Likelihood analysis of the flavour anomalies and $g-2$ in the general two Higgs doublet model

We present a likelihood analysis of the general two Higgs doublet model, using the most important currently measured flavour observables, in view of the anomalies in charged current tree-level and neutral current one-loop rare decays of B mesons in b → cl$ \overline{\nu} $ and b → sμ$^{+}$μ$^{−}$ transitions, respectively. We corroborate that the model explains the latter and it is able to simultaneously fit the experimental values of the R(D) charged current ratio at 1σ, but it can not accommodate the D$^{*}$ charmed meson observables R(D$^{*}$) and F$_{L}$(D$^{*}$). We find that the fitted values for the angular observables in b → sμ$^{+}$μ$^{−}$ transitions exhibit better agreement with the general two Higgs double model in comparison to the SM. We also make predictions for future collider observables BR(t → ch), BR(h → bs), BR(h → τμ), BR(B$_{s}$ → τ$^{+}$τ$^{−}$), BR(B$^{+}$ → K$^{+}$τ$^{+}$τ$^{−}$) and the flavour violating decays of the τ lepton, BR(τ → 3μ) and BR(τ → μγ). The model predicts values of BR(t → ch), BR(B$_{s}$ → τ$^{+}$τ$^{−}$) and BR(B$^{+}$ → K$^{+}$τ$^{+}$τ$^{−}$) that are out of reach of future experiments, but its predictions for BR(h → bs) and BR(h → τμ) are within the future sensitivity of the HL-LHC or the ILC. We also find that the predictions for the τ → 3μ and τ → μγ decays are well within the projected limits of the Belle II experiment. Finally, using the latest measurement of the Fermilab Muon g − 2 Collaboration, we performed a simultaneous fit to ∆a$_{μ}$ constrained by the charged anomalies, finding solutions at the 1σ level. Once the neutral anomalies are included, however, a simultaneous explanation is unfeasible.