An interesting model of dark matter involves a hidden sector decoupled from Standard Model (SM) fields except for some portal interaction. A concrete realization of this is the Hidden Abelian Higgs Model, which gives rise to decays of the SM Higgs boson into a pair of new bosons, called $Z_{\mathrm{d}}$ or dark photons. This note explores prospects for the search for such dark photons at the ILC with $\sqrt{s}=250$ GeV, where the dark photons decay promptly. For the $H\rightarrow Z_{\mathrm{d}}Z_{\mathrm{d}}\rightarrow 4\ell$ ($\ell = e,\mu$) final state, it follows closely recent similar searches at the LHC, while for the $2\ell2j$ and $4j$ final states a multivariate analysis approach is used. This study has not been approved by the SiD consortium.
Comment: 20 pages, 6 figures. Submitted to the Proceedings of the US Community Study on the Future of Particle Physics (Snowmass 2021)