$\bar B_c \to \eta_c$, $\bar B_c \to J/\psi$ and $\bar B \to D^{(*)}$ semileptonic decays including new physics
We apply the general formalism derived in N. Penalva et al. [Phys. Rev. D 101, 113004 (2020)] to the semileptonic decay of pseudoscalar mesons containing a $b$ quark. While present $B\to D^{(*)}$ data give the strongest evidence in favor of lepton flavor universality violation, the observables that are normally considered are not able to distinguish between different new physics (NP) scenarios. In the above reference we discussed the relevant role that the various contributions to the double differential decay widths $d^2\Gamma/(d\omega d\cos\theta_\ell)$ and $d^2\Gamma/(d\omega dE_\ell)$ could play to this end. Here $\omega$ is the product of the two hadron four-velocities, $\theta_\ell$ is the angle made by the final lepton and final hadron three-momenta in the center of mass of the final two-lepton system, and $E_\ell$ is the final charged lepton energy in the laboratory system. The formalism was applied there to the analysis of the $\Lambda_b\to\Lambda_c$ semileptonic decay showing the new observables were able to tell apart different NP scenarios. Here we analyze the $\bar B_c\to \eta_c \tau\bar\nu_\tau$, $\bar B_c\to J/\psi\tau\bar\nu_\tau$, $\bar B\to D\tau\bar\nu_\tau$ and $\bar B\to D^*\tau\bar\nu_\tau$ semileptonic decays. We show that, as a general rule, the $\bar B_c \to J/\psi$ observables, even including $\tau$ polarization, are less optimal for distinguishing between NP scenarios than those obtained from $\bar B_c \to \eta_c$ decays, or those presented in N. Penalva et al. for the related $\Lambda_b \to \Lambda_c$ semileptonic decay. Finally, we show that $\bar B\to D$ and $\bar B_c\to \eta_c$, and $\bar B\to D^*$ and $\bar B_c\to J/\psi$ decay observables exhibit similar behaviors.