Gamma-Ray Burst Neutrino Background and Star Formation History in the   Universe
  We estimate the flux of the GRB neutrino background and compute the event rate at SK and TITAND in the collapsar model, assuming that GRB formation rate is proportional to the star formation rate. We find that the flux and the event rate depend sensitively on the mass-accretion rate. Although the detection of signals from GRBs seems to be difficult by SK, we find that we can detect them by TITAND (optimistically about 20 events per year in the energy range where the energy of anti-electron neutrino is larger than 50 MeV). Therefore, we show that we will obtain the informations on the mass-accretion rate of collapsar by observing the GRB neutrino background, which, in turn, should give us informations on the total explosion energy of GRBs. 
S. Nagataki, K. Kohri, S. Ando and K. Sato