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

TL;DR

Future $e^+e^-$ colliders like CEPC and FCC-ee could significantly advance the search for lepton-flavour-violating $Z$ decays, especially $Z o au ext{lepton}$, providing a promising avenue for discovering new physics.

Contribution

This study evaluates the discovery potential of LFV $Z$ decays at future colliders using a model-independent EFT approach, highlighting the sensitivity to new physics.

Findings

$Z o au ext{lepton}$ decays can be probed at future colliders.

$Z o ext{muon} e$ rates are beyond expected sensitivities.

Future colliders can match the sensitivity of low-energy LFV experiments.

Abstract

In this work we assess the potential of discovering new physics by searching for lepton-flavour-violating (LFV) decays of the $Z$ boson, $Z\to \ell_i \ell_j$, 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 $\mathcal O\left(10^{12}\right)$ $Z$ 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 $\mu$ and $\tau$ decays on the operators that can induce $Z\to \ell_i \ell_j$. We find that, while the $Z\to \mu e$ rates are beyond the expected sensitivities, a Tera Z factory is promising for $Z\to \tau\ell$ decays, probing New Physics at the same level of future low-energy LFV observables.