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