Search for the $Z^\prime$ boson decaying to a right-handed neutrino pair in leptophobic $\mathrm{U(1)}$ models

The $U(1)$ extensions of the Standard Model contain a heavy neutral gauge boson $Z^\prime$. If leptophobic, the boson can evade the stringent bounds from the dilepton resonance searches. We consider two theoretically well-motivated examples of leptophobic $U(1)$ extensions in which the $Z'$ decays to right-handed neutrinos (RHNs) with substantial branchings. The coexistence of a leptophobic $Z^\prime$ and the RHNs opens up a new possibility of searching for these particles simultaneously through the production of a $Z^\prime$ at the LHC and its decay to a RHN pair. For this decay to occur, the RHNs need to be lighter than the $Z^\prime$. Hence, we study this process in an inverse seesaw setup where the RHNs can be in the TeV range. However, in this case, they have a pseudo-Dirac nature, i.e., a RHN pair would produce only opposite-sign lepton pairs, as opposed to the Majorana-type neutrinos, which can produce both same- and opposite-sign lepton pairs. Hence, the final state we study has a same-flavour opposite-sign lepton pair plus hadronically-decaying boosted $W$ bosons. Our analysis shows that the high luminosity LHC can discover a TeV-scale leptophobic $Z^\prime$ decaying via a RHN pair in a wide range of available parameters. Interestingly, large parameter regions beyond the reach of future dijet-resonance searches can be probed exclusively through our channel.