# Lepton polarization asymmetries in rare semi-tauonic $ b \rightarrow s $ exclusive decays at FCC-$ee$

## TL;DR

This paper explores the potential of future FCC-ee collider experiments to measure tau polarization asymmetries in rare $b$-hadron decays, providing new insights into short-distance physics and lepton flavor universality violations.

## Contribution

It proposes a method to reconstruct tau polarization asymmetries in rare $b$-hadron decays at FCC-ee, highlighting their importance for probing new physics.

## Key findings

- High boosts of $b$-hadrons enable full decay kinematics reconstruction.
- Potential for large statistics from $Z o bar{b}$ decays.
- Identification of theoretically clean polarization observables.

## Abstract

We consider measurements of exclusive rare semi-tauonic $b$-hadron decays, mediated by the $b \rightarrow s \tau^+ \tau^-$ transition, at a future high energy circular electron-positron collider (FCC-$ee$). We argue that the high boosts of $b$-hadrons originating from on-shell $Z$ boson decays allow for a full reconstruction of the decay kinematics in hadronic $\tau$ decay modes (up to discrete ambiguities). This, together with the potentially large statistics of $Z\to b\bar b$, opens the door for the experimental determination of $\tau$ polarizations in these rare $b$-hadron decays. In light of the current experimental situation on lepton flavor universality in rare semileptonic $B$ decays, we discuss the complementary short-distance physics information carried by the $\tau$ polarizations and suggest suitable theoretically clean observables in the form of single- and double-$\tau$ polarization asymmetries.