Common explanation to the $R_{K^{(*)}}$, $R_{D^{(*)}}$ and $\epsilon^\prime/\epsilon$ anomalies in a 3HDM+$\nu_R$ and connections to neutrino physics
Scalar theories can account for the current $R_{D^{(*)}}$ measurements through a vector operator $\bar{c}_L \gamma_{\mu} b_L\,\bar{\tau}_L \gamma^{\mu}\nu_L$ induced at the loop level. Once the vector contribution is considered on top of a subdominant tree-level scalar component, the predicted value of $R_{D^{(*)}}$ falls within the $1\sigma$ region indicated by the experiments. We explicitly demonstrate this claim in the framework of a three Higgs doublet model extended with GeV scale right-handed neutrinos, by matching the anomalous signal for perturbative values of the involved couplings and respecting the bounds from complementary flavour physics measurements. Remarkably, we furthermore show that the proposed framework can be employed to simultaneously explain also the present $R_{K^{(*)}}$ measurement, as well as the deviation in $\epsilon'/\epsilon$ currently being debated in the literature. These results are obtained by considering the contribution of relatively light right-handed neutrinos which are fundamental in mediating the processes behind the anomalous signals. In this way our findings reveal a new possible connection that links the flavour anomalies to the phenomenology of extended Higgs sector and neutrino physics.