Z lepton flavour violation as a probe for new physics at future e^+e^- colliders

In this work we assess the potential of discovering new physics by searching for lepton-flavour-violating (LFV) decays of the Z boson, Z→ℓ _i ℓ _j , at the proposed circular e^+e^- colliders CEPC and FCC-ee. Both projects plan to run at the Z -pole as a “Tera Z factory”, i.e., collecting 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 μ and τ decays on the operators that can induce Z→ℓ _i ℓ _j . We find that, while the Z→μ e rates are beyond the expected sensitivities, a Tera Z factory is promising for Z→τℓ decays, probing New Physics at the same level of future low-energy LFV observables.