  We investigate the possibility of detecting light long-lived particle (LLP)
produced by high energy cosmic ray colliding with atmosphere. The LLP may
penetrate the atmosphere and decay into a pair of muons near/in the neutrino
telescope. Such muons can be treated as the detectable signal for neutrino
telescope. This study is motivated by recent cosmic electron/positron
observations which suggest the existence of $O(TeV)$ dark matter and new light
$O(GeV)$ particle. It indicates that dark sector may be complicated, and there
may exist more than one light particles, for example the dark gauge boson $A'$
and associated dark Higgs boson $h'$. In this work, we discuss the scenario
with $A'$ heavier than $h'$ and $h'$ is treated as LLP. Based on our numerical
estimation, we find that the large volume neutrino telescope IceCube has the
capacity to observe several tens of di-muon events for favorable parameters if
the decay length of LLP can be comparable with the depth of atmosphere. The
challenge here is how to suppress the muon backgrounds induced by cosmic rays
and atmospheric neutrinos.
