L007 $\mathcal{B}(\tau^-\to\mu^-\gamma)$
Tau to $\mu \gamma$ charged-lepton-flavor-violating dipole decay Status REVIEWED VERIFIED Medium Code: NO Priority Medium
PDG / equivalent values
| Observable | Value | Year | Experiment / source | Provenance |
|---|---|---|---|---|
| Branching fraction upper limit for $\tau^- \to \mu^- \gamma$ | 4.2e-8 | 2025 | Particle Data Group 2025 PDGLive tau decay summary, PDGID S035.31 | source ↑ |
| Branching fraction upper limit for $\tau^+- \to \mu^+- \gamma$ | 4.2e-8 | 2021 | Belle Collaboration full-data tau -> l gamma search | source ↑ |
| Branching fraction upper limit for $\tau \to \mu \gamma$ | 4.4e-8 | 2010 | BaBar Collaboration full-data tau -> l gamma search | source ↑ |
| Projected branching-fraction sensitivity for $\tau \to \mu \gamma$ | ? | 2019 | Belle II Physics Book | source ↑ |
Why this constrains the RS scan
In warped lepton-flavor extensions, this mode constrains the same class of
brane-localized or loop-induced charged-lepton dipoles as \(\mu\to e\gamma\),
but with the \(\tau\mu\) flavor spurion instead of the \(e\mu\) spurion. It is
therefore not part of the quark \(\Delta F=2\) scan lane, but it is a useful
cross-check of any future lepton-sector implementation: models that suppress
\(\mu\to e\gamma\) through alignment can still leave enhanced tau-sector LFV.
The Perez--Randall warped-neutrino source records the lepton-MFV/GIM-like
assumptions under which charged-lepton flavor violation is controlled.
What's changed since the original paper
Since the arXiv:0804.1954 RS flavor baseline, the experimental limit was
sharpened by the full-data \(B\)-factory searches. BaBar's post-2008
full-data search used \((963\pm7)\times10^6\) tau decays and set
\(\mathcal{B}(\tau\to\mu\gamma)<4.4\times10^{-8}\) at \(90\%\) C.L.
(
L007.yaml:prior\_experimental\_limit). Belle's 2021 full-data update
improved the canonical \(\tau\to\mu\gamma\) value to \(4.2\times10^{-8}\). The
the author pass found no Belle II measurement superseding Belle for this channel; the
sidecar records only a Belle II Physics Book projection of
\(<5\times10^{-9}\) with \(50\,{\rm ab}^{-1}\), not a current bound.Validity and model dependence
Experimentally this is a clean null search for charged-lepton flavor violation,
with negligible Standard Model rates. Its RS interpretation is model-dependent:
the bound constrains a dipole coefficient or lepton-flavor spurion only after a
choice of lepton localization, flavor symmetry, Yukawa normalization, and KK
mass convention. The catalog should classify it as robust experimentally but
lepton-extension-only and dipole-model-dependent for this repo.
Code coverage in this repo
NO. The required catalog grep over
quarkConstraints/, qcd/,
flavorConstraints/, neutrinos/, yukawa/,
warpConfig/, solvers/, scanParams/, and
tests/ found no \(\tau\to\mu\gamma\) implementation. The adjacent
code surface is only \(\mu\to e\gamma\): flavorConstraints/muToEGamma.py:1
documents that process, lines 16--18 fix the \((1,2)\) element, line 75 defines
check\_mu\_to\_e\_gamma, and scanParams/scan.py:523--524 calls
that checker in scans. Those lines are reusable design evidence, not L007
coverage.Implementation difficulty
MEDIUM. A future implementation can reuse the existing LFV dipole
pattern, but it must generalize the flavor indices and rate normalization from
\(\mu\to e\gamma\) to tau decays, add a tau-sector branching-ratio limit, and
decide whether the same RS lepton-spurion assumptions apply. No new hadronic
matrix elements, lattice inputs, or QCD running are needed.
Reason: The repo has an adjacent $\mu \to e \gamma$ dipole pattern, but L007 needs a generalized lepton-dipole observable with tau-mu flavor indices, tau lifetime/normalization, and a process-specific branching-ratio limit. No new hadronic matrix elements, lattice inputs, or QCD running are needed.
Key references
Process-local source keys before bibliography consolidation:
PDG2025\_TauMuGamma, Belle2021\_TauLGamma,
BaBar2010\_TauLGamma, BelleIIPhysicsBook2019\_TauLFV,
CFW2008\_RSWarpedFlavor, and
PerezRandall2008\_WarpedNeutrinos.