With the full data sample of $772\times {10}^{6}B\overline{B}$ pairs recorded by the Belle detector at the KEKB electron-positron collider, the decay $\overline{B}\to D^{*}{\tau }^{-}{\overline{\nu }}_{\tau }$ is studied with the hadronic $\tau$ decays ${\tau }^{-}\to {\pi }^{-}{\nu }_{\tau }$ and ${\tau }^{-}\to {\rho }^{-}{\nu }_{\tau }$. The $\tau$ polarization $P_{\tau }(D^{*})$ in two-body hadronic $\tau$ decays is measured, as well as the ratio of the branching fractions $R(D^{*})=\mathcal{B}(\overline{B}\to D^{*}{\tau }^{-}{\overline{\nu }}_{\tau })/\mathcal{B}(\overline{B}\to D^{*}{\ell }^{-}{\overline{\nu }}_{\ell })$, where ${\ell }^{-}$ denotes an electron or a muon. Our results, $P_{\tau }(D^{*})=-0.38\pm 0.51{(\text{stat})}_{-0.16}^{+0.21}(\text{syst})$ and $R(D^{*})=0.270\pm 0.035{(\text{stat})}_{-0.025}^{+0.028}(\text{syst})$, are consistent with the theoretical predictions of the standard model. The polarization values of $P_{\tau }(D^{*})>+0.5$ are excluded at the 90% confidence level.

• Received 31 August 2017

DOI:https://doi.org/10.1103/PhysRevD.97.012004

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Published by the American Physical Society