Coherent Neutrino Propagation in a Dense Medium

Motivated by the effect of matter on neutrino oscillations (the MSW effect) we have studied the propagation of neutrinos in a dense medium. The dispersion relation for massive neutrinos in a medium is known to have a minimum at nonzero momentum p ∼ GF ρ/ √ 2. We have studied in detail the origin and consequences of this dispersion relation for both Dirac and Majorana neutrinos both in a toy model with only neutral currents and a single neutrino flavour and in a realistic “Standard Model” with two neutrino flavours. For a range of neutrino momenta near the minimum of the dispersion relation, Dirac neutrinos are trapped by their coherent interactions with the medium. This effect does not lead to the trapping of Majorana neutrinos. Motivated by the effect of matter on neutrino oscillations (the MSW effect ), there have been several works in recent years aimed at understanding in a more complete way the propagation of one or more flavours of massive neutrinos in matter (such as in the Sun, in Neutron Stars or in Supernovae for which the density difference 〈ρe− − ρe+〉 6 = 0). In our recent paper we presented the results of our study of some of the unusual features of this problem. We were particularly interested in effects at low neutrino momentum and in effects due to the minimum which the dispersion relation has at nonzero momentum. In this presentation we begin by examining in some detail a simple model with only a single neutrino flavour in which the neutrino propagates in a background of electrons. This model will show many of the essential features of the more realistic models. We shall then simply state the results in these other cases including the case of the Standard Model both with Dirac and Majorana neutrinos. The reader is referred to our paper 2 for more details. We begin by considering a simplified model in which a Dirac neutrino propagates in an electron “gas” to which it couples only via the neutral current interaction. Our model may be described by the following Lagrangian