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We present a likelihood analysis of the general two Higgs doublet model,using the most important currently measured flavour observables, in view of theanomalies in charged current tree-level and neutral current one-loop raredecays of $B$ mesons in $b\to c l \overline{\nu}$ and $b\to s\mu^{+}\mu^{-}$transitions, respectively. We corroborate that the model explains the latterand it is able to simultaneously fit the experimental values of the $R(D)$ratio at $1\sigma$, but it can not accommodate the $R(D^{*})$ and$F_{L}(D^{*})$ observables. We find that the fitted values for the angularobservables in $b\to s\mu^{+}\mu^{-}$ transitions exhibit better agreement withthe general two Higgs double model in comparison to the SM. We also makepredictions for future collider observables $\mathrm{BR}(t\to ch)$,$\mathrm{BR}(h\to bs)$, $\mathrm{BR}(h\to \tau\mu)$,$\mathrm{BR}(B_{s}\rightarrow\tau^{+}\tau^{-})$, $\mathrm{BR}(B^{+}\rightarrowK^{+}\tau^{+}\tau^{-})$ and the flavour violating decays of the $\tau$ lepton,$\mathrm{BR}(\tau\rightarrow3\mu)$ and $\mathrm{BR}(\tau\to\mu\gamma)$. Themodel predicts values of $\mathrm{BR}(t\to ch)$,$\mathrm{BR}(B_{s}\rightarrow\tau^{+}\tau^{-})$ and$\mathrm{BR}(B^{+}\rightarrow K^{+}\tau^{+}\tau^{-})$ that are out of reach offuture experiments, but its predictions for $\mathrm{BR}(h\to bs)$ and$\mathrm{BR}(h\to \tau\mu)$ are within the future sensitivity of the HL-LHC orthe ILC. We also find that the predictions for the $\tau\rightarrow3\mu$ and$\tau\to\mu\gamma$ decays are well within the projected limits of the Belle IIexperiment. Finally, using the latest measurement of the Fermilab Muon $g-2$Collaboration, we performed a simultaneous fit to $\Delta a_{\mu}$ constrainedby the charged anomalies, finding solutions at the $1\sigma$ level. Once theneutral anomalies are included, however, a simultaneous explanation isunfeasible.

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