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For a general $H_b\to H_c\tau\bar\nu_\tau$ decay we analyze the role of the$\tau$ polarization vector ${\cal P}^\mu$ in the context of lepton flavoruniversality violation studies. We use a general phenomenological approach thatincludes, in addition to the Standard Model (SM) contribution, vector, axial,scalar, pseudoscalar and tensor new physics (NP) terms which strength isgoverned by, complex in general, Wilson coefficients. We show that both in thelaboratory frame, where the initial hadron is at rest, and in the center ofmass of the two final leptons, a $\vec {\cal P}$ component perpendicular to theplane defined by the three-momenta of the final hadron and the $\tau$ lepton isonly possible for complex Wilson coefficients, being a clear signal for physicsbeyond the SM as well as time reversal (or CP-symmetry) violation. We makespecific evaluations of the different polarization vector components for the$\Lambda_b\to\Lambda_c$, $\bar B_c\to\eta_c,J/\psi$ and $\bar B\to D^{(*)}$semileptonic decays, and describe NP effects in the complete two-dimensionalspace associated with the independent kinematic variables on which thepolarization vector depends. We find that the detailed study of ${\cal P}^\mu$has great potential to discriminate between different NP scenarios for $0^-\to0^-$ decays, but also for $\Lambda_b \to \Lambda_c$ transitions. For thislatter reaction, we pay special attention to corrections to the SM predictionsderived from complex Wilson coefficients contributions.

New physics and the tau polarization vector in $b\to c \tau \bar\nu_\tau$ decays