Catalog · Top / Higgs / EW · T017

T017 $\mathcal{B}(Z\to\mu^\pm\tau^\mp)$

Lepton-flavor-violating Z decay Z $ \to \mu \tau$

Status REVIEWED VERIFIED High Code: NO Priority Medium

PDG / equivalent values

Observable	Value	Year	Experiment / source	Provenance
B(Z $ \to \mu^+- \tau^-+$), charge-summed PDG listing	< 6.5e-6 branching fraction	2025	PDG2025:T017:zmutau_limit	source ↑
B(Z $ \to \mu \tau$), ATLAS combination with previous $hadronic-\tau$ analyses	< 6.5e-6 branching fraction	2021	ATLAS2021:T017:zmutau_combined_limit	source ↑
B(Z $ \to \mu \tau$), ATLAS leptonically decaying $\tau$ analysis only	< 7.2e-6 branching fraction	2021	ATLAS2021:T017:zmutau_leptonic_tau_limit	source ↑
ATLAS dataset for leptonically decaying $\tau$ Z LFV search	139 fb^-1 at sqrt(s) = 13 TeV integrated luminosity and collision energy	2021	ATLAS2021:T017:dataset	source ↑
B(Z $ \to \mu \tau$), CMS direct search	< 12.0e-6 branching fraction	2025	CMS2025:T017:zmutau_limit	source ↑
CMS dataset for Z LFV direct search	138 fb^-1 at sqrt(s) = 13 TeV integrated luminosity and collision energy	2025	CMS2025:T017:dataset	source ↑

Why this constrains the RS scan

Warped or partially composite lepton sectors can generate non-diagonal neutral currents after the charged-lepton mass matrix is diagonalized. $Z\to\mu\tau$ is therefore a direct probe of effective off-diagonal $Z_{\mu\tau}$ couplings from lepton localization, gauge-boson mixing, or flavor-symmetry breaking. It is relevant to a lepton/electroweak extension of the pipeline, not to the present quark $\Delta F=2$ implementation.

What's changed since the original paper

The arXiv:0804.1954 warped-flavor baseline predates the LHC $Z$-LFV program. The main post-2008 experimental development is the ATLAS $\tau$-channel search and combination, which established the current strongest observed $\mu\tau$ limit at the $10^{-6}$ branching-fraction level (ATLAS2021:T017:zmutau\_combined\_limit). CMS later performed a Run-2 search covering all three charged-lepton flavor pairs in one analysis, providing an independent 2025 check of the $\mu\tau$ channel. Future-factory studies also changed the context: Tera-$Z$ proposals with $\mathcal{O}(10^{12})$ produced $Z$ bosons are especially promising for $Z\to\tau\ell$ modes, whereas $Z\to\mu e$ remains more tightly constrained by low-energy observables (CalibbiMarcanoRoy2021:T017:teraZ).

Validity and model dependence

Experimentally this is a clean direct upper limit on a forbidden Standard Model decay. Applying it as a scan cut assumes the usual inclusive $Z$ production and total-width normalization used by the collaborations. As an RS constraint it is model-dependent: the same flavor spurions may also induce $\tau\to\mu\gamma$, $\tau\to\mu\mu\mu$, or Higgs LFV, so this entry should be treated as a direct collider constraint on $Z_{\mu\tau}$, not a complete LFV likelihood.

Code coverage in this repo

Coverage is NO. The required broad greps and a targeted search for $Z \to \mu \tau$ , $Z \to \tau \mu$ , Zmutau, and related LFV $Z$ strings across quarkConstraints/, qcd/, flavorConstraints/, neutrinos/, yukawa/, warpConfig/, solvers/, scanParams/, and tests/ found no $Z\to\mu\tau$ observable implementation. The only charged-lepton LFV backend seen is $\mu\to e\gamma$ (flavorConstraints/muToEGamma.py:75), called by the scan at scanParams/scan.py:524; the modern quark phenomenology policy is limited to $\epsilon_K$, $K$, $B_d$, $B_s$, and $D^0$ (quarkConstraints/modern/phenomenology.py:23).

Linked evidence (opens GitHub blob at flavor-catalog-website/2026q2):

Implementation difficulty

Production integration is HIGH. The external limit is easy to store, but a faithful RS constraint needs a new LFV $Z$-coupling convention, left- and right-handed lepton operator matching, model-dependent gauge/mass mixing inputs, and a policy for combining direct $Z$-pole searches with tau LFV and Higgs LFV constraints.

Reason: The repo lacks LFV Z operators and lepton-sector electroweak matching; production use would need a new Z_mu_tau coupling convention, left/right operator mapping, RS gauge/mass mixing inputs, and a combination policy with tau LFV and Higgs LFV constraints.

Key references

PDG2025ZLFVListing; ATLAS2021ZLFVTau; CMS2025ZLFV; CalibbiMarcanoRoy2021ZLFV; CsakiFalkowskiWeiler2008WarpedFlavor; PerezRandall2008WarpedLeptonFlavor.

value < 6.5e-6

RESOLVED

Match snapshot line 17

L14: 
L15: Gamma66  e+- mu-+    LF    [c] < 2.62 x 10^-7    CL=95%
L16: Gamma67  e+- tau-+   LF    [c] < 5.0  x 10^-6    CL=95%
L17: Gamma68  mu+- tau-+  LF    [c] < 6.5  x 10^-6    CL=95%
L18: 
L19: Footnote [c]:
L20: The value is for the sum of the charge states or particle/antiparticle states

value < 6.5e-6

RESOLVED

Match snapshot line 30

L27: analysis to B(Z -> e tau) < 7.0 x 10^-6 and B(Z -> mu tau) < 7.2 x 10^-6 at
L28: 95% confidence level. The combination with the previously published analyses
L29: sets the strongest constraints to date: B(Z -> e tau) < 5.0 x 10^-6 and
L30: B(Z -> mu tau) < 6.5 x 10^-6 at 95% confidence level.

value < 7.2e-6

RESOLVED

Match snapshot line 27

L24: combined with the results of a similar ATLAS search in the final state in
L25: which the tau-lepton decays hadronically, using the same data set as well as
L26: Run 1 data. The Z -> l tau branching fractions are constrained in this
L27: analysis to B(Z -> e tau) < 7.0 x 10^-6 and B(Z -> mu tau) < 7.2 x 10^-6 at
L28: 95% confidence level. The combination with the previously published analyses
L29: sets the strongest constraints to date: B(Z -> e tau) < 5.0 x 10^-6 and
L30: B(Z -> mu tau) < 6.5 x 10^-6 at 95% confidence level.

value 139 fb^-1 at sqrt(s) = 13 TeV

RESOLVED

Match snapshot line 23

L20: Relevant abstract extract:
L21: A search for lepton-flavor-violating Z -> e tau and Z -> mu tau decays with
L22: pp collision data recorded by the ATLAS detector at the LHC is presented. This
L23: analysis uses 139 fb^-1 of Run 2 pp collisions at sqrt(s)=13 TeV and is
L24: combined with the results of a similar ATLAS search in the final state in
L25: which the tau-lepton decays hadronically, using the same data set as well as
L26: Run 1 data. The Z -> l tau branching fractions are constrained in this

value 138 fb^-1 at sqrt(s) = 13 TeV

RESOLVED

Match snapshot line 24

L21: A search for flavor violating decays of the Z boson to charged leptons is
L22: performed using data from proton-proton collisions at sqrt(s) = 13 TeV
L23: collected with the CMS detector at the LHC, corresponding to an integrated
L24: luminosity of 138 fb^-1. Each of the decays Z -> e mu, Z -> e tau, and
L25: Z -> mu tau is considered. The data are consistent with the backgrounds
L26: expected from standard model processes. For the Z -> e mu channel the observed
L27: (expected) 95% confidence level upper limit on the branching fraction is