Displaced fat-jets and tracks to probe boosted right-handed neutrinos in the $U(1)_{B-L}$ model

We investigate the pair-production of Right-Handed Neutrinos (RHNs) via a $B-L$ $Z'$ boson and the detection prospects at the High-Luminosity run of the LHC (HL-LHC) and a future $pp$ collider (FCC-hh). We focus on RHN states with a mass of $10-70$ GeV which naturally results in displaced vertices for small active-sterile mixing strengths. Being produced through a mass resonance with $m_{Z'} \ge 1$ TeV, the RHNs are heavily boosted, leading to collimated decay products that give rise to fat-jets. We investigate the detection prospect of dedicated signatures in the inner detector and the muon spectrometer, namely a pair of displaced fat-jets and the associated tracks, respectively. We find that both the HL-LHC and FCC-hh can be sensitive to small active-sterile mixing $V_{\mu N} > 10^{-6}$ and $V_{\mu N} > 10^{-7}$ with the number of events reaching $\mathcal{O}(10)$ and $\mathcal{O}(10^3)$, respectively. This allows probing the generation of light neutrino masses through the Seesaw mechanism in this scenario.