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

We report the first measurement of the Michel parameter ${\xi }^{\mathrm{\prime }}$ 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 ${\xi }^{\mathrm{\prime }}=0.22\pm 0.94(\text{stat})\pm 0.42(\text{syst})$, which is in agreement with the standard model prediction of ${\xi }^{\mathrm{\prime }}=1$. 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.