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

Abstract

The meson decays $B\to D\tau \nu$ and $B\to D^{\ast }\tau \nu$ 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 $B\to D^{(\ast )}\tau \nu$ with polarized $\tau$ leptons and unpolarized $D^{(\ast )}$ 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.

20 pages + appendices, 5 figures