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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 $b\to c l \overlineν$ and $b\to sμ^{+}μ^{-}$ transitions, respectively. We corroborate that the model explains the latter and it is able to simultaneously fit the experimental values of the $R(D)$ ratio at $1σ$, but it can not accommodate the $R(D^{*})$ and $F_{L}(D^{*})$ observables. We find that the fitted values for the angular observables in $b\to sμ^{+}μ^{-}$ transitions exhibit better agreement with the general two Higgs double model in comparison to the SM. We also make predictions for future collider observables $\mathrm{BR}(t\to ch)$, $\mathrm{BR}(h\to bs)$, $\mathrm{BR}(h\to τμ)$, $\mathrm{BR}(B_{s}\rightarrowτ^{+}τ^{-})$, $\mathrm{BR}(B^{+}\rightarrow K^{+}τ^{+}τ^{-})$ and the flavour violating decays of the $τ$ lepton, $\mathrm{BR}(τ\rightarrow3μ)$ and $\mathrm{BR}(τ\toμγ)$. The model predicts values of $\mathrm{BR}(t\to ch)$, $\mathrm{BR}(B_{s}\rightarrowτ^{+}τ^{-})$ and $\mathrm{BR}(B^{+}\rightarrow K^{+}τ^{+}τ^{-})$ that are out of reach of future experiments, but its predictions for $\mathrm{BR}(h\to bs)$ and $\mathrm{BR}(h\to τμ)$ are within the future sensitivity of the HL-LHC or the ILC. We also find that the predictions for the $τ\rightarrow3μ$ and $τ\toμγ$ 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 $Δa_μ$ constrained by the charged anomalies, finding solutions at the $1σ$ level. Once the neutral anomalies are included, however, a simultaneous explanation is unfeasible.