A Complete Framework for Tau Polarimetry in $B\to D^{(*)}\tau\nu$ Decays

The meson decays $B\to D\tau\nu$ and $B\to D^* \tau \nu$ are sensitive probes of the $b\to c\tau\nu$ transition. In this work we present a complete framework to obtain the maximum information on the physics of $B\to D^{(*)}\tau\nu$ with polarized $\tau$ leptons and unpolarized $D^{(*)}$ mesons. Focusing on the hadronic decays $\tau\to \pi\nu$ and $\tau\to\rho\nu$, we show how to extract seven $\tau$ asymmetries from a fully differential analysis of the final-state kinematics. At Belle II with $50~\text{ab}^{-1}$ of data, these asymmetries could potentially be measured with percent level statistical uncertainty. This would open a new window into possible new physics contributions in $b\to c\tau\nu$ and would allow us to decipher its Lorentz and gauge structure.