$R_{D^{(\ast )}}$, $R_{K^{(\ast )}}$ and neutrino mass in the 2HDM-III with right-handed neutrinos

Abstract

Given that the two-Higgs-doublet model of type III (2HDM-III) has the potential to address the $R_{D^{(\ast )}}$ anomalies while the resolution to the $R_{K^{(\ast )}}$ deficits requires new degrees of freedom within this framework, we consider in this paper a unified scenario where the low-scale type-I seesaw mechanism is embedded into the 2HDM-III, so as to accommodate the $R_{D^{(\ast )}}$ and $R_{K^{(\ast )}}$ anomalies as well as the neutrino mass. We first revisit the $R_{D^{(\ast )}}$ anomalies and find that the current world-averaged results can be addressed at $2\sigma$ level without violating the bound from the branching ratio $\mathcal{B}(B_c^{-}\to {\tau }^{-}\bar{\nu })⩽30\%$. The scenario predicts two sub-eV neutrino masses based on a decoupled heavy Majorana neutrino and two nearly degenerate Majorana neutrinos with mass around the electroweak scale. For the $R_{K^{(\ast )}}$ anomalies, the same scenario can generate the required Wilson coefficients in the direction $C_{9\mu }^{\mathrm{NP}}=-C_{10\mu }^{\mathrm{NP}}<0$, with $\mathcal{O}(1)$ Yukawa couplings for the muon and the top quark.

Comments: 32 pages, 4 figures; More discussions and references added, final version to be published in JHEP