Dark Sector Physics with a Primary Electron Beam Facility at CERN

In this Expression of Interest, we propose a primary electron beam facility with the main motivations being (i) dark sector experiments, and (ii) to enable a suite of development projects in acceleration technology. We also present a detailed description of an experiment, the Light Dark Matter eXperiment, LDMX, which could make use of this facility to probe thermal dark matter over a majority of the viable sub-GeV mass range. We show that LDMX can achieve orders of magnitude more sensitivity than any previous or currently envisioned experiment. LDMX uses missing momentum to search for dark matter produced via {\\it dark bremsstrahlung} produced in the interaction of electrons on a thin target. This requires a low-current, high repetition rate electron beam, with optimal energy of $\\sim 16~$\\GeV. We propose to create this electron beam at CERN by restoring the SPS's electron acceleration capability.