Charged-Higgs on $R_{D^{(*)}}$, $\tau$ polarization, and FBA

We study the influence of a charged-Higgs on the excess of branching fraction ratio, $R_M = BR(\bar B \to M \tau \bar\nu_\tau)/BR(\bar B \to M \ell \bar \nu_\ell)$ $(M=D, D^*)$, in a generic two-Higgs-doublet model. In order to investigate the lepton polarization, the detailed decay amplitudes with lepton helicity are given. When the charged-Higgs is used to resolve excesses, it is found that two independent Yukawa couplings are needed to explain the $R_D$ and $R_{D^*}$ anomalies. We show that when the upper limit of $BR(B_c \to \tau \bar \nu_\tau)<30\%$ is included, $R_D$ can be significantly enhanced while $R_{D^*}<0.27$. With the $BR(B_c\to \tau \bar \nu_\tau)$ constraint, we find that the $\tau$-lepton polarizations can be still affected by the charged-Higgs effects, where the standard model (SM) predictions are obtained as: $P^\tau_{D} \approx 0.324$ and $P^\tau_{D^*}\approx -0.500$, and they can be enhanced to be $P^\tau_{D} \approx 0.5$ and $P^\tau_{D^*} \approx -0.41$ by the charged-Higgs. The integrated lepton froward-backward asymmetry (FBA) is also studied, where the SM result is $\bar A^{D^{(*)},\tau}_{FB} \approx -0.359(0.064)$, and they can be enhanced (decreased) to be $\bar A^{D^{(*)},\tau}_{FB} \approx -0.33 (0.02)$.