Pseudo-Dirac neutrinos via a mirror world and depletion of ultrahigh energy neutrinos

We propose a particle physics explanation of the nonobservation of muon neutrino events at IceCube coincident with gamma ray bursts (GRBs) at the rates predicted by the standard Bahcall-Waxman model, in terms of neutrino oscillations. Our model is based on assuming that (a) all neutrinos are pseudo-Dirac particles and (b) there exists a mirror world interacting gravitationally with the observed world. This scenario has three sterile neutrinos associated with each flavor of ordinary neutrinos. Very tiny mass splitting between these neutrinos is assumed to arise from lepton number violating dimension-five Planck scale suppressed operators. We show that if a mass splitting of 10(-15) eV(2) is induced between the four mass eigenstates of a given species, then its flux will be suppressed at IceCube energies by a factor of 4 compared to GRB model predictions. Hierarchies in mass splitting among different flavors may result in different amounts of suppression of each flavor, and based on this we predict a difference in the flavor ratios of the observed neutrinos that is significantly different compared to the standard three-flavor prediction of 1: 1: 1, which could serve as a test for this model.