L009 $\mathcal{B}(\tau^-\to\mu^-\mu^+\mu^-)$
Tau to three muons 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 $\tau^- \to \mu^- \mu^+ \mu^-$ | 1.9e-8 | 2025 | Particle Data Group 2025 tau listing | source ↑ |
| Branching fraction upper limit for $\tau^- \to \mu^- \mu^+ \mu^-$ | 1.9e-8 | 2024 | Belle II Collaboration | source ↑ |
| Branching fraction upper limit for $\tau^- \to \mu^- \mu^+ \mu^-$ | ? | 2026 | LHCb Collaboration Run 2 preprint | source ↑ |
Why this constrains the RS scan
This mode tests lepton-sector flavor violation that need not be dipole
dominated. In warped or composite-flavor extensions, flavor-nonuniversal
lepton profiles, KK gauge exchange, flavor-changing \(Z\) couplings, or
scalar exchange can generate effective \(\tau\mu\mu\mu\) operators. The
observable is therefore complementary to \(\tau\to\mu\gamma\) and
\(\mu\to e\gamma\): dipoles can feed the three-muon final state through an
off-shell photon, but the four-lepton final state is also directly sensitive
to contact LFV.
What's changed since the original paper
Relative to the arXiv:0804.1954 RS-flavor baseline, the experimental
frontier moved to \(10^{-8}\)-level limits
(
L009.yaml:pdg\_or\_equivalent.rs\_context;
L009.yaml:pdg\_or\_equivalent.historical\_experimental\_limits). Belle
and BaBar published full three-lepton tau searches in 2010, reaching
\(2.1\times 10^{-8}\) and \(3.3\times 10^{-8}\), respectively
(L009.yaml:pdg\_or\_equivalent.historical\_experimental\_limits[0] and
L009.yaml:pdg\_or\_equivalent.historical\_experimental\_limits[1]).
LHCb demonstrated a hadron-collider tau-to-three-muons program, setting
\(4.6\times 10^{-8}\) with Run 1 data and \(1.9\times 10^{-8}\) with Run 2
(L009.yaml:pdg\_or\_equivalent.historical\_experimental\_limits[2];
L009.yaml:pdg\_or\_equivalent.post\_pdg\_update). Belle II now
supplies the PDG benchmark, \(1.9\times 10^{-8}\)
(L009.yaml:pdg\_or\_equivalent.primary\_current\_limit).Validity and model dependence
Experimentally this is a clean upper limit on a forbidden charged-LFV decay.
As a constraint on the current quark-scan code it is lepton-extension-only:
the present quark $\Delta F = 2$ pipeline has no direct tau-lepton matching. As a
future RS constraint, the translation is model dependent because a dipole-only
assumption, a contact-operator assumption, and a full lepton-sector EFT can
give different correlations with \(\tau\to\mu\gamma\), \(\mu\to e\gamma\), and
\(\mu\to 3e\).
Code coverage in this repo
NO. Targeted greps over
quarkConstraints/,
qcd/, flavorConstraints/, neutrinos/,
yukawa/, warpConfig/, solvers/,
scanParams/, and tests/ found no implementation of
\(\tau\to3\mu\), tau four-lepton LFV, or contact LFV. The adjacent LFV code is
only \(\mu\to e\gamma\): flavorConstraints/muToEGamma.py:1,
flavorConstraints/muToEGamma.py:75, and scanParams/scan.py:524.
The modern phenomenology surface is neutral-meson mixing only, see
quarkConstraints/modern/phenomenology.py:23.Implementation difficulty
MEDIUM. A first implementation needs a new four-lepton LFV observable
and a convention for lepton-flavor Wilson coefficients or RS matching. It
does not require lattice inputs or hadronic long-distance treatment, but a
production-grade implementation should decide whether to include dipole/contact
interference and correlations with the existing \(\mu\to e\gamma\) lane.
Reason: A new four-lepton/contact LFV observable and lepton-sector Wilson-coefficient convention are needed. A first bound does not require lattice inputs or hadronic long-distance calculations, but correlations with dipoles and other LFV modes must be specified.
Key references
Process-local raw keys:
PDG2025\_Tau3Mu,
BelleII2024\_Tau3Mu, LHCb2026\_Tau3Mu,
LHCb2015\_Tau3Mu, Belle2010\_Tau3Leptons,
BaBar2010\_Tau3Leptons, and CFW2008\_RSWarpedFlavor.