The Dark Phases of the N2HDM

We discuss the dark phases of the Next-to-2-Higgs Doublet model. The model is an extension of the Standard Model with an extra doublet and an extra singlet that has four distinct CP-conserving phases, three of which provide dark matter candidates. We discuss in detail the vacuum structure of the different phases and the issue of stability at tree-level of each phase. Taking into account the most relevant experimental and theoretical constraints, we found that there are combinations of measurements at the Large Hadron Collider that could single out a specific phase. The measurement of $h_{125} \to \gamma \gamma$ together with the discovery of a new scalar with specific rates to $\tau^+ \tau^-$ or $\gamma \gamma$ could exclude some phases and point to a specific phase.