Stars as Laboratories for Fundamental Physics - MPP Theory Group

Particle Dispersion and Decays in Media 227
6.5 Plasmon Decay in Neutrinos 34
6.5.1 Millicharged Neutrinos
Transverse and longitudinal electromagnetic excitations in a plasma
are both kinematically able to decay into neutrino pairs (Fig. 6.10) of
sufficiently small mass, namely 2m ν < K 2 where K is the plasmon 35
four-momentum. In the following, the neutrinos are always taken to
be massless relative to the plasma frequency and so K 2 > 0 is required
which restricts longitudinal excitations to k < k 1 , the wave number
where their dispersion relation crosses the light cone.
Fig. 6.10. Plasmon decay in neutrinos.
In addition, a ν-γ-interaction is required which does not exist in
the standard model. Still, plasmon decays occur because the medium
itself mediates an effective coupling as will become clear below. As an
easy start, however, consider the hypothesis that neutrinos carry small
electric charges (“millicharges”). Interestingly, this possibility is not
excluded by the structure of the standard model and has received some
recent attention in the literature (Sect. 7.3.2).
With a neutrino millicharge e ν the interaction with the electromagnetic
vector potential A is the standard expression
L int = −ie ν ψ ν γ α ψ ν A α . (6.75)
The spin-summed squared matrix element is of the form
∑
|M| 2 = M αβ P α P β (6.76)
spins
where explicitly
M αβ = 4e 2 ν Z (g αβ + 2ϵ ∗ αϵ β ). (6.77)
Here, Z is the renormalization constant (Sect. 6.2.3 and 6.3.6), P and
P are the ν and ν four-momenta, and ϵ is the plasmon polarization
vector for which one uses the basis vectors of Eqs. (6.27) and (6.28).
34 I closely follow Haft (1993).
35 In this section the term “plasmon” refers to both transverse and longitudinal
electromagnetic excitations in a medium.