Measurement of the $\tau$ Lepton Polarization and $R\left(D^{*}\right)$ in the Decay $\overline{B}\to D^{*}{\tau }^{-}{\overline{\nu }}_{\tau }$

Here, we discuss the first measurement of the $\tau$ lepton polarization $P_{\tau }\left(D^{*}\right)$ in the decay $\overline{B}\to D^{*}{\tau }^{-}{\overline{\nu }}_{\tau }$ as well as a new measurement of the ratio of the branching fractions $R\left(D^{*}\right)=B(\overline{B}\to D^{*}{\tau }^{-}{\overline{\nu }}_{\tau })/B(\overline{B}\to D^{*}{\ell }^{-}{\overline{\nu }}_{\ell })$, where ${\ell }^{-}$ denotes an electron or a muon, and the $\tau$ is reconstructed in the modes ${\tau }^{-}\to {\pi }^{-}{\nu }_{\tau }$ and ${\tau }^{-}\to {\rho }^{-}{\nu }_{\tau }$. We use the full data sample of $772\times 10^{6}B\overline{B}$ pairs recorded with the Belle detector at the KEKB electron-positron collider. Our findings, $P_{\tau }\left(D^{*}\right)=-0.38\pm 0.51{\left(\text{stat}\right)}_{-0.16}^{+0.21}\left(\text{syst}\right)$ and $R\left(D^{*}\right)=0.270\pm 0.035{\left(\text{stat}\right)}_{-0.025}^{+0.028}\left(\text{syst}\right)$, are consistent with the theoretical predictions of the standard model.