Stars as Laboratories for Fundamental Physics - MPP Theory Group

274 Chapter 7
A related process to scattering by photon exchange is the spinprecession
in a macroscopic magnetic or electric field into r.h. states of
the same or another flavor, i.e. electromagnetic oscillation into “wronghelicity”
states. Such effects will be studied in Sect. 8.4 in the general
context of neutrino oscillations. In principle, this process can be important
at modifying the measurable l.h. solar neutrino flux as discussed
in Sect. 10.7 in the context of the solar neutrino problem. Spin oscillations
can also be important in supernovae where strong magnetic fields
exist, although a detailed understanding remains elusive at the present
time (Sect. 11.4).
The most interesting process caused by dipole moments is the photon
decay into neutrino pairs, γ → νν, which is enabled in media where
the photon dispersion relation is such that ω 2 − k 2 > 0. It is the most
interesting process because it occurs even in the absence of dipole moments
due to a medium-induced neutrino-photon coupling (Chapter 6).
This is the dominant standard neutrino emission process from stars for
a wide range of temperatures and densities. Details of both the standard
and the dipole-induced “plasma process” depend on complicated
fine points of the photon dispersion relation in media that were taken
up in Chapter 6.
The salient features, however, can be understood in an approximation
where photons in a medium (“transverse plasmons”) are treated as
particles with an effective mass equal to the plasma frequency ω P which
in a nonrelativistic medium is ω 2 P = 4παn e /m e with the electron density
n e and electron mass m e . The decay rate of these electromagnetic
excitation in their own rest frame is then
Γ γ = µ 2 ν
ω 3 P
24π
with
µ 2 ν = ∑ i,j
(
|µij | 2 + |ϵ ij | 2) , (7.26)
while in the frame of the medium where the photon has the energy ω a
Lorentz factor ω P /ω must be included. The sum includes all final-state
neutrino flavors with m i ≪ ω P ; otherwise phase-space modifications
occur, and even a complete suppression of the decay by a neutrino
mass threshold. In contrast with Eq. (7.25) relevant for the scattering
rate, no destructive interference effects between magnetic and electric
dipole amplitudes occur.
Transition moments would allow for the radiative decay ν i → ν j γ.
Again, because a neutrino charge radius or anapole moment vanish in
the Q 2 → 0 limit relevant for free photons, radiative neutrino decays are
most generally characterized by their magnetic and electric transition