Title: Exploring Neutrino Compositeness with invisible and displaced signals

Abstract: With the advent of new high energy, luminous neutrino sources, it is possible to test whether or not the neutrino is coupled to some strongly interacting sterile sector. If the confinement scale of the sterile sector is below the center of mass energy of the collisions the neutrinos disintegrate into dark-sector jets. As the dark shower evolves, dark bound states form and eventually decay into Standard Model particles with finite lifetimes. If these decays occur outside the detector, the resulting invisible jet manifests as missing energy which can only be tested through the overall enhancement of the neutral current cross section. Alternatively, if decays happen at macroscopic distances from the interaction point, they generate a distinctive visible signature known as an emerging jet. We explore the interplay of these signatures and assess the sensitivity to this scenario of upcoming experiments such as SHiP and the Forward Physics Facility at CERN, as well as from other probes such as particle decays and colliders. Together, these searches offer an unprecedented path to discover new strongly coupled physics in the neutrino sector.