Measurement of the τ Lepton Polarization and R ( D * ) in the Decay B ¯ → D * τ − ν ¯ τ

We report the first measurement of the $ensuremath{tau}$ lepton polarization ${P}_{ensuremath{tau}}({D}^{*})$ in the decay $overline{B}ensuremath{rightarrow}{D}^{*}{ensuremath{tau}}^{ensuremath{-}}{overline{ensuremath{nu}}}_{ensuremath{tau}}$ as well as a new measurement of 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, and the $ensuremath{tau}$ is reconstructed in the modes ${ensuremath{tau}}^{ensuremath{-}}ensuremath{rightarrow}{ensuremath{pi}}^{ensuremath{-}}{ensuremath{nu}}_{ensuremath{tau}}$ and ${ensuremath{tau}}^{ensuremath{-}}ensuremath{rightarrow}{ensuremath{rho}}^{ensuremath{-}}{ensuremath{nu}}_{ensuremath{tau}}$. We use the full data sample of $772ifmmodetimeselsetexttimesfi{}1{0}^{6}text{ }text{ }Boverline{B}$ pairs recorded with the Belle detector at the KEKB electron-positron collider. Our results, ${P}_{ensuremath{tau}}({D}^{*})=ensuremath{-}0.38ifmmodepmelsetextpmfi{}0.51{(text{stat})}_{ensuremath{-}0.16}^{+0.21}(text{syst})$ and $R({D}^{*})=0.270ifmmodepmelsetextpmfi{}0.035{(text{stat})}_{ensuremath{-}0.025}^{+0.028}(text{syst})$, are consistent with the theoretical predictions of the standard model.