Two-loop stability of singlet extensions of the SM with dark matter

We present a study of the high energy stability of a minimal complex singlet extension of the Standard Model with or without dark matter (CxSM). We start by obtaining the beta functions of the couplings of the theory from the eective potential and then perform the RGE evolution for the allowed parameter space of the model at the electroweak scale. We obtain the scale up to which the model survives and combine this information with all the LHC measurements as well as bounds from dark matter detection experiments as well as the relic density best measurement from Planck. We conclude that scenarios which solve both the dark matter and stability problems must contain a dark particle heavier than 50 GeV and a new visible state (mixing with the SM-like Higgs) heavier than 170 GeV.