  We study the $d^2 \Gamma_d /(d\omega d\cos\theta_d) $, $d\Gamma_d
/d\cos\theta_d$ and $ d\Gamma_d /dE_d $ distributions, which are defined in
terms of the visible energy and polar angle of the charged particle from the
$\tau-$decay in $b\to c \tau\, (\mu \bar \nu_\mu \nu_\tau,\pi
\nu_\tau,\rho\nu_\tau) \bar\nu_\tau$ reactions. The first two contain
information on the transverse tau-spin, tau-angular and tau-angular-spin
asymmetries of the $H_b\to H_c\tau\bar\nu_\tau$ parent decay and, from a
dynamical point of view, they are richer than the commonly used one, $d^2
\Gamma_d /(d\omega dE_d) $, since the latter only depends on the tau
longitudinal polarization. We pay attention to the deviations with respect to
the predictions of the standard model (SM) for these new observables,
considering new physics (NP) operators constructed using both right- and
left-handed neutrino fields, within an effective field-theory approach. We
present results for $\Lambda_b\to\Lambda_c\tau\, (\mu \bar \nu_\mu
\nu_\tau,\pi\nu_\tau,\rho\nu_\tau)\bar\nu_\tau$ and $\bar B \to D^{(*)}\tau\,
(\mu \bar \nu_\mu \nu_\tau,\pi\nu_\tau,\rho\nu_\tau) \bar\nu_\tau$ sequential
decays and discuss their use to disentangle between different NP models. In
this respect, we show that $d\Gamma_d /d\cos\theta_d$, which should be measured
with sufficiently good statistics, becomes quite useful, especially in the
$\tau\to \pi \nu_\tau$ mode. The study carried out in this work could be of
special relevance due to the recent LHCb measurement of the lepton flavor
universality ratio ${\cal R}_{\Lambda_c}$ in agreement with the SM. The
experiment identified the $\tau$ using its hadron decay into
$\pi^-\pi^+\pi^-\nu_\tau$, and this result for ${\cal R}_{\Lambda_c}$, which is
in conflict with the phenomenology from the $b$-meson sector, needs
confirmation from other tau reconstruction channels.
