Interaction of ultra-energetic cosmic neutrinos with a thermal gas of relic neutrinos

Abstract

We use the formalism of finite-temperature field theory to study the interactions of ultra-high energy (UHE) cosmic neutrinos with the thermal background of relic neutrinos. From the imaginary part of the neutrino self-energy, calculated in terms of the Z boson propagator near the resonance, we derive general expressions for the UHE neutrino transmission probability. This allows us to take into account the thermal effects introduced by the momentum distribution of the relic neutrinos. We compare our results with the approximate expressions existing in the literature and discuss the influence of thermal effects on the absorption dips in the context of realistic UHE neutrino fluxes and favoured neutrino mass schemes.