C P asymmetries of B ¯ → X s / X d γ in models with three Higgs doublets

Direct $CP$ asymmetries (${\mathcal{A}}_{CP}$) in the inclusive decays of $\overline{B}\ensuremath{\rightarrow}{X}_{s}\ensuremath{\gamma}$ and $\overline{B}\ensuremath{\rightarrow}{X}_{s+d}\ensuremath{\gamma}$ of the order of 1% will be probed at the BELLE II experiment. In this work, three such asymmetries are studied in the context of a three-Higgs-doublet model (3HDM), and it is shown that all three ${\mathcal{A}}_{CP}$ can be as large as the current experimental limits. Of particular interest is the ${\mathcal{A}}_{CP}$ for $\overline{B}\ensuremath{\rightarrow}{X}_{s+d}\ensuremath{\gamma}$, which is predicted to be effectively zero in the Standard Model (SM). A measurement of 2.5% or more for this observable with the full BELLE II data would give $5\ensuremath{\sigma}$ evidence for physics beyond the SM. We display parameter space in the 3HDM for which such a clear signal is possible.