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 $b\to c l \overline{ \nu}$ and $b\to s\mu^{ +}\mu^{ -}$ 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 $1\sigma$, but it can not accommodate the $R(D^{ *})$ and $F_{ L}(D^{ *})$ observables. We find that the fitted values for the angular observables in $b\to s\mu^{ +}\mu^{ -}$ transitions exhibit better agreement with the general two Higgs double model in comparison to the SM. We also make predictions for future collider observables $\mathrm{ BR}(t\to ch)$, $\mathrm{ BR}(h\to bs)$, $\mathrm{ BR}(h\to \tau\mu)$, $\mathrm{ BR}(B_{ s}\rightarrow\tau^{ +}\tau^{ -})$, $\mathrm{ BR}(B^{ +}\rightarrow K^{ +}\tau^{ +}\tau^{ -})$ and the flavour violating decays of the $\tau$ lepton, $\mathrm{ BR}(\tau\rightarrow3\mu)$ and $\mathrm{ BR}(\tau\to\mu\gamma)$. The model 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 of future 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 or the 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 II experiment. Finally, using the latest measurement of the Fermilab Muon $g-2$ Collaboration, we performed a simultaneous fit to $\Delta a_{ \mu}$ constrained by the charged anomalies, finding solutions at the $1\sigma$ level. Once the neutral anomalies are included, however, a simultaneous explanation is unfeasible.
Categories: hep-ph