# Enhanced $Z$ boson decays as a new probe of first-order electroweak phase transition at future lepton colliders

## TL;DR

This paper explores how enhanced Z boson decays can serve as a new way to investigate the electroweak phase transition at future lepton colliders, linking it to dark matter and muon g-2 anomalies.

## Contribution

It demonstrates that strong first-order electroweak phase transition conditions lead to observable effects in Z decays, providing a novel experimental probe.

## Key findings

- Enhanced Z decays due to phase transition conditions
- Future colliders can effectively explore electroweak phase transition
- Correlation between phase transition and muon g-2 anomaly

## Abstract

We study phenomenological consequences of the strong first-order electroweak phase transition in an extension of the standard model with an inert doublet and vector-like leptons motivated by the muon $g-2$ anomaly and dark matter. We find that a condition for the strong first-order electroweak phase transition inevitably induces a large logarithmic enhancement in $Z$ boson decays, which relegates the explanation of the anomalous muon $g-2$ at below 2$\sigma$ level. Our analysis shows that future lepton collider experiments, especially the Giga-$Z$ at the International Linear Collider and Tera-$Z$ at the Circular Electron Positron Collider as well as Future Circular Collider have great capability to explore the nature of the electroweak phase transition, which is complementary to conventional approaches via measurements of the triple Higgs boson coupling and gravitational waves.