Clockwork Higgs portal model for freeze-in dark matter

The clockwork mechanism can explain interactions which are dimensionally very weak without the need for very large mass scales. We present a model in which the clockwork mechanism generates the very small Higgs portal coupling and dark matter particle mass necessary to explain cold dark matter via the freeze-in mechanism. We introduce a TeV-scale scalar clockwork sector which couples to the Standard Model via the Higgs portal. The dark matter particle is the lightest scalar of the clockwork sector. We show that the freeze-in mechanism is dominated by decay of the heavy clockwork scalars to light dark matter scalars and Higgs bosons. In the model considered, we find that freeze-in dark matter is consistent with the clockwork mechanism for global charge $q$ in the range $2 \lesssim q \lesssim 4$ when the number of massive scalars is in the range $10 \leq N \leq 20$. The dark matter scalar mass and portal coupling are independent of $q$ and $N$. For a typical TeV-scale clockwork sector, the dark matter scalar mass is predicted to be of the order of a MeV.