First measurement of the Michel parameter ${\xi }^{\prime }$ in the ${\tau }^{-}\to {\mu }^{-}{\bar{\nu }}_{\mu }{\nu }_{\tau }$ decay at Belle

Abstract

We report the first measurement of the Michel parameter ${\xi }^{\prime }$ in the ${\tau }^{-}\to {\mu }^{-}{\bar{\nu }}_{\mu }{\nu }_{\tau }$ decay with a new method proposed just recently. The measurement is based on the reconstruction of the ${\tau }^{-}\to {\mu }^{-}{\bar{\nu }}_{\mu }{\nu }_{\tau }$ events with subsequent muon decay-in-flight in the Belle central drift chamber. The analyzed data sample of $988{\text{fb}}^{-1}$ collected by the Belle detector corresponds to approximately $912\times 10^6$ ${\tau }^{+}{\tau }^{-}$ pairs. We measure ${\xi }^{\prime }=0.22\pm 0.94(\text{stat})\pm 0.42(\text{syst})$, which is in agreement with the standard model prediction of ${\xi }^{\prime }=1$. Statistical uncertainty dominates in this study, being a limiting factor, while systematic uncertainty is well under control. Our analysis proved the practicability of this promising method and its prospects for further precise measurement in future experiments.

arXiv comment6 pages, 4 figures, published in Phys. Rev. Lett