Catalog · Secondary · K020

K020 $K^+ \to \pi^+ e^{\pm}\mu^{\mp}$

LFV charged-kaon semileptonic decay

Status REVIEWED VERIFIED High Code: NO Priority Medium

PDG / equivalent values

Observable	Value	Year	Experiment / source	Provenance
BR(K+ $ \to \pi^+ \mu^+$ e-)	$BR(K+ \to \pi^+ \mu^+ e^-) < 1.3 x 10^-11 (90% CL)$ 90% CL (upper_limit)	2025	PDG Live / PDG API listing S010.29, 2025 edition	source ↑
BR(K+ $ \to \pi^+ \mu^+$ e-) Sher/BNL E865 final	$BR(K+ \to \pi^+ \mu^+ e^-) < 2.1 x 10^-11 (90% CL, BNL E865 only)$ 90% CL (upper_limit)	2005	A. Sher et al. (BNL E865), Phys. Rev. D 72, 012005 (2005)	source ↑
BR(K+ $ \to \pi^+ \mu^-$ e+)	$BR(K+ \to \pi^+ \mu^- e^+) < 6.6 x 10^-11 (90% CL)$ 90% CL (upper_limit)	2025	PDG Live / PDG API listing S010.25, 2025 edition	source ↑

Why this constrains the RS scan

This is a SECONDARY this catalog wave entry; see flavor\_catalog/PRIORITY\_TIERS.md for the tier policy. K020 is a charged-kaon LFV companion to the neutral-kaon LFV channel K019. At the quark level it probes $\Delta S=1$ semileptonic LFV transitions $s\to d\,e\mu$, not the already implemented $\Delta F=2$ meson-mixing lane. In a quark-only anarchic RS scan it is outside the minimal implemented surface, but in lepton-bulk or seesaw-extended RS models nonuniversal fermion localization can generate off-diagonal quark and lepton couplings to KK gauge bosons, shifted $Z$ bosons, or Higgs/scalar states. Those effects match onto vector, scalar, or tensor four-fermion operators of the form $(\bar s\Gamma d)(\bar e\Gamma'\mu)$. Dipole LFV constraints such as $\mu\to e\gamma$ are correlated through the same lepton-sector spurions but do not by themselves implement the $K\to\pi e\mu$ rate.

What's changed since the original paper

The BNL E865 Sher et al. 2005 paper remains the canonical source for $K^+\to\pi^+\mu^+e^-$, with a $2.1\times10^{-11}$ E865-only limit and $1.3\times10^{-11}$ after combination with earlier E865 and E777 data. The key post-2008 experimental update is NA62 2021, arXiv:2105.06759, which sets ${\cal B}(K^+\to\pi^+\mu^-e^+)<6.6\times10^{-11}$ and improves the previous limit by about one order of magnitude for that charge assignment. For post-CFW theory context, Beneke, Moch, and Rohrwild 2015 (arXiv:1508.01705) provide a full 5D RS treatment of charged-lepton flavor violation, including dipole, $\mu\to3e$, conversion, and custodial-model effects. Angelescu, Faroughy, and Sumensari 2020 (arXiv:2002.05684) give a modern EFT treatment of quark-lepton LFV operators and explicitly list low-energy semileptonic modes such as $K\to\pi \ell_k^\pm\ell_l^\mp$. These sources matter because K020 cannot be obtained by reusing a pure kaon-mixing Wilson coefficient or the existing $\mu\to e\gamma$ dipole check.

Validity and model dependence

Experimentally, these are clean upper limits on forbidden SM processes, so the observable entry is an upper-limit constraint rather than an averaged nonzero measurement. The mapping to RS parameters is model dependent. A usable constraint needs a convention for the lepton bulk profiles or seesaw spurions, the quark-lepton operator basis, and the $K\to\pi$ hadronic form factors for vector/scalar/tensor structures. The two charge assignments should be kept separate because models with chiral lepton couplings can populate them differently. Existing $\mu\to e\gamma$, $\mu\to3e$, and conversion limits can dominate in many lepton-sector choices, but they do not eliminate the need for a semileptonic kaon rate when quark-flavor violation is present.

Code coverage in this repo

NO. A repository search over quarkConstraints/, qcd/, flavorConstraints/, neutrinos/, yukawa/, warpConfig/, solvers/, scanParams/, and tests/. The K020-specific grep found only generic LFV metadata and the existing $\mu\to e\gamma$ dipole module, e.g. flavorConstraints/muToEGamma.py:75 and scanParams/scan.py:524. Broader greps find the implemented $\Delta F=2$ surfaces such as quarkConstraints/deltaf2.py:755 for $\Delta m_K$, and the modern policy system list at quarkConstraints/modern/phenomenology.py:23 contains only $\varepsilon_K$, $K$, $B_d$, $B_s$, and $D0$. There is no $K^+\to\pi^+e\mu$ observable, likelihood, operator basis, or test.

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

Implementation difficulty

HIGH. A production implementation would need a new $\Delta S=1$ semileptonic LFV operator basis, RS matching for simultaneous quark and lepton flavor violation, and a $K\to\pi e\mu$ rate calculation with the relevant hadronic form factors. The existing $\Delta F=2$ and $\mu\to e\gamma$ code paths cannot be adapted by a threshold change or a simple constant replacement.

Reason: Requires a new $\Delta S = 1$ semileptonic LFV operator basis, $K \to \pi$ form-factor/rate calculation, and lepton-sector RS matching; existing $\Delta F = 2$ and $\mu \to e \gamma$ machinery cannot provide this observable.

Key references

Process-local source keys before bibliography consolidation: PDG2025\_Kplus\_LFV\_semileptonic, Sher2005\_Kplus\_piplus\_mup\_em, NA622021\_Kplus\_piplus\_mum\_ep, CFW2008\_RS\_flavor, BenekeMochRohrwild2015\_RS\_LFV, and AngelescuFaroughySumensari2020\_semileptonic\_LFV.

related_data_identifier S010R49

RESOLVED

Match snapshot line 18

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display BR(K+ -> pi+ mu+ e-) < 1.3 x 10^-11 (90% CL)

RESOLVED

Match snapshot line 7

L4: Listing URLs: https://pdgapi.lbl.gov/listings/S010.29 and https://pdgapi.lbl.gov/listings/S010.25
L5: 
L6: --- Selected summary rows from S010 branching_fractions ---
L7: S010.29	K+ --> pi+ mu+ e-	<1.3 E-11	90.0	OUR AVERAGE
L8: S010.25	K+ --> pi+ mu- e+	<6.6 E-11	90.0	OUR AVERAGE
L9: 
L10: --- Listing S010.29: K+ --> pi+ mu+ e- ---

display BR(K+ -> pi+ mu+ e-) < 2.1 x 10^-11 (90% CL, BNL E865 only)

AMBIGUOUS

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related_data_identifier S010R39

RESOLVED

Match snapshot line 143

L140:   "description": "K+ --> pi+ mu- e+",
L141:   "related_data": [
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L144:       "description": "G(K+ --> pi+ mu- e+)/G(total)",
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L146:       "measurements": [

display BR(K+ -> pi+ mu- e+) < 6.6 x 10^-11 (90% CL)

RESOLVED

Match snapshot line 8

L5: 
L6: --- Selected summary rows from S010 branching_fractions ---
L7: S010.29	K+ --> pi+ mu+ e-	<1.3 E-11	90.0	OUR AVERAGE
L8: S010.25	K+ --> pi+ mu- e+	<6.6 E-11	90.0	OUR AVERAGE
L9: 
L10: --- Listing S010.29: K+ --> pi+ mu+ e- ---
L11: {