Beyond $\mathcal{R}(D^{(\ast )})$ with the general 2HDM-III for $b\to c\tau \nu$

We review the parameter regions allowed by measurements of $\mathcal{R}(D^{(\ast )})$ and by a theoretical limit on ${\cal B}(B_{c}\to\tau\nu)$ in terms of generic scalar and pseudoscalar new physics couplings, $g_s$ and $g_p$. We then use these regions as constraints to predict the ranges for additional observables in $b\to c\tau \nu$ including the differential decay distributions $d\mathrm{\Gamma }\mathrm{/}d{q}^2$; the ratios $\mathcal{R}(J\mathrm{/}\psi )$ and $\mathcal{R}({\mathrm{\Lambda }}_c)$; and the tau-lepton polarisation in $B\to D^{(\star )}\tau \nu$, with emphasis on the CP violating normal polarisation. Finally we map the allowed regions in $g_s$ and $g_p$ into the parameters of four versions of the Yukawa couplings of the general 2HDM-III model. We find that the model is still viable but could be ruled out by a confirmation of a large $\mathcal{R}(J\mathrm{/}\psi )$.