L010 $\mathcal{B}(\tau^-\to e^-e^+e^-)$
Tau 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 $\tau^- \to e^-$ e+ $e^-$ | 2.7e-8 | 2025 | PDG live tau branching-ratio datablock S035R58, 2025 update | source ↑ |
| Branching fraction upper limit for $\tau^- \to e^-$ e+ $e^-$ | 2.7e-8 | 2010 | Belle Collaboration | source ↑ |
| Branching fraction upper limit for $\tau^- \to e^-$ e+ $e^-$ | 2.9e-8 | 2010 | BaBar Collaboration | source ↑ |
Why this constrains the RS scan
This mode tests lepton-sector flavor violation that is not forced to be
dipole dominated. Warped lepton extensions can generate
\(\tau eee\) through flavor-nonuniversal lepton profiles, KK neutral-gauge
exchange, flavor-changing \(Z\) couplings, or scalar exchange. It is therefore
complementary to \(\tau\to e\gamma\) and \(\mu\to e\gamma\): an off-shell
photon can contribute, but contact four-lepton operators can be the leading
effect in models with tree-level lepton-current misalignment.
What's changed since the original paper
Relative to the arXiv:0804.1954 RS-flavor baseline, the direct experimental
bound became a B-factory \(10^{-8}\)-level constraint in 2010
(
L010.yaml:pdg\_or\_equivalent.rs\_context;
L010.yaml:pdg\_or\_equivalent.primary\_experiment). Belle set the
current PDG-selected limit \(2.7\times10^{-8}\), and BaBar reached the
comparable \(2.9\times10^{-8}\) limit
(L010.yaml:pdg\_or\_equivalent.primary\_current\_limit;
L010.yaml:pdg\_or\_equivalent.supporting\_experiment). No newer LHCb
electron-mode value is used here: the snapshotted LHCb source is for the
all-muon companion mode only
(L010.yaml:pdg\_or\_equivalent.lhcb\_context). For prospects, the
Belle II Physics Book quotes \(50~{\rm ab}^{-1}\) sensitivity at the
\(\mathcal{O}(10^{-9})\)--\(\mathcal{O}(10^{-10})\) level for favorable
low-background tau LFV modes
(L010.yaml:pdg\_or\_equivalent.prospects).Validity and model dependence
Experimentally this is a clean upper limit on a forbidden charged-LFV decay.
Its interpretation in the present quark-scan repository is lepton-extension
only: there is no tau-sector matching or four-lepton LFV observable in the
current scan. As a future RS constraint it is model dependent because
dipole-only, contact-operator, and full lepton-EFT assumptions give different
correlations with \(\tau\to e\gamma\), \(\tau\to 3\mu\), \(\mu\to e\gamma\),
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
\(\tau\to3e\), tau four-lepton LFV, or charged-lepton contact LFV. The
adjacent implemented LFV surface is only \(\mu\to e\gamma\):
flavorConstraints/muToEGamma.py:75 and
scanParams/scan.py:524. The modern phenomenology registry is limited
to neutral-meson systems at 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 calculations, but a
production implementation should specify 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. No lattice inputs or hadronic long-distance calculations are required for a first bound.
Key references
Process-local raw keys:
PDG2025\_Tau3E,
Belle2010\_Tau3Leptons, BaBar2010\_Tau3Leptons,
BelleIIPhysicsBook2019\_TauLFV,
LHCb2026\_Tau3MuContext,
AgasheBlechmanPetriello2006\_RSLFV, and
CFW2008\_RSWarpedFlavor.