Polarization measurements in $\bar{ B} \to D^{ (\ast)} \tau \overline{ \nu}$ are useful to check consistency in new physics explanations for the $R_{ D}$ and $R_{ D^{ \ast}}$ anomalies. In this paper, we investigate the $D^{ \ast}$ and $\tau$ polarizations and focus on the new physics contributions to the fraction of a longitudinal $D^{ \ast}$ polarization ($F_{ L}^{ D^{ \ast}}$), which is recently measured by the Belle collaboration $F_{ L}^{ D^{ \ast}} = 0.60 \pm 0.09$, in model-independent manner and in each single leptoquark model (${ \rm R}_2$, ${ \rm S}_1$ and ${ \rm U}_1$) that can naturally explain the $R_{ D^{ (\ast)}}$ anomalies. It is found that $\mathcal{ B}(B_c^{ +} \to \tau^{ +} \nu)$ severely restricts deviation from the Standard Model (SM) prediction of $F_{ L, \textrm{ SM}}^{ D^{ \ast}} = 0.46 \pm 0.04$ in the leptoquark models: [0.43, 0.44], [0.42, 0.48], and [0.43, 0.47] are predicted as a range of $F_{ L}^{ D^{ \ast}}$ for the ${ \rm R}_2$, ${ \rm S}_1$, and ${ \rm U}_1$ leptoquark models, respectively, where the current data of $R_{ D^{ (\ast)}}$ is satisfied at $1\,\sigma$ level. It is also shown that the $\tau$ polarization observables can much deviate from the SM predictions. The Belle II experiment, therefore, can check such correlations between $R_{ D^{ (\ast)}}$ and the polarization observables, and discriminate among the leptoquark models.
Categories: hep-ph hep-ex