Measurement of the $\tau$ lepton polarization and $R(D^{\ast })$ in the decay $\bar{B}\to D^{\ast }{\tau }^{-}{\bar{\nu }}_{\tau }$

We report the first measurement of the $\tau$ lepton polarization $P_{\tau }(D^{\ast })$ in the decay $\bar{B}\to D^{\ast }{\tau }^{-}{\bar{\nu }}_{\tau }$ as well as a new measurement of the ratio of the branching fractions $R(D^{}) = $\mathcal{B}$(\bar {B} \rightarrow D^ \tau^- \bar{\nu}\tau) / $\mathcal{B}$(\bar{B} \rightarrow D^* \ell^- \bar{\nu}\ell)$,where$\ell^-$denotesanelectronoramuon,andthe$\tau$isreconstructedinthemodes$\tau^- \rightarrow \pi^- \nu_\tau$and$\tau^- \rightarrow \rho^- \nu_\tau$. We use the full data sample of $772\times {10}^6$ $B\bar{B}$ pairs recorded with the Belle detector at the KEKB electron-positron collider. Our results, $P_{\tau }(D^{\ast })=-0.38\pm 0.51{(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{.})}_{-0.16}^{+0.21}(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}\mathrm{.})$ and $R(D^{\ast })=0.270\pm 0.035{(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{.})}_{-0.025}^{+0.028}(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}\mathrm{.})$, are consistent with the theoretical predictions of the Standard Model.