We present the first measurement of the Michel parameter ${\mathrm{<ruby><rb>\xi </rb><rt>くしー</rt></ruby>}}^{\prime }$ in the ${\mathrm{<ruby><rb>\tau </rb><rt>たう</rt></ruby>}}^{-}\to {\mathrm{<ruby><rb>\mu </rb><rt>みゅー</rt></ruby>}}^{-}{\overline{\mathrm{<ruby><rb>\nu </rb><rt>にゅー</rt></ruby>}}}_{\mathrm{<ruby><rb>\mu </rb><rt>みゅー</rt></ruby>}}{\mathrm{<ruby><rb>\nu </rb><rt>にゅー</rt></ruby>}}_{\mathrm{<ruby><rb>\tau </rb><rt>たう</rt></ruby>}}$ decay using the full data sample of $988{\mathrm{fb}}^{-1}$ collected by the Belle detector operating at the KEKB asymmetric energy $e^{+}{e}^{-}$ collider. The method is based on the reconstruction of the ${\mathrm{<ruby><rb>\mu </rb><rt>みゅー</rt></ruby>}}^{-}\to e^{-}{\overline{\mathrm{<ruby><rb>\nu </rb><rt>にゅー</rt></ruby>}}}_e{\mathrm{<ruby><rb>\nu </rb><rt>にゅー</rt></ruby>}}_{\mathrm{<ruby><rb>\mu </rb><rt>みゅー</rt></ruby>}}$ decay-in-flight in the Belle central drift chamber and relies on the correlation between muon spin and its daughter electron momentum. We study the main sources of the background that can imitate the signal decay, such as kaon and pion decays-in-flight and charged particle scattering on the detector material. Highly efficient methods of their suppression are developed and applied to select 165 signal-candidate events. We obtain ${\mathrm{<ruby><rb>\xi </rb><rt>くしー</rt></ruby>}}^{\prime }=0.22\pm 0.94\pm 0.42$ where the first uncertainty is statistical, and the second one is systematic. The result is in agreement with the Standard Model prediction of ${\mathrm{<ruby><rb>\xi </rb><rt>くしー</rt></ruby>}}^{\prime }=1$.

• Received 21 March 2023
• Accepted 7 June 2023

DOI:https://doi.org/10.1103/PhysRevD.108.012003

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Published by the American Physical Society