Boosted displaced decay of right-handed neutrinos at CMS, ATLAS and MATHUSLA

We investigate boosted displaced signatures in the Type-I seesaw mechanism associated with the $B-L$ gauge symmetry. Such events arise from decays of right-handed neutrinos depending on their Yukawa couplings and masses. Considering two scenarios: (a) three degenerate right-handed neutrinos whose Yukawa couplings are reconstructed from the observed neutrino masses and mixing; (b) only one right-handed neutrino which decouples from the observed neutrino mass generation and thus its coupling can be arbitrarily small, a detailed PYTHIA based simulation is performed to determine the parameter regions of the $B-L$ gauge boson mass, the neutrino Yukawa couplings, and the right-handed neutrino mass sensitive to CMS, ATLAS, proposed FCC-hh detector and MATHUSLA at the centre of mass energies of 14, 27 and 100 TeV via displaced signatures. We also show in detail how the boost effect enhances the displaced decay lengths, especially for the longitudinal ones, and hinders the probe of Majorana nature of neutrinos.