Towards the optimal beam dump experiment to search for feebly interacting particles

Future searches for new physics beyond the Standard Model are without doubt in need of a diverse approach and experiments with complementary sensitivities to different types of classes of models. One of the directions that should be explored is feebly interacting particles (FIPs) with masses below the electroweak scale. The interest in FIPs has significantly increased in the last ten years. Searches for FIPs at colliders have intrinsic limitations in the region they may probe, significantly restricting exploration of the mass range $m_{\text{FIP}} < 5-10$ GeV/c$^2$. Beam dump-like experiments, characterized by the possibility of extremely high luminosity at relatively high energies and the effective coverage of the production and decay acceptance, are the perfect option to generically explore the ``coupling frontier'' of the light FIPs. Several proposals for beam-dump detectors are currently being considered by CERN for implementation at the SPS ECN3 beam facility. In this we paper we analyse in depth how the characteristic geometric parameters of a beam dump experiment influence the signal yield. We apply an inclusive approach by considering the phenomenology of different types of FIPs. From the various production modes and kinematics, we demonstrate that the optimal layout that maximises the production and decay acceptance consists of a detector located on the beam-axis, at the shortest possible distance from the target defined by the systems required to suppress the beam-induced backgrounds.