Measurement of the $tau$ lepton polarization and $R(D^*)$ in the decay $bar{B} to D^* tau^- bar{ u}_tau$

We report the first measurement of the $tau$ lepton polarization $P_tau(D^*)$ in the decay $bar{B} rightarrow D^* tau^- bar{ u}_tau$ as well as a new measurement of 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, and the $tau$ is reconstructed in the modes $tau^- rightarrow pi^- u_tau$ and $tau^- rightarrow rho^- u_tau$. 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, $P_tau(D^*) = -0.38 pm 0.51 {rm (stat.)} ^{+0.21}_{-0.16} {rm (syst.)}$ 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.