HECATE: A long lived particle detector concept for the FCC-ee or CEPC

The next generation of circular high energy collider is expected to be a lepton collider, FCC-ee at CERN or CEPC in China. However, the civil engineering concepts foresee to equip these colliders with bigger detector caverns than one would need for a lepton collider, so that they can be used for a hadron collider that may be installed in the same tunnel without further civil engineering. This opens up the possibility to install extra instrumentation at the cavern walls to search for new long-lived particles at the lepton collider. We use the example of heavy neutral leptons to show that such an installation could improve the sensitivity to the squared mixing parameter by almost half an order of magnitude.