Catalog · Kaon · K017

K017 $R_K = \Gamma(K^+ \to e^+ \nu_e(\gamma)) / \Gamma(K^+ \to \mu^+ \nu_\mu(\gamma))$

Charged-kaon leptonic lepton-universality ratio

Status REVIEWED VERIFIED Medium Code: NO Priority Low

PDG / equivalent values

Observable	Value	Year	Experiment / source	Provenance
PDG API / PDG Live summary S010R28	2.488 dimensionless decay-rate ratio	2025	PDG API / PDG Live summary S010R28	source ↑
NA62 Collaboration, Phys. Lett. B 719 (2013) 326	2.488 dimensionless decay-rate ratio	2013	NA62 Collaboration, Phys. Lett. B 719 (2013) 326	source ↑
KLOE Collaboration, Eur. Phys. J. C 64 (2009) 627	2.493 dimensionless decay-rate ratio	2009	KLOE Collaboration, Eur. Phys. J. C 64 (2009) 627	source ↑
Cirigliano and Rosell, JHEP 0710 (2007) 005	2.477 dimensionless decay-rate ratio	2007	Cirigliano and Rosell, JHEP 0710 (2007) 005	source ↑

Why this constrains the RS scan

This is not a neutral-meson $\Delta F=2$ observable and does not probe the existing quark scan's KK-gluon mixing lane directly. Its value is that the ratio cancels the common $V_{us}$, $f_K$, and much of the kaon-rate normalization, leaving a helicity-suppressed charged-current LFU test (FlaviaNet:Kaon2010). Nonminimal warped models with lepton localization, heavy neutral leptons, nonunitary charged currents, charged scalars, or nonuniversal $W$-coupling shifts can modify $K_{e2}$ relative to $K_{\mu2}$. In a quark-only RS interpretation it should therefore be cataloged as a lepton-extension or charged-current diagnostic, not as a hard bound on the current anarchic quark fit.

What's changed since the original paper

The 2008 CFW baseline predates the precision $R_K$ consolidation and did not make this charged-current LFU ratio a central RS constraint (CsakiFalkowskiWeiler:RSFlavor2008). Since then, KLOE published a precise inclusive measurement in 2009 (KLOE:RK2009), the FlaviaNet kaon working group consolidated post-2008 kaon-decay inputs in 2010 (FlaviaNet:Kaon2010), and NA62 superseded earlier charged-kaon data with its 2007--2008 data set in 2013 (NA62:RK2013). The modern PDG average is driven by those post-2008 measurements. The theory reference value was already clean before 2008, but the experimental precision now makes $R_K$ a useful null test for scalar or right-handed charged-current effects that evade many hadronic uncertainties.

Validity and model dependence

As a measured ratio, $R_K$ is robust and experimentally clean, provided the radiative convention is kept fixed: the PDG/NA62 ratio includes internal bremsstrahlung, while direct-emission radiation is separated. Its mapping onto this repository's default model is model-dependent. A minimal quark flavor scan with no nonstandard charged-current lepton sector has no direct parameter controlling this observable, whereas a 5D lepton extension or charged-scalar completion could generate visible effects through chirality- enhanced scalar amplitudes or lepton-nonuniversal $W$ couplings.

Code coverage in this repo

NO. The required coverage greps across quarkConstraints/, qcd/, flavorConstraints/, neutrinos/, yukawa/, warpConfig/, solvers/, scanParams/, and tests/ find no $K^+\to e^+\nu$, $K^+\to\mu^+\nu$, $K_{\ell2}$, or $R_K$ implementation. The nearest surfaces are the $\Delta F=2$ default inputs in quarkConstraints/deltaf2.py:209 and the modern policy fence quarkConstraints/modern/phenomenology.py:23, which enumerates only $\varepsilon_K$, $K$, $B_d$, $B_s$, and $D0$.

Implementation difficulty

MEDIUM. A catalog-to-code implementation would need a new charged-current leptonic-decay observable, including the SM amplitude, radiative-convention bookkeeping, and whatever BSM operator basis the PI wants to expose. The ratio avoids new lattice matrix elements, but it is not covered by the existing $\Delta F=2$ SLL/SLR/VLL/VRR/LR machinery.

Reason: Needs a new charged-current leptonic-decay observable and BSM operator/matching convention; no new lattice input is needed because the ratio cancels f_K, but existing $\Delta F = 2$ machinery does not cover it.

Key references

Process-local reference keys before bibliography consolidation: PDG2025:K017RK, NA62:RK2013, KLOE:RK2009, CiriglianoRosell:RKSM2007, FlaviaNet:Kaon2010, and CsakiFalkowskiWeiler:RSFlavor2008.

value_summary R_K = Gamma(K+ -> e+ nu_e)/Gamma(K+ -> mu+ nu_mu) = (2.488 +/- 0.009) x 10^{-5}

RESOLVED

Match snapshot line 17

L14:   value: 2.488452029520296E-5
L15:   error_positive: 9.441409926605985E-8
L16:   error_negative: 9.441409926605985E-8
L17:   value_text: "(2.488+-0.009)E-5"
L18:   type: "OUR AVERAGE"
L19: 
L20: Related listing anchor from S010.11:

value_summary R_K = (2.488 +/- 0.007_stat +/- 0.007_syst) x 10^{-5}

RESOLVED

Match snapshot line 14

L11: The NA62 experiment at CERN collected a dedicated charged-kaon sample during
L12: 2007-2008 and measured the ratio R_K = Gamma(K+- -> e+- nu) /
L13: Gamma(K+- -> mu+- nu).  The paper reports
L14: R_K = (2.488 +- 0.007_stat +- 0.007_syst) x 10^{-5}.
L15: 
L16: Catalog extraction notes:
L17: This is the dominant modern measurement used in the PDG S010R28 average.  The

value_summary R_K = (2.493 +/- 0.025_stat +/- 0.019_syst) x 10^{-5}

RESOLVED

Match snapshot line 13

L10: Value excerpt for kaon LFU:
L11: KLOE measured R_K = Gamma(K -> e nu(gamma))/Gamma(K -> mu nu(gamma)).
L12: The PDG S010R28 listing records the KLOE input as
L13: R_K = (2.493 +- 0.025_stat +- 0.019_syst) x 10^{-5}.
L14: 
L15: Catalog extraction notes:
L16: The PDG listing footnote states that this ratio includes internal

value_summary R_K^SM = (2.477 +/- 0.001) x 10^{-5}

RESOLVED

Match snapshot line 12

L9: 
L10: Value excerpt for kaon LFU:
L11: The Standard Model prediction used by the kaon LFU literature is
L12: R_K^SM = (2.477 +- 0.001) x 10^{-5}.
L13: 
L14: Catalog extraction notes:
L15: The calculation includes radiative corrections through O(e^2 p^4) in chiral