Catalog · Secondary · K021

K021 $K_L \to \pi^0 e^{\pm}\mu^{\mp}$

LFV neutral-kaon semileptonic decay

Status REVIEWED VERIFIED High Code: NO Priority Low

PDG / equivalent values

Observable	Value	Year	Experiment / source	Provenance
$BR(K_L \to $ pi0 $e^+- \mu^-+$), summed charge states	< 7.6 x 10^-11 (90% CL) 90% CL (upper_limit)	2025	PDG Review of Particle Physics, K_L0 listing, 2025 update	source ↑
$BR(K_L \to $ pi0 $\mu$ e)	< 7.56 x 10^-11 (90% CL) 90% CL (upper_limit)	2008	E. Abouzaid et al. (KTeV Collaboration), Phys. Rev. Lett. 100, 131803 (2008)	source ↑
BR(K+ $ \to \pi^+ \mu^-$ e+)	6.6e-11 dimensionless branching fraction 90% CL (upper_limit)	2021	R. Aliberti et al. (NA62 Collaboration), Phys. Rev. Lett. 127, 131802 (2021)	source ↑
BR(K+ $ \to \pi^- \mu^+$ e+)	4.2e-11 dimensionless branching fraction 90% CL (upper_limit)	2021	R. Aliberti et al. (NA62 Collaboration), Phys. Rev. Lett. 127, 131802 (2021)	source ↑
BR(pi0 $ \to \mu^-$ e+)	3.2e-10 dimensionless branching fraction 90% CL (upper_limit)	2021	R. Aliberti et al. (NA62 Collaboration), Phys. Rev. Lett. 127, 131802 (2021)	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. It is a $\Delta S=1$, neutral-current LFV channel. In an RS/anarchic flavor pipeline it is sensitive to products of flavor off-diagonal quark and lepton couplings, for example tree-level exchange of KK gauge bosons or flavor-violating $Z$-like states generating $(\bar s\gamma_\alpha d)(\bar e\gamma^\alpha\mu)$-type operators. The same fermion-localization profiles that set quark FCNCs also set the charged-lepton overlaps; in lepton-bulk variants the Perez--Randall seesaw/neutrino-Yukawa spurions control charged-LFV misalignment. Dipole constraints such as $\mu\to e\gamma$ probe a different operator class but constrain the same leptonic flavor sector, while scalar or Higgs-flavor contributions would need separate chirality and hadronic form-factor treatment.

What's changed since the original paper

The direct neutral-mode experimental situation has not moved beyond KTeV in the PDG 2025 listing: the K021 limit remains the 2008 KTeV result. The main post-2008 experimental development is adjacent rather than superseding: NA62 reported 2017--2018 searches for $K^+\to\pi^+\mu^-e^+$, $K^+\to\pi^-\mu^+e^+$, and $\pi^0\to\mu^-e^+$, setting $90\%$-CL limits at the $10^{-11}$--$10^{-10}$ level and improving the charged-kaon and pion LFV reach by about one order of magnitude. The theory context changed more substantially. Crivellin, D'Ambrosio, Hoferichter, and Tunstall (arXiv:1601.00970) formulated rare kaon LFV/LFU tests in terms of four-fermion operators for $K\to\pi\ell\ell'$ and $K\to\ell\ell'$. Angelescu, Faroughy, and Sumensari (arXiv:2002.05684) gave numerical low-energy formulae for semileptonic LFV meson decays and showed how LHC dilepton tails complement flavor limits. Roy and Valencia (arXiv:2410.05859) and Delzanno et al. (arXiv:2411.13497) updated the SMEFT perspective by matching rare-kaon/CLFV operators to high-$p_T$, electroweak, and low-energy probes with RG running and operator correlations.

Validity and model dependence

The experimental upper limit is cleanly usable as a branching-ratio cap, but the RS interpretation is model-dependent. A catalog implementation must choose an effective-operator basis, charge-state convention, $K\to\pi$ vector and scalar form factors, and the mapping from 5D fermion localization to off-diagonal quark and lepton couplings. There is no Standard Model long-distance amplitude to subtract at an observable level for LFV, but there is also no current repo machinery for the required $\Delta S=1$ semileptonic LFV matching. Correlations with $K_L\to e^\pm\mu^\mp$, $K^+\to\pi^+e^\pm\mu^\mp$, $\mu\to e\gamma$, and $\mu\to e$ conversion should be kept explicit.

Code coverage in this repo

NO. The required grep sweep across quarkConstraints/, qcd/, flavorConstraints/, neutrinos/, yukawa/, warpConfig/, solvers/, scanParams/, and tests/ found no K021 implementation and no generic $s\to d e\mu$ semileptonic LFV surface. Existing nearby code covers kaon $\Delta F=2$ mixing, for example quarkConstraints/deltaf2.py:1 and quarkConstraints/deltaf2.py:615, plus a separate $\mu\to e\gamma$ NDA dipole check in flavorConstraints/muToEGamma.py:1; neither computes $K_L\to\pi^0 e^\pm\mu^\mp$.

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

Implementation difficulty

HIGH. A pure EFT rate is standard once semileptonic LFV Wilson coefficients are supplied, but this repository does not yet have the needed $\Delta S=1$ semileptonic operator basis, $K\to\pi$ form-factor interface, or RS matching for simultaneous quark and lepton flavor violation. Integrating K021 consistently with the existing RS scan would therefore require new cross-sector matching rather than only adding a numerical limit.

Reason: Requires new $\Delta S = 1$ semileptonic LFV operators, $K \to \pi$ form-factor plumbing, and RS matching for simultaneous quark and lepton off-diagonal couplings; existing $\Delta F = 2$ and $\mu \to e \gamma$ code is not sufficient.

Key references

Process-local source keys before bibliography consolidation: PDG2025\_KL\_pi0emu, KTeV2008\_KL\_pi0emu, CFW2008\_composite\_pgh\_flavor, PerezRandall2008\_warped\_neutrinos, CrivellinDAmbrosioHoferichterTunstall2016\_rare\_kaon\_lfv, NA622021\_Kplus\_pi\_mu\_e, AngelescuFaroughySumensari2020\_lfv\_dilepton\_tails, RoyValencia2024\_highpt\_rare\_kaon\_smeft, and DelzannoFuyutoGonzalezSolisMereghetti2024\_mue\_smeft.

display < 7.6 x 10^-11 (90% CL)

AMBIGUOUS

Match 1 of 2 snapshot line 14

L11:   Charge conjugation x parity (CP) or Lepton Family number (LF)
L12:   violating modes, or Delta S = 1 weak neutral current (S1) modes.
L13: 
L14:   Gamma_37  pi0 mu+- e-+    LF [a]   < 7.6 x 10^-11   CL=90%
L15: 
L16:   [a] The value is for the sum of the charge states or particle/antiparticle
L17:       states indicated.

Match 2 of 2 snapshot line 32

L29: 
L30: Interpretation for K021:
L31:   PDG's current canonical upper limit is
L32:   BR(K_L -> pi0 mu+- e-+) < 7.6 x 10^-11 at 90% CL,
L33:   for the summed charge states.

display < 7.56 x 10^-11 (90% CL)

RESOLVED

Match snapshot line 17

L14: the K_L meson in three decay modes. It observed no events in the signal region
L15: for any of the modes studied and set 90% CL upper limits:
L16: 
L17:   BR(K_L -> pi0 mu e) < 7.56 x 10^-11
L18:   BR(K_L -> pi0 pi0 mu e) < 1.64 x 10^-10
L19:   BR(pi0 -> mu e) < 3.59 x 10^-10
L20:

value 6.6e-11

AMBIGUOUS

Match 1 of 2 snapshot line 16

L13: NA62 searched for K+ -> pi- mu+ e+, K+ -> pi+ mu- e+, and pi0 -> mu- e+
L14: using 2017-2018 CERN data. No evidence was found. The 90% CL limits were:
L15: 
L16:   BR(K+ -> pi- mu+ e+) < 4.2 x 10^-11
L17:   BR(K+ -> pi+ mu- e+) < 6.6 x 10^-11
L18:   BR(pi0 -> mu- e+) < 3.2 x 10^-10
L19:

Match 2 of 2 snapshot line 17

L14: using 2017-2018 CERN data. No evidence was found. The 90% CL limits were:
L15: 
L16:   BR(K+ -> pi- mu+ e+) < 4.2 x 10^-11
L17:   BR(K+ -> pi+ mu- e+) < 6.6 x 10^-11
L18:   BR(pi0 -> mu- e+) < 3.2 x 10^-10
L19: 
L20: The abstract states these results improve previous results for these decay

value 4.2e-11

AMBIGUOUS

Match 1 of 2 snapshot line 16

L13: NA62 searched for K+ -> pi- mu+ e+, K+ -> pi+ mu- e+, and pi0 -> mu- e+
L14: using 2017-2018 CERN data. No evidence was found. The 90% CL limits were:
L15: 
L16:   BR(K+ -> pi- mu+ e+) < 4.2 x 10^-11
L17:   BR(K+ -> pi+ mu- e+) < 6.6 x 10^-11
L18:   BR(pi0 -> mu- e+) < 3.2 x 10^-10
L19:

Match 2 of 2 snapshot line 17

L14: using 2017-2018 CERN data. No evidence was found. The 90% CL limits were:
L15: 
L16:   BR(K+ -> pi- mu+ e+) < 4.2 x 10^-11
L17:   BR(K+ -> pi+ mu- e+) < 6.6 x 10^-11
L18:   BR(pi0 -> mu- e+) < 3.2 x 10^-10
L19: 
L20: The abstract states these results improve previous results for these decay

value 3.2e-10

RESOLVED

Match snapshot line 18

L15: 
L16:   BR(K+ -> pi- mu+ e+) < 4.2 x 10^-11
L17:   BR(K+ -> pi+ mu- e+) < 6.6 x 10^-11
L18:   BR(pi0 -> mu- e+) < 3.2 x 10^-10
L19: 
L20: The abstract states these results improve previous results for these decay
L21: modes by one order of magnitude.

value 7.56e-11

AMBIGUOUS

Match 1 of 2 snapshot line 17

L14: the K_L meson in three decay modes. It observed no events in the signal region
L15: for any of the modes studied and set 90% CL upper limits:
L16: 
L17:   BR(K_L -> pi0 mu e) < 7.56 x 10^-11
L18:   BR(K_L -> pi0 pi0 mu e) < 1.64 x 10^-10
L19:   BR(pi0 -> mu e) < 3.59 x 10^-10
L20:

Match 2 of 2 snapshot line 23

L20: 
L21: Role in K021:
L22:   This is the experiment input behind the current PDG K_L -> pi0 mu+- e-+
L23:   limit. PDG rounds the K021 limit to < 7.6 x 10^-11.