K009 $K_L \to pi0 \mu^+ \mu^-$
Long-lived neutral-kaon rare semileptonic muon mode Status REVIEWED VERIFIED High Code: NO Priority Low
PDG / equivalent values
| Observable | Value | Year | Experiment / source | Provenance |
|---|---|---|---|---|
| PDG/API $BR(K_L \to $ pi0 $\mu^+ \mu^-$) canonical limit | <3.8e-10 branching fraction | 2026 | Particle Data Group 2026 pdgLive listing S013.16 / S013R30 | source ↑ |
| KTeV 1997-data $BR(K_L \to $ pi0 $\mu^+ \mu^-$) limit | <3.8e-10 branching fraction | 2000 | KTeV 2000 arXiv hep-ex/0001006 | source ↑ |
| KTeV 1997-data observed candidates for $K_L \to $ pi0 $\mu^+ \mu^-$ | 2 events | 2000 | KTeV 2000 arXiv hep-ex/0001006 | source ↑ |
| KTeV 1997-data expected background for $K_L \to $ pi0 $\mu^+ \mu^-$ | 0.87 events | 2000 | KTeV 2000 arXiv hep-ex/0001006 | source ↑ |
| $BR(K_S \to $ pi0 $\mu^+ \mu^-$) supporting indirect-CP input | 2.9e-9 branching fraction | 2026 | Particle Data Group 2026 pdgLive listing S012.15 / NA48 | source ↑ |
| NA48 observed $K_S \to $ pi0 $\mu^+ \mu^-$ candidates | 6 events | 2004 | NA48 2004 arXiv hep-ex/0409011 | source ↑ |
| NA48 expected background for $K_S \to $ pi0 $\mu^+ \mu^-$ | 0.22 events | 2004 | NA48 2004 arXiv hep-ex/0409011 | source ↑ |
| Isidori-Smith-Unterdorfer rate decomposition normalization for $K_L \to $ pi0 $\mu^+ \mu^-$ | 1e-12 branching fraction normalization | 2004 | Isidori, Smith, Unterdorfer, Eur. Phys. J. C 36 (2004) 57 | source ↑ |
| $C_{mix}^\mu$ coefficient in $K_L \to $ pi0 $\mu^+ \mu^-$ decomposition | $3.7 |a_S|^2$ coefficient multiplying 1e-12 branching fraction | 2004 | Isidori, Smith, Unterdorfer, Eur. Phys. J. C 36 (2004) 57 | source ↑ |
| $C_{int}^\mu$ coefficient in $K_L \to $ pi0 $\mu^+ \mu^-$ decomposition | 1.6 |a_S| coefficient multiplying 1e-12 branching fraction | 2004 | Isidori, Smith, Unterdorfer, Eur. Phys. J. C 36 (2004) 57 | source ↑ |
| $C_{dir}^\mu$ coefficient in $K_L \to $ pi0 $\mu^+ \mu^-$ decomposition | 1.0 coefficient multiplying 1e-12 branching fraction | 2004 | Isidori, Smith, Unterdorfer, Eur. Phys. J. C 36 (2004) 57 | source ↑ |
| $C_{CPC}^\mu$ coefficient in $K_L \to $ pi0 $\mu^+ \mu^-$ decomposition | 5.2 coefficient multiplying 1e-12 branching fraction | 2004 | Isidori, Smith, Unterdorfer, Eur. Phys. J. C 36 (2004) 57 | source ↑ |
| $|a_S|$ input for $K_L \to $ pi0 $\mu^+ \mu^-$ decomposition | 1.2 dimensionless | 2004 | Isidori, Smith, Unterdorfer, Eur. Phys. J. C 36 (2004) 57 | source ↑ |
| Constructive-interference SM expectation for $BR(K_L \to $ pi0 $\mu^+ \mu^-$) | 1.5e-11 branching fraction | 2004 | Isidori, Smith, Unterdorfer, Eur. Phys. J. C 36 (2004) 57 | source ↑ |
Why this constrains the RS scan
This mode probes \(s\to d\mu^+\mu^-\) semileptonic and electroweak-penguin
structures, not the \(\Delta F=2\) KK-gluon mixing lane currently implemented.
In RS or anarchic-flavor variants it is sensitive to flavor-changing \(Z\)
couplings, heavy neutral gauge exchange, and short-distance vector/axial
operators. The muon mode's CP-conserving two-photon contribution is
numerically important in the author theory decomposition, so a future signal would
require separating CPV short-distance information from long-distance hadronic
input.
What's changed since the original paper
No post-2008 experimental result was found that supersedes the KTeV/PDG
\(K_L\to\pi^0\mu^+\mu^-\) limit. The supporting short-lived mode remains the
NA48/PDG \(K_S\to\pi^0\mu^+\mu^-\) value
\((2.9^{+1.5}_{-1.2}\pm0.2)\times10^{-9}\), based on six observed events and
\(0.22^{+0.18}_{-0.11}\) expected background events
(
na48\_ks\_pi0mumu\_pdgLive.txt,
na48\_ks\_pi0mumu\_arxiv.txt). Since arXiv:0804.1954, the main
developments are interpretive: exploratory lattice work has started on
long-distance \(K\to\pi\ell^+\ell^-\) amplitudes
(christ\_feng\_juettner\_lawson\_portelli\_sachrajda2016\_lattice\_arxiv.txt),
and the Snowmass rare-kaon white paper keeps
\(K_{L,S}\to\pi^0\ell^+\ell^-\) branching ratios and spectra in the
short-distance rare-kaon program
(aebischer\_buras\_kumar2022\_rare\_kaon\_arxiv.txt).Validity and model dependence
Class: long-distance-limited and CP-decomposition-dependent. The
Isidori--Smith--Unterdorfer decomposition writes the rate as mixing,
interference, direct, and CP-conserving pieces multiplying \(10^{-12}\). For
the muon mode the coefficients are
\[
C_{\rm mix}^{\mu}=(3.7\pm0.1)|a_S|^2,\quad
C_{\rm int}^{\mu}=(1.6\pm0.1)|a_S|,\quad
C_{\rm dir}^{\mu}=1.0\pm0.1,\quad
C_{\rm CPC}^{\mu}=5.2\pm1.6,
\]
with \(|a_S|=1.2\pm0.2\). The same paper quotes the constructive-interference
SM expectation as \((1.5\pm0.3)\times10^{-11}\), well below the current
experimental limit. These numerical theory inputs are recorded in the YAML
theory\_decomposition block and trace to
isidori\_smith\_unterdorfer2004\_kl\_pi0mumu\_arxiv.txt.Code coverage in this repo
NO. Targeted greps over
quarkConstraints/, qcd/,
flavorConstraints/, neutrinos/, yukawa/,
warpConfig/, solvers/, scanParams/, and
tests/ found no \(K_L\to\pi^0\mu^+\mu^-\), \(K_S\to\pi^0\mu^+\mu^-\),
\(a_S\), or \(s\to d\mu^+\mu^-\) implementation. Existing nearby kaon coverage
is \(\Delta F=2\), e.g. quarkConstraints/deltaf2.py:209 and the modern
policy list at quarkConstraints/modern/phenomenology.py:23.Implementation difficulty
HIGH. A production constraint needs a new \(\Delta S=1\) semileptonic
observable, short-distance \(s\to d\mu^+\mu^-\) matching, CPV/interference
bookkeeping tied to \(K_S\to\pi^0\mu^+\mu^-\), and a long-distance
two-photon/CPC treatment. The existing \(\Delta F=2\) SLL/SLR/VLL/VRR/LR
basis is not sufficient.
Reason: Requires a new $\Delta S = 1$ semileptonic rare-kaon observable, short-distance $s \to d$ mu+mu- matching, indirect/direct CP separation with interference, and long-distance two-photon/CPC inputs. Existing $\Delta F = 2$ SLL/SLR/VLL/VRR/LR machinery does not cover this mode.
Key references
Process-local source keys before bibliography consolidation:
PDG2026:K009, KTeV2000:KLPi0MuMu,
NA482004:KSPi0MuMu,
IsidoriSmithUnterdorfer2004:KLPi0MuMu,
CFW2008:RSFlavor, ChristEtAl2016:KPiLLLattice, and
AebischerBurasKumar2022:RareKaons.