Detecting light long-lived particle produced by cosmic ray

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.