First measurement of the Michel parameter $ξ^\prime$ in the $τ^-\toμ^-\barν_μν_τ$ decay at Belle
We report the first measurement of the Michel parameter $ξ^\prime$ in the $τ^-\toμ^-\barν_μν_τ$ decay with a new method proposed just recently. The measurement is based on the reconstruction of the $τ^-\toμ^-\barν_μν_τ$ 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 $912\times10^6$ $τ^+ τ^-$ pairs. We measure $ξ^\prime=0.22\pm0.94(\text{stat})\pm0.42(\text{syst})$, which is in agreement with the standard model prediction of $ξ^\prime=1$. 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.