Indirect searches for sterile neutrinos at a high-luminosity Z-factory

Abstract

A future high-luminosity $Z$-factory will offer the possibility to study rare $Z$ decays, as those leading to lepton flavour violating final states. Processes such as $Z\to {\ell }_1^{\mp }{\ell }_2^{\pm }$ are potentially complementary to low-energy (high-intensity) observables of lepton flavour violation. In this work we address the impact of new sterile fermions on lepton flavour violating $Z$ decays, focusing on potential searches at FCC-ee (TLEP), and taking into account experimental and observational constraints on the sterile states. We consider a minimal extension of the Standard Model by one sterile fermion state, and two well-motivated frameworks of neutrino mass generation, the Inverse Seesaw embedded into the Standard Model, and the $\nu$MSM. Our study shows that sterile neutrinos can give rise to contributions to BR($Z\to {\ell }_1^{\mp }{\ell }_2^{\pm }$) within reach of the FCC-ee. We also discuss the complementarity between a high-luminosity $Z$-factory and low-energy charged lepton flavour violation facilities.

29 pages, 28 figures

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