  A certain class of new physics models includes long-lived particles which are
singlet under the Standard Model (SM) gauge group.A displaced vertex is a
spectacular signature to probe such particles productions at the high energy
colliders, with a negligible SM background. In the context of the minimal
gauged $B-L$ extended SM, we consider a pair creation of Majorana right-handed
neutrinos (RHNs) at the high energy colliders through the production of the SM
and the $B-L$ Higgs bosons and their subsequent decays into RHNs. With
parameters reproducing the neutrino oscillation data, we show that the RHNs are
long-lived and their displaced vertex signature can be observed at the next
generation displaced vertex search experiments, such as the HL-LHC, the
MATHUSLA, the LHeC, and the FCC-eh.We find that the lifetime of the RHNs is
controlled by the lightest light neutrino mass, which leads to a correlation
between the displaced vertex search and the search limit of the future
neutrinoless double beta-decay experiments.
