Addendum to "Impact of polarization observables and $B_c\to \tau \nu$ on new physics explanations of the $b\to c\tau \nu$ anomaly"

In this addendum to arXiv:1811.09603 we update our results including the recent measurement of $\mathcal{R}(D)$ and $\mathcal{R}(D^{\ast })$ by the Belle collaboration: $\mathcal{R}(D{)}_{\mathrm{B}\mathrm{e}\mathrm{l}\mathrm{l}\mathrm{e}}=0.307\pm 0.037\pm 0.016$ and ${\cal R}(D^)_{\rm Belle}=0.283\pm0.018\pm0.014$, resulting in the new HFLAV fit result $\mathcal{R}(D)=0.340\pm 0.027\pm 0.013$, ${\cal R}(D^) = {0.295\pm0.011 \pm 0.008 }$,exhibitinga$3.1,\sigma$ tension with the Standard Model. We present the new fit results and update all figures, including the relevant new collider constraints. The updated prediction for $\mathcal{R}({\mathrm{\Lambda }}_c)$ from our sum rule reads ${\cal R}(\Lambda_c)= $\mathcal{R}$_{\rm SM}(\Lambda_c) \left( 1.15 \pm 0.04 \right) = 0.38 \pm 0.01 \pm 0.01$. We also comment on theoretical predictions for the fragmentation function $f_c$ of $b\to B_c$ and their implication on the constraint from $B_{u\mathrm{/}c}\to \tau \nu$ data.