AbstractIn this work we assess the potential of discovering new physics by searching for lepton-flavour-violating (LFV) decays of the Z boson, $$Z\rightarrow \ell _i \ell _j$$
Z
→
ℓ
i
ℓ
j
, at the proposed circular $$e^+e^-$$
e
+
e
-
colliders CEPC and FCC-ee. Both projects plan to run at the Z-pole as a “Tera Z factory”, i.e., collecting $${\mathcal {O}}\left( 10^{12} \right) $$
O
10
12
Z decays. In order to discuss the discovery potential in a model-independent way, we revisit the LFV Z decays in the context of the Standard Model effective field theory and study the indirect constraints from LFV $$\mu $$
μ
and $$\tau $$
τ
decays on the operators that can induce $$Z\rightarrow \ell _i \ell _j$$
Z
→
ℓ
i
ℓ
j
. We find that, while the $$Z\rightarrow \mu e$$
Z
→
μ
e
rates are beyond the expected sensitivities, a Tera Z factory is promising for $$Z\rightarrow \tau \ell $$
Z
→
τ
ℓ
decays, probing New Physics at the same level of future low-energy LFV observables.
Effects of longitudinal short-distance constraints on the hadronic light-by-light contribution to the muon $$\mathbf {g-2}$$