  We study the signal of long-lived sterile neutrino at the LHC produced
through the decay of the $W$ boson. It decays into charged lepton and jets. The
characteristic signature is a hard prompt lepton and a lepton from the
displaced decay of the sterile neutrino, which leads to a bundle of displaced
tracks with large transverse impact parameter. Different from other studies, we
neither reconstruct the displaced vertex nor place requirement on its invariant
mass to maintain sensitivity for low sterile neutrino masses. Instead, we focus
on the displaced track from the lepton. A difficulty for low mass sterile
neutrino study is that the displaced lepton is usually \textit{non-isolated}.
Therefore, leptons from heavy flavor quark is the major source of background.
We closely follow a search for displaced electron plus muon search at CMS and
study their control regions, which is related to our signal regions, in great
detail to develop a robust estimation of the background for our signals. After
further optimization on the signal limiting the number of jets, low $H_T$ and
large lepton displacement $d_0$ to suppress SM background, we reach an
exclusion sensitivity of about $10^{-8}$ ($10^{-5}$) for the mixing angle
square at 10 (2) GeV sterile neutrino mass respectively. The strategy we
propose can cover the light sterile masses complimentary to beam dump and
forward detector experiments.
