arXiv · 2102.00752
The hadronic $\tau$ decay $\tau^-\to K_1^-\nu_\tau \to (K^-\omega) \nu_\tau\to (K^- \pi^+\pi^-\pi^0)\nu_\tau $ and the axial vector mixing angle
Abstract
We propose to measure the $\tau^-\to K_1^-\nu_\tau \to (K^-\omega) \nu_\tau\to (K^- \pi^+\pi^-\pi^0)\nu_\tau $ decay in order to determine the $K_1$ axial vector mixing angle $\theta_{K_1}$. We derive, for the first time, the differential decay rate formula for this decay mode. Using the obtained result, we perform a sensitivity study for the Belle (II) experiment. We will show that the $K^-\pi^+\pi^-\pi^0$ spectrum of the $\tau^-\to K_1^-\nu_\tau \to (K^-\omega) \nu_\tau\to (K^- \pi^+\pi^-\pi^0)\nu_\tau $ decay can discriminate the two solutions $\theta_{K_1}=\sim 30^{\circ}$ or $\sim 60^{\circ}$ observed in the other measurements.
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K. Hayasaka, Z. Huang, E. Kou. 2021-02-01. The hadronic $\tau$ decay $\tau^-\to K_1^-\nu_\tau \to (K^-\omega) \nu_\tau\to (K^- \pi^+\pi^-\pi^0)\nu_\tau $ and the axial vector mixing angle. https://doi.org/10.1140/epjc%2Fs10052-021-09303-5
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