Stars as Laboratories for Fundamental Physics - MPP Theory Group

170 Chapter 5
Fig. 5.3. Function F (κ 2 ) according to Eq. (5.10).
5.2.2 Plasmon Decay and Coalescence
Several authors have used the plasma frequency ω P instead of the
Debye-Hückel wave number as a screening scale. In a nondegenerate
plasma kS/ω 2 P 2 ≈ m e /T (Sect. 6.3) and so they overestimated the emission
rate. Another source of confusion are statements that the decay
γ → γa was another axion emission process enabled by the 2γ coupling.
This issue can be easily clarified, but one needs to draw heavily on the
discussion of photon dispersion of Sect. 6.3.
A medium allows for both transverse and longitudinal electromagnetic
excitations. In a nondegenerate and nonrelativistic plasma the
dispersion relation of the former is ωT 2 −kT 2 = ωP 2 (plasma frequency ω P )
while the latter oscillate essentially with a fixed frequency ω L = ω P ,
independently of their wave number. Therefore, the plasmon decay
process γ T → γ L a as well as the plasmon coalescence γ T γ L → a are
indeed kinematically possible for k L > ω P .
It is easy to calculate the inverse lifetime of transverse excitations
against these processes
∫
d 3 k L d 3 k a 1
Γ γT →a =
Z
2ω L (2π) 3 2ω a (2π) 3 T Z L |M| 2 (2π) 4
2ω T
[ δ 4 ]
(K T + K L − K a )
×
+ δ4 (K T − K L − K a )
, (5.11)
e ω L/T
− 1
1 − e −ω L/T
where Z T,L are the vertex renormalization factors. Here, the first term
in square brackets corresponds to coalescence and so it involves a Bose-
Einstein occupation number for the initial-state γ L . The second term