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

Abstract

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 $b\to cl\overline{\nu }$ 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 $R(D^{\ast })$ and $F_L(D^{\ast })$ 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 $\mathrm{BR}(t\to ch)$, $\mathrm{BR}(h\to bs)$, $\mathrm{BR}(h\to \tau \mu )$, $\mathrm{BR}(B_s\to {\tau }^{+}{\tau }^{-})$, $\mathrm{BR}(B^{+}\to K^{+}{\tau }^{+}{\tau }^{-})$ and the flavour violating decays of the $\tau$ lepton, $\mathrm{BR}(\tau \to 3\mu )$ and $\mathrm{BR}(\tau \to \mu \gamma )$. The model predicts values of $\mathrm{BR}(t\to ch)$, $\mathrm{BR}(B_s\to {\tau }^{+}{\tau }^{-})$ and $\mathrm{BR}(B^{+}\to K^{+}{\tau }^{+}{\tau }^{-})$ 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 $\tau \to 3\mu$ 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.

49 pages, 18 figures, new references, fixed typos

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