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

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 flavor universality violation studies. We use a general phenomenological approach that includes, in addition to the Standard Model (SM) contribution, vector, axial, scalar, pseudoscalar and tensor new physics (NP) terms which strength is governed by, complex in general, Wilson coefficients. We show that both in the laboratory frame, where the initial hadron is at rest, and in the center of mass of the two final leptons, a $\vec {\cal P}$ component perpendicular to the plane defined by the three-momenta of the final hadron and the $\tau$ lepton is only possible for complex Wilson coefficients, being a clear signal for physics beyond the SM as well as time reversal (or CP-symmetry) violation. We make specific 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-dimensional space associated with the independent kinematic variables on which the polarization vector depends. We find that the detailed study of ${\cal P}^\mu$ has great potential to discriminate between different NP scenarios for $0^-\to 0^-$ decays, but also for $\Lambda_b \to \Lambda_c$ transitions. For this latter reaction, we pay special attention to corrections to the SM predictions derived from complex Wilson coefficients contributions.
Comment: 34 latex pages, 10 figures, 1 table. Enlarged and modified discussion. New references and one new figure added