A broad class of models in which electroweak symmetry breaking originates from dynamics in a singlet dark sector, and is transferred to the Standard Model via the Higgs portal, predicts in general strongly suppressed Higgs boson mixing with a singlet scalar. In this work we point out that at present this class of models allows for the second phenomenologically acceptable solution with almost maximal mixing between the Higgs and the scalar singlet. This scenario predicts an almost degenerate twin peak Higgs signal which is presently indistinguishable from a single peak, due to the limited LHC mass resolution. Because of that, the LHC experiments measure inclusive Higgs rates that all must exactly agree with Standard Model predictions due to sum rules. We show that if the dark sector and Standard Model communicate only via the singlet messenger scalar that mixes with the Higgs, the spin independent direct detection cross section of dark matter is suppressed by the scalar mass degeneracy, explaining its non-observation so far.

6 pages, 3 figures, 1 table. Final version to be published in Physics Letters B