Near or far detectors? A case study for long-lived particle searches at electron-positron colliders

We explore the discovery potential for long-lived particles at 250-GeV ILC. The goal is to investigate possible gains of a dedicated far detector over main ILD. For concreteness, we perform our study sub-GeV axion-like $a$ produced via $e^+e^- \to \gamma$ or Z \gamma (a\gamma)\gamma$ and decaying into pairs charged leptons. In ideal case zero background perfect detection efficiency, find that detectors placed in planned underground cavities large cuboid on ground can enhance sensitivity pseudo-scalars best moderately. On other hand, ILD itself environment search particles, due its excellent angular coverage radial thickness. with cross sections few picobarns, could probe lifetimes up 300$\,$ns, proper decay lengths 100$\,$m, 250$\,$fb$^{-1}$ data. through weak interactions, ILC reach an even higher than searches displaced vertices meson decays Belle II. Our findings apply similarly proposed electron-positron experiments high coverage, such as FCC-ee CEPC.