Natural multi-Higgs model with dark matter andCPviolation

Abstract

We explore an extension of the inert doublet model which allows also for $CP$ violation in the Higgs sector. This necessitates two noninert doublets. The lightest neutral scalar of the inert doublet is a candidate for dark matter. Scanning over parameters we preserve the abundance of the dark matter in agreement with the WMAP data. We also impose all relevant collider and theoretical constraints to determine the allowed parameter space for which both the dark matter is appropriate and $CP$ is violated. In addition we find regions where the cutoff of the model originating from naturality arguments can be substantially lifted compared to its standard model value, reaching $\sim 2–3\mathrm{TeV}$.