Stars as Laboratories for Fundamental Physics - MPP Theory Group

Particle Dispersion and Decays in Media 195
circular photon polarizations acquire different refractive indices. In this
sense all media are optically active for neutrinos where only the lefthanded
states interact while the right-handed ones are “sterile.” For
Majorana neutrinos the helicity-plus states are equivalent to ν’s which
acquire an opposite energy shift from ν so that there is an energy gap
between ν(p) and ν(p). Therefore, in a medium the majoron decays
ν → νχ or χ → νν become possible where the majoron χ is a massless
particle (Sect. 6.8).
The interaction of ν µ and ν τ with a normal medium is different
from that of ν e because of a charged-current ν e -e − scattering amplitude.
Therefore, normal media are “flavor birefringent” in the sense
that the medium induces different dispersion relations for neutrinos
of different flavors. The importance of this effect for neutrino oscillations,
which effectively measure relative phases in the propagation of
different-flavored neutrinos, cannot be overstated.
It must be stressed that usually all particles acquire nontrivial dispersion
relations in media although it depends on the detailed circumstances
whether or not the refractive effect is significant. For example,
until recently one found statements in the literature that in a sufficiently
dense medium where ω P > 2m e photons were damped by electromagnetic
pair production γ → e + e − . However, this is incorrect because the
charged leptons also acquire a medium-induced effective mass which is
so large that this decay never occurs (Braaten 1991). On the other
hand, the above majoron decay is only possible because the majorons
χ are Nambu-Goldstone bosons and thus remain massless even in a
medium, at least to lowest order (Sect. 6.8).
Besides modifying the dispersion relation of particles it is also possible
that the presence of the medium allows for entirely new excitations.
The best known example is the longitudinal polarization state of the
electromagnetic field which exists in a plasma in addition to the usual
states with transverse polarization. These “plasmons” were first discussed
by Langmuir (1926). Another example from electromagnetism
are the “plasminos,” spin- 1 excitations of a plasma that were discussed
2
for the first time only very recently (Klimov 1981; Weldon 1982b, 1989;
Pisarski 1989; Braaten 1992). For many purposes such (quantized) collective
modes play the same role as the usual particles. For example,
in a medium both photons and plasmons can decay into neutrinos and
thus contribute to the plasma process of neutrino emission.
In the present chapter I will follow up these questions in detail.
While the dispersion relations and couplings of particles in media are
formally best dealt with in terms of field theory at finite temperature