CP violation in $B\to D\tau \nu_{\tau}$ using multi-pion tau decays

Present experimental datas have shown a 3.8$\sigma$ level discrepancy with the standard model in $\overline{B}\to D^{(*)}\tau\bar{\nu}_{\tau}$. Some new physics models have been considered to explain this discrepancy possibly with new source of the CP violation. In this paper, we construct CP violating observables by using multi-pion decays in $B\to D\tau\nu_{\tau}$, and estimate sensitivity of these observables to generic CP violating operators. We also discuss possibilities of CP violation in leptoquark models and in 2HDM of type-III.