UHE neutrino damping in a thermal gas of relic neutrinos

We present a calculation of the damping of an ultra-energetic cosmic neutrino (UHEν) travelling through the thermal gas of relic neutrinos, using the formalism of finite-temperature field theory. From the self-energy diagram due to Z exchange, we obtain the annihilation cross-section for an UHEν interacting with an antineutrino from the background. This method allows us to derive the full expression for the UHEν transmission probability, taking into account the momentum of relic neutrinos. We discuss the effect of thermal motion on the shape of the absorption dips for different UHEν fluxes as well as in the context of relic neutrino clustering. We find that for ratios of the neutrino mass to the relic background temperature 102 or smaller, the thermal broadening of the absorption lines could significantly affect the determination of the neutrino mass and of the characteristics of the population of UHEν sources.