Thermal effects on the absorption of ultra-high energy neutrinos by the cosmic neutrino background

We use the formalism of finite-temperature field theory to study the interactions of ultra-high energy (UHE) cosmic neutrinos with the background of relic neutrinos and to derive general expressions for the UHE neutrino transmission probability. This approach 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 favoured neutrino mass schemes, as well as in the case of clustered relic neutrinos.Comment: 3 pages, 2 figures. Prepared for the Proceedings of the 9th International Conference on Topics in Astroparticle and Underground Physics (TAUP 2005), Zaragoza (Spain), September 10-14, 200

UHE neutrino damping in a thermal gas of relic neutrinos

We present a calculation of the damping of an ultra-energetic (UHE) cosmic neutrino 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 UHE neutrino interacting with an antineutrino from the background. This method allows us to derive the full expressions for the UHE neutrino transmission probability, taking into account the momentum of relic neutrinos. We compare our results with the approximations in use in the literature. We discuss the effect of thermal motion on the shape of the absorption dips for different UHE neutrino 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 $10^2$ 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 UHE sources.Comment: 18 pages, 6 figures. Typos corrected. More accurate treatment of the interaction with relic neutrino clusters. Accepted for publication in Astroparticle Physic

Langmuir Wave Generation Through A Neutrino Beam Instability

A standard version of a kinetic instability for the generation of Langmuir waves by a beam of electrons is adapted to describe the analogous instability due to a beam of neutrinos. The interaction between a Langmuir wave and a neutrino is treated in the one-loop approximation to lowest order in an expansion in $1/M_W^2$ in the standard electroweak model. It is shown that this kinetic instability is far too weak to occur in a suggested application to the reheating of the plasma behind a stalled shock in a type II supernova (SN). This theory is also used to test the validity of a previous analysis of a reactive neutrino beam instability and various shortcomings of this theory are noted. In particular, it is noted that relativistic plasma effects have a significant effect on the calculated growth rates, and that any theoretical description of neutrino-plasma interactions must be based directly on the electroweak theory. The basic scalings discussed in this paper suggest that a more complete investigation of neutrino-plasma processes should be undertaken to look for an efficient process capable of driving the stalled shock of a type II SN.Comment: 23 pages, incl. 5 postscript figure