Freeze-in dark matter from a sub-Higgs mass clockwork sector via the Higgs portal

The clockwork mechanism allows extremely weak interactions and small mass scales to be understood in terms of the structure of a theory. A natural application of the clockwork mechanism is the freeze-in mechanism for dark matter production. Here we consider a Higgs portal freeze-in dark matter model based on a scalar clockwork sector with a mass scale which is less than the Higgs boson mass. The dark matter scalar is the lightest scalar of the clockwork sector. Freeze-in dark matter is produced by the decay of thermal Higgs bosons to the clockwork dark matter scalars. We show that the mass of the dark matter scalar is typically in the 1-10 keV range and may be warm enough to have an observable effect on perturbation growth and Lyman-a observations. Clockwork Higgs portal freeze-in models have a potentially observable collider phenomenology, with the Higgs boson decaying to missing energy in the form of pairs of long-lived clockwork sector scalars, plus a distribution of different numbers of quark and lepton particle-antiparticle pairs. The branching ratio to different numbers of quark and lepton pairs is determined by the clockwork sector parameters (the number of clockwork scalars N and the clockwork charge q), which could therefore be determined experimentally if such Higgs decay modes are observed. In the case of a minimal standard model observable sector, the combination of nucleosynthesis and Lyman-alpha constraints is likely to exclude on-shell Higgs decays to clockwork scalars, although off-shell Higgs decays would still be possible. On-shell Higgs decays to clockwork scalars can be consistent with cosmological constraints in simple extensions of the standard model with light singlet scalars.