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

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 ${\xi }^{\prime }$, ${\xi }^{\prime \prime }$, ${\eta }^{\prime \prime }$, ${\alpha }^{\prime }/A$, and ${\beta }^{\prime }/A$ is estimated. For the latter, only one Michel parameter, ${\xi }^{\prime }$, for which the sensitivity is maximum, is considered.

Comments: 17 pages, 5 figures