The role of right-handed neutrinos in $b\to c \tau\, (\pi \nu_\tau, \rho \nu_\tau, \mu \bar \nu_\mu \nu_\tau) \bar\nu_\tau$ from visible final-state kinematics

In the context of lepton flavor universality violation (LFUV) studies, we fully derive a general tensor formalism to investigate the role that left- and right-handed neutrino new-physics (NP) terms may have in $b\to c \tau\bar\nu_\tau$ transitions. We present, for several extensions of the Standard Model (SM), numerical results for the $\Lambda_b\to\Lambda_c\tau\bar\nu_\tau$ semileptonic decay, which is expected to be measured with precision at the LHCb. This reaction can be a new source of experimental information that can help to confirm, or maybe rule out, LFUV presently seen in $\bar B$ meson decays. The present study analyzes observables that can help in distinguishing between different NP scenarios that otherwise provide very similar results for the branching ratios, which are our currently best hints for LFUV. Since the $\tau$ lepton is very short-lived, we consider three subsequent $\tau$-decay modes, two hadronic $\pi\nu_\tau$ and $\rho\nu_\tau$ and one leptonic $\mu\bar\nu_\mu\nu_\tau$, which have been previously studied for $\bar B\to D^{(*)}$ decays. Within the tensor formalism that we have developed in previous works, we re-obtain the expressions for the differential decay width written in terms of visible (experimentally accessible) variables of the massive particle created in the $\tau$ decay. There are seven different $\tau$ angular and spin asymmetries that are defined in this way and that can be extracted from experiment. Those asymmetries provide observables that can help in constraining possible SM extensions.