Long-lived heavy neutral leptons at lepton colliders as a probe of left-right-symmetric models

Left-right symmetric models (LRSM) were proposed to reconcile the apparent parity violation in weak interactions with our intrinsic notion of fundamental parity symmetry. It was quickly realized that LRSM offers a viable framework for explaining neutrino masses by incorporating right-handed neutrinos, N, into its spectrum. In this study, we investigate for the first time the potential of future lepton colliders (including the FCC-ee, CEPC, ILC, CLIC, and a muon collider) to detect signals stemming from N's, focusing primarily on displaced vertex signals, and on prompt signals to a lesser degree. Our results demonstrate that these signals can effectively probe the characteristic scales of LRSM, providing evidence that would be unobtainable through any other experimental means.