Probing new physics in $\bar{B}^0 \to D^{(\ast)} \tau^- \bar\nu_{\tau}$ using the longitudinal, transverse, and normal polarization components of the tau lepton

We study the longitudinal, transverse, and normal polarization components of the tau lepton in the decays $\bar{B}^0 \to D^{(\ast)} \tau^- \bar\nu_{\tau}$ and discuss their role in searching for new physics (NP) beyond the standard model (SM). Starting with a model-independent effective Hamiltonian including non-SM four-Fermi operators, we obtain experimental constraints on different NP scenarios and investigate their effects on the polarization observables. In the SM the longitudinal and transverse polarizations of the tau lepton differ substantially from the corresponding zero lepton mass values of $P_L=-1$ and $P_T=0$. In addition, $P_L$ and $P_T$ are very sensitive to NP effects. For the transverse polarization this holds true, in particular, for the effective tensor operator in the case of $\bar{B}^0 \to D^\ast$ and for the scalar operator in the case of $\bar{B}^0 \to D$. The $T$-odd normal polarization $P_N$, which is predicted to be negligibly small in the SM, can be very sizable assuming NP complex Wilson coefficients. We also discuss in some detail how the three polarization components of the tau lepton can be measured with the help of its subsequent leptonic and semihadronic decays.