Measurement of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>τ</mml:mi></mml:math> lepton polarization and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>R</mml:mi><mml:mo mathvariant="bold" stretchy="false">(</mml:mo><mml:msup><mml:mi>D</mml:mi><mml:mo>*</mml:mo></mml:msup><mml:mo mathvariant="bold" stretchy="false">)</mml:mo></mml:math> in the decay <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mover accent="true"><mml:mi>B</mml:mi><mml:mo stretchy="false">¯</mml:mo></mml:mover><mml:mo stretchy="false">→</mml:mo><mml:msup><mml:mi>D</mml:mi><mml:mo>*</mml:mo></mml:msup><mml:msup><mml:mi>τ</mml:mi><mml:mo>−</mml:mo></mml:msup><mml:msub><mml:mover accent="true"><mml:mi>ν</mml:mi><mml:mo stretchy="false">¯</mml:mo></mml:mover><mml:mi>τ</mml:mi></mml:msub></mml:math> with one-prong hadronic <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>τ</mml:mi></mml:math> decays at Belle

With the full data sample of $772\ifmmode\times\else\texttimes\fi{}{10}^{6}\text{ }\text{ }B\overline{B}$ pairs recorded by the Belle detector at the KEKB electron-positron collider, the decay $\overline{B}\ensuremath{\rightarrow}{D}^{*}{\ensuremath{\tau}}^{\ensuremath{-}}{\overline{\ensuremath{\nu}}}_{\ensuremath{\tau}}$ is studied with the hadronic $\ensuremath{\tau}$ decays ${\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\nu}}_{\ensuremath{\tau}}$ and ${\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\rho}}^{\ensuremath{-}}{\ensuremath{\nu}}_{\ensuremath{\tau}}$. The $\ensuremath{\tau}$ polarization ${P}_{\ensuremath{\tau}}({D}^{*})$ in two-body hadronic $\ensuremath{\tau}$ decays is measured, as well as the ratio of the branching fractions $R({D}^{*})=\mathcal{B}(\overline{B}\ensuremath{\rightarrow}{D}^{*}{\ensuremath{\tau}}^{\ensuremath{-}}{\overline{\ensuremath{\nu}}}_{\ensuremath{\tau}})/\mathcal{B}(\overline{B}\ensuremath{\rightarrow}{D}^{*}{\ensuremath{\ell}}^{\ensuremath{-}}{\overline{\ensuremath{\nu}}}_{\ensuremath{\ell}})$, where ${\ensuremath{\ell}}^{\ensuremath{-}}$ denotes an electron or a muon. Our results, ${P}_{\ensuremath{\tau}}({D}^{*})=\ensuremath{-}0.38\ifmmode\pm\else\textpm\fi{}0.51{(\text{stat})}_{\ensuremath{-}0.16}^{+0.21}(\text{syst})$ and $R({D}^{*})=0.270\ifmmode\pm\else\textpm\fi{}0.035{(\text{stat})}_{\ensuremath{-}0.025}^{+0.028}(\text{syst})$, are consistent with the theoretical predictions of the standard model. The polarization values of ${P}_{\ensuremath{\tau}}({D}^{*})&gt;+0.5$ are excluded at the 90% confidence level.