Measurement of the $tau$ lepton polarization and $R(D^*)$ in the decay $bar{B} rightarrow D^* tau^- bar{ u}_tau$ 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 $bar{B} rightarrow D^* tau^- bar{ u}_tau$ is studied with the hadronic $tau$ decays $tau^- rightarrow pi^- u_tau$ and $tau^- rightarrow rho^- u_tau$. The $tau$ polarization $P_tau(D^*)$ in two-body hadronic $tau$ decays is measured, as well as the ratio of the branching fractions $R(D^{*}) = mathcal{B}(bar {B} rightarrow D^* tau^- bar{ u}_tau) / mathcal{B}(bar{B} rightarrow D^* ell^- bar{ u}_ell)$, where $ell^-$ denotes an electron or a muon. Our results, $P_tau(D^*) = -0.38 pm 0.51 {rm (stat)} ^{+0.21}_{-0.16} {rm (syst)}$ 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.