  We derive compact expressions for the helicity amplitudes of the many-body $B
\to D^{(*)}(\to DY)\tau(\to X\nu)\nu$ decays, specifically for $X = \ell \nu$
or $\pi$ and $Y = \pi$ or $\gamma$. We include contributions from all ten
possible new physics four-Fermi operators with arbitrary couplings. Our results
capture interference effects in the full phase space of the visible $\tau$ and
$D^*$ decay products which are missed in analyses that treat the $\tau$ or
$D^*$ or both as stable. The $\tau$ interference effects are sizable, formally
of order $m_\tau/m_B$ for the standard model, and may be of order unity in the
presence of new physics. Treating interference correctly is essential when
considering kinematic distributions of the $\tau$ or $D^*$ decay products, and
when including experimentally unavoidable phase space cuts. Our amplitude-level
results also allow for efficient exploration of new physics effects in the
fully differential phase space, by enabling experiments to perform such studies
on fully simulated Monte Carlo datasets via efficient event reweighing. As an
example, we explore a class of new physics interactions that can fit the
observed $R(D^{(*)})$ ratios, and show that analyses including more
differential kinematic information can provide greater discriminating power for
new physics, than single kinematic variables alone.

High Energy Physics - Phenomenology;High Energy Physics - Experiment