L002 $\mathcal{B}(\mu^+\to e^+e^-e^+)$
Muon to three electrons charged-lepton-flavor-violating four-lepton decay Status REVIEWED VERIFIED Medium Code: NO Priority Medium
PDG / equivalent values
| Observable | Value | Year | Experiment / source | Provenance |
|---|---|---|---|---|
| Branching fraction upper limit for $\mu^+ \to $ e+ e- e+ | 1e-12 | 2026 | Particle Data Group 2026 pdgLive muon listing, datablock S004R4 | source ↑ |
| $\Gamma(\mu \to $ 3e) / $\Gamma(\mu \to $ e 2nu) | 1e-12 | 1988 | SINDRUM Collaboration, U. Bellgardt et al. | source ↑ |
Why this constrains the RS scan
In a warped lepton extension, \(\mu\to 3e\) probes flavor-violating neutral
currents and four-lepton operators generated by KK gauge exchange, \(Z\)-like
mixing, or other lepton-current misalignment. It is complementary to L001:
\(\mu\to e\gamma\) is dominantly dipole-like in the current repo, while
\(\mu\to 3e\) can be tree-level/contact dominated and therefore has different
dependence on lepton localization and five-dimensional Yukawa assumptions.
The Agashe--Blechman--Petriello RS LFV analysis already treated rare muon decays
as part of the lepton-sector flavor test set.
What's changed since the original paper
Relative to the arXiv:0804.1954 RS-flavor baseline, the experimental limit has
not yet been superseded in PDG; SINDRUM still sets the catalog value. The main
post-2008 change is the Mu3e program at PSI: the phase-I detector design,
published in 2021, is built for \(10^8\) muon decays per second and a
\(2\times10^{-15}\) single-event sensitivity
(
L002.yaml:prospects). The 2025 status note records a phase-I
sensitivity scale of \(\mathcal{O}(10^{-15})\) and an upgraded scale of
\(\mathcal{O}(10^{-16})\). On the theory side, the sidecar source
crivellin2017\_mu\_e\_eft\_arxiv1702\_03020.txt covers systematic
EFT/RG analyses of \(\mu\to e\gamma\), \(\mu\to 3e\), and coherent conversion
below \(m_W\), including QED/QCD operator mixing.Validity and model dependence
The experimental interpretation is robust: the Standard-Model rate with massive
neutrinos is negligible, quoted by Mu3e status material as
\(\mathcal{O}(10^{-54})\), so an observation would be new physics. The mapping
to this repo is model-dependent because a four-lepton Wilson basis, dipole
interference convention, and possible RG evolution must be chosen. This entry
should be classified as lepton-extension-only and contact-operator sensitive,
not as a quark-scan constraint.
Code coverage in this repo
NO. The required greps over
quarkConstraints/, qcd/,
flavorConstraints/, neutrinos/, yukawa/,
warpConfig/, solvers/, scanParams/, and
tests/ found no \(\mu\to 3e\), Mu3e, or four-lepton-contact
implementation. The only adjacent charged-lepton LFV path is the dipole
\(\mu\to e\gamma\) checker at flavorConstraints/muToEGamma.py:75 and
its scan call at scanParams/scan.py:524, which do not evaluate
\(\mu\to 3e\).
Linked evidence (opens GitHub blob at flavor-catalog-website/2026q2):
Implementation difficulty
MEDIUM. A minimal implementation needs a new low-energy
\(\mu\to 3e\) observable formula, a four-lepton Wilson/operator convention, and
a matching hook from the RS lepton-sector parameters. It should not require
lattice matrix elements or hadronic long-distance inputs. A production EFT
treatment with QED/QCD RG mixing and correlated \(\mu\to e\gamma\),
\(\mu\to 3e\), and \(\mu\)-to-\(e\) conversion fits would raise the integration
difficulty.
Reason: Missing implementation needs a new four-lepton/contact LFV operator convention, branching-ratio formula, and RS lepton-sector matching hook. It does not require lattice inputs or hadronic long-distance calculations for a first implementation.
Key references
Process-local source keys before bibliography consolidation:
PDG2026\_MuonS004R4, SINDRUM1988\_Mu3e,
Mu3eTDR2021, Mu3eStatus2025,
CrivellinDavidsonPrunaSigner2017\_MuEFT,
AgasheBlechmanPetriello2006\_RSLFV, and CFW2008.