(\bar{\nu}\gamma^\mu(1-\gamma_5)\nu)$, a choice of neutrino-flavor treatment, and a convention for SM--NP interference. The Buras--Venturini SM number also assumes no new-physics infection in the $\DeltaFtwo$ inputs used to remove CKM ambiguities, so a checker should keep that assumption visible if the catalog later turns this process into a hard bound.

Code coverage in this repo

NO. The required grep sweep finds kaon mixing, generic neutrino-mass utilities, and the catalog planning row, but no implementation of $K^+\to\pi^+\nu\bar{\nu}$, no $\Delta F=1$ $s\to d\nu\bar{\nu}$ operator, and no branching-ratio acceptance gate. The closest quark-code surfaces are the $\DeltaFtwo$ entries in quarkConstraints/deltaf2.py and the modern policy list MODERN\_PHENOMENOLOGY\_SYSTEM\_IDS = (epsilon\_K, K, B\_d, B\_s, D0).

Implementation difficulty

MEDIUM. The observable needs a new $\Delta F=1$ semileptonic operator basis and a branching-ratio formula with SM--NP interference, but the hadronic input is standard and this channel does not require the angular likelihood machinery needed for many $b\to s\ell\ell$ observables. The difficulty would become HIGH only if the catalog requires a full RS tower and neutrino-sector matching rather than an EFT Wilson input.

Reason: Requires a new $\Delta F = 1$ semileptonic $s \to d$ $\nu \bar{\nu}$ operator basis and branching-ratio formula with SM--NP interference, but uses standard clean hadronic input.

Key references

Process-local reference keys before bibliography consolidation: NA62:KpPipNunu2026, NA62:KpPipNunu2025, BurasVenturini:KpPipNunu2022, BrodGorbahnStamou:KpPipNunu2021, and CsakiFalkowskiWeiler:RSFlavor2008.

value_summary B(K+ -> pi+ nu nubar) = (9.6^{+1.9}_{-1.8}) x 10^{-11}

RESOLVED

Match snapshot line 20

L17:   with the new data while reducing the background in proportion.
L18: - Branching-ratio result used as the current experimental-equivalent value in
L19:   this K004 draft:
L20:   B(K+ -> pi+ nu nubar) = (9.6^{+1.9}_{-1.8}) x 10^{-11}.
L21: - The abstract describes the result as compatible with the Standard Model
L22:   prediction and with precision better than 20%.
L23:

value_summary B(K+ -> pi+ nu nubar) = (13.0^{+3.3}_{-3.0}) x 10^{-11}

RESOLVED

Match snapshot line 17

L14: Relevant extracted facts:
L15: - Data sample: NA62 2021--2022 data are combined with 2016--2018 data.
L16: - Published combined branching-ratio result:
L17:   B(K+ -> pi+ nu nubar) = (13.0^{+3.3}_{-3.0}) x 10^{-11}.
L18: - Event-count context: 51 signal candidates were observed; the expected
L19:   background was 18^{+3}_{-2} events.
L20: - The arXiv abstract identifies this as an observation with signal

value_summary B(K+ -> pi+ nu nubar)_SM = (8.60 +/- 0.42) x 10^{-11}

RESOLVED

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L12: - The paper constructs rare-decay Standard Model predictions designed to avoid
L13:   direct dependence on the inclusive/exclusive |V_cb| and |V_ub| tensions.
L14: - The charged-kaon Standard Model benchmark used in this K004 draft is:
L15:   B(K+ -> pi+ nu nubar)_SM = (8.60 +/- 0.42) x 10^{-11}.
L16: - The same abstract quotes:
L17:   B(K_L -> pi0 nu nubar)_SM = (2.94 +/- 0.15) x 10^{-11}.
L18: - The authors describe these as determinations obtained under the assumption

value_summary BR(K+ -> pi+ nu nubar) = 7.73(61) x 10^{-11}

RESOLVED

Match snapshot line 15

L12: - The paper provides an updated Standard Model prediction for the rare
L13:   K -> pi nu nubar decay modes and summarizes the SM status of epsilon_K.
L14: - Charged-mode result:
L15:   BR(K+ -> pi+ nu nubar) = 7.73(61) x 10^{-11}.
L16: - Neutral-mode result:
L17:   BR(K_L -> pi0 nu nubar) = 2.59(29) x 10^{-11}.
L18: - The abstract states that the uncertainties are dominated by parametric input.