New physics searches via angular distributions of $ \bar{B} \to D^* (\to D \pi) \tau (\to \ell \nu_\tau \bar{\nu}_\ell) \bar{\nu}_\tau$ decays
The study of $\bar{B} \to D^* \tau {\bar{\nu}}_\tau$ angular distribution can be used to obtain information about new physics (or beyond the Standard Model) couplings, which are motivated by various $B$ anomalies. However, the inability to measure precisely the three-momentum of the $\tau$ lepton hinders such measurements, as the tau decay contains one or more undetected neutrinos. Here, we present a measurable angular distribution of $\bar{B} \to D^* \tau {\bar{\nu}}_\tau$ by considering the additional decay $\tau \to \ell \nu_\tau \bar{\nu}_\ell$, where $\ell \in \{ e , \mu \}$. The full process used is $\bar{B} \to D^* (\to D \pi) \tau (\to \ell \nu_\tau \bar{\nu}_\ell) \bar{\nu}_\tau$, in which only the $\ell$ and $D^*$ are reconstructed. A fit to the experimental angular distribution of this process can be used to extract information on new physics parameters. To demonstrate the feasibility of this approach, we generate simulated data for this process and perform a sensitivity study to obtain the expected statistical errors on new physics parameters from experiments in the near future. We obtain a sensitivity of the order of 5% for the right-handed current and around 6% for the tensor current. In addition, we use the recent lattice QCD data on $B \to D^*$ form factors and obtain correlations between form factors and new physics parameters.