Analysing the charged scalar boson contribution to the charged-current $B$ meson anomalies

Abstract: Experimental measurements collected by the BABAR, Belle, and LHCb experiments on different observables associated with the semileptonic transition $b \to c \tau \bar{\nu}\tau$, indicate the existence of disagreement respect with the Standard Model predictions. We analyse the charged scalar boson contributions to these charged-current $B$ meson anomalies within the framework of two Higgs doublet model with the most general Yukawa couplings to quarks and leptons from the third generation, involving left-handed and right-handed (sterile) neutrinos. We perform a phenomenological study of the Yukawa couplings parameter space that accommodates these anomalies. We consider the most recent data from HFLAV world-average and Belle combination, and the upper limits ${\rm BR}(B_c^- \to \tau^- \bar{\nu}{\tau}) < 30\%$ and $10\%$. In addition, we include in our study the prospect measurements on $R(D^{(\ast)})$ that the Belle II experiment could achieve and explore, for the first time, the future implications for the corresponding charged scalar Yukawa couplings. This analysis updates the existing literature and includes new important observables. Our results show that current experimental $b\rightarrow c \tau \bar{\nu}\tau$ data and Belle II projection favor the interpretation of a charged scalar boson interacting with right-handed neutrinos. Furthermore, as a side analysis regarding the charged scalar boson interpretation, we revisit the relation between $R(D^\ast)$ and ${\rm BR}(B_c^- \to \tau^- \bar{\nu}{\tau})$ by investigating whether the claim that pseudoscalar new physics interpretations of $R(D^{\ast})$ are implausible due to the $B_c$ lifetime is still valid, to the light of the recent data and Belle II prospects on $R(D^{\ast})$. Lastly, we reexamine addressing the $R(D^{(\ast)})$ anomalies in the context of the 2HDM of Type II.