Status of the semileptonic $B$ decays and muon g-2 in general 2HDMs with right-handed neutrinos

In this paper, we study the extended Standard Model (SM) with an extra Higgs doublet and right-handed neutrinos. If the symmetry to distinguish the two Higgs doublets is not assigned, flavor changing neutral currents (FCNCs) involving the scalars are predicted even at the tree level. We investigate the constraints on the FCNCs at the one-loop level, and especially study the semileptonic $B$ meson decays, e.g. $B to D^{(*)} tau u$ and $B to K^{(*)} ll$ processes, where the SM predictions are more than $2 sigma$ away from the experimental results. We also consider the flavor-violating couplings involving right-handed neutrinos and discuss if the parameters to explain the excesses of the semileptonic $B$ decays can resolve the discrepancy in the the anomalous muon magnetic moment. Based on the analysis, we propose the smoking-gun signals of our model at the LHC.