Common explanation to the $R_{K^{(*)}}$, $R_{D^{(*)}}$ and $\epsilon^\prime/\epsilon$ anomalies in a 3HDM+$\nu_R$ and connections to neutrino physics

Understand

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.