On the detection of TeV gamma-rays from GRB with km-cube neutrino   telescopes --- I. Muon event rate from single GRBs
  This is a preliminary study to examine the prospect of detecting TeV photons from $\gamma$-ray bursts (GRB) using km-size neutrino telescopes, specifically for the ANTARES neutrino telescope. Although optimized to detect upgoing neutrino-induced muons, neutrino telescopes nevertheless have a potential to detect high-energy photons by detecting downgoing muons from the electromagnetic cascade induced by the interaction of TeV photons with the Earth's atmosphere. The photon energy spectrum of a GRB is modeled by a simple power law and is normalized by simple energy considerations. Taking into account the absorption of TeV photons by cosmic infrared backgrounds, an optical depth table calculated from a model by \cite{fin10} is used and the arriving number of photons on top of the Earth atmosphere is determined. Muon production in the atmosphere is determined by considering two main channels of muon production: Pion photoproduction and direct muon pair production. The muon energy loss during their traverse from the surface to the bottom of the sea is determined using the standard muon energy loss formula. Assuming different detector sizes, the number of detectable muons from single GRB events located at different redshifts and zenith distances is determined. The background is calculated assuming it consists primarily of cosmic ray-induced downgoing muons. The detection significance is calculated and it can be concluded that to obtain at least $3\sigma$ detection significance, a typical GRB has to be located at redshift $z \lesssim 0.07$ if the detector's muon effective area is $A^{\mu}_{\rm eff} \sim 10^{-2}\;{\rm km}^{2}$, or redshift $z \lesssim 0.15$, if the muon effective area is $A^{\mu}_{\rm eff} \sim 1\;{\rm km}^{2}$. 
Tri L. Astraatmadja
astro-ph.HE hep-ph