Measurement of the $\tau$ lepton polarization and $R(D^{\ast })$ in the decay $\bar{B}\to D^{\ast }{\tau }^{-}{\bar{\nu }}_{\tau }$ with one-prong hadronic $\tau$ decays at Belle

With the full data sample of $772\times {10}^6$ $B\bar{B}$ pairs recorded by the Belle detector at the KEKB electron-positron collider, the decay $\bar{B} \rightarrow D^* \tau^- \bar{\nu}\tau$isstudiedwiththehadronic$\tau$decays$\tau^- \rightarrow \pi^- \nu\tau$and$\tau^- \rightarrow \rho^- \nu_\tau$\mathrm{.}The$\tau$polarization$P_\tau(D^)$intwo-bodyhadronic$\tau$decaysismeasured,aswellastheratioofthebranchingfractions$R(D^{}) = $\mathcal{B}$(\bar {B} \rightarrow D^* \tau^- \bar{\nu}\tau) / $\mathcal{B}$(\bar{B} \rightarrow D^* \ell^- \bar{\nu}\ell)$,where$\ell^-$denotesanelectronoramuon\mathrm{.}Ourresults,$P_\tau(D^) = -0.38 \pm 0.51 {\rm (stat)} ^{+0.21}_{-0.16} {\rm (syst)}$and$R(D^) = 0.270 \pm 0.035{\rm (stat)} ^{+0.028}{-0.025}{\rm (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.