  Sterile neutrinos, if they exist, are potential harbingers for physics beyond
the Standard Model. They have the capacity to shed light on our flavor sector,
grand unification frameworks, dark matter sector and origins of baryon
anti-baryon asymmetry. There have been a few seminal studies that have broached
the subject of sterile neutrinos with low, electroweak-scale masses (i.e.
$\Lambda_{\text{\tiny{QCD}}} \ll m_{N_R} \ll m_{W^\pm}$) and investigated their
reach at hadron colliders using lepton jets. These preliminary studies
nevertheless assume background-free scenarios after certain selection criteria
which are overly optimistic and untenable in realistic situations. These lead
to incorrect projections. The unique signal topology and challenging hadronic
environment also make this mass-scale regime ripe for a careful investigation.
With the above motivations, we attempt to perform the first systematic study of
low, electroweak-scale, right-handed neutrinos at hadron colliders, in this
unique signal topology. There are currently no active searches at hadron
colliders for sterile neutrino states in this mass range, and we frame the
study in the context of the $13\,\rm{TeV}$ high-luminosity Large Hadron
Collider and the proposed FCC-hh/SppC $100\,\rm{TeV}$ $pp$-collider.
