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

Abstract

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 $\bar{B}\to D^{\ast }{\tau }^{-}{\bar{\nu }}_{\tau }$ is studied with the hadronic $\tau$ decays ${\tau }^{-}\to {\pi }^{-}{\nu }_{\tau }$ and ${\tau }^{-}\to {\rho }^{-}{\nu }_{\tau }$. The $\tau$ polarization $P_{\tau }(D^{\ast })$ in two-body hadronic $\tau$ decays is measured, as well as the ratio of the branching fractions $R(D^{\ast })=\mathcal{B}(\bar{B}\to D^{\ast }{\tau }^{-}{\bar{\nu }}_{\tau })/\mathcal{B}(\bar{B}\to D^{\ast }{\ell }^{-}{\bar{\nu }}_{\ell })$, where ${\ell }^{-}$ denotes an electron or a muon. Our results, $P_{\tau }(D^{\ast })=-0.38\pm 0.51{(\mathrm{stat})}_{-0.16}^{+0.21}(\mathrm{syst})$ and $R(D^{\ast })=0.270\pm 0.035{(\mathrm{stat})}_{-0.025}^{+0.028}(\mathrm{syst})$, are consistent with the theoretical predictions of the Standard Model. The polarization values of $P_{\tau }(D^{\ast })>+0.5$ are excluded at the 90\% confidence level.

17 pages, 11 figures, submitted to Physical Review D

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