A new method for measurement of the Michel parameters that describe the daughter muon polarization in the $\tau^- \to \mu^- \bar{\nu}_\mu\nu_\tau$ decay

TL;DR

This paper introduces a novel method for directly measuring all Michel parameters related to muon polarization in tau decay, with feasibility studies for future collider experiments including Super Charm-Tau Factory and Belle II.

Contribution

It presents the first detailed method for direct measurement of all Michel parameters in tau decay and evaluates its feasibility in upcoming collider experiments.

Findings

Feasibility of measuring Michel parameters at Super Charm-Tau Factory.

Sensitivity estimates for Michel parameters at Belle II.

Method enables direct access to tau decay polarization parameters.

Abstract

This paper provides a detailed description of the method for the first direct measurement of all Michel parameters in the $\tau^- \to \mu^- \bar{\nu}_\mu\nu_\tau$ decay related to the polarization of the daughter muon. An application of the suggested method in the existing and future experiments at $e^+e^-$ colliders is considered. We have performed a feasibility study for the future Super Charm-Tau Factory and Belle II experiments. For the first one, the sensitivity to the Michel parameters $\xi'$, $\xi''$, $\eta''$, $\alpha'/A$, and $\beta'/A$ is estimated. For the latter, only one Michel parameter, $\xi'$, for which the sensitivity is maximum, is considered.