Stars as Laboratories for Fundamental Physics - MPP Theory Group

168 Chapter 5
The main point for the present discussion is that pseudoscalar massless
or low-mass bosons are a natural consequence of certain extensions
of the standard model, and that these particles couple to photons according
to Eq. (5.1) with a strength
g aγ =
α
πf a
C aγ , (5.5)
where f a is the energy scale of symmetry breaking and C aγ is a modeldependent
factor of order unity. (For axions, model-dependent details
of the couplings are discussed in Chapter 14.) In the following I will
explore a variety of consequences arising from this interaction.
5.2 Primakoff Process in Stars
5.2.1 Screened Cross Section and Emission Rate
The two-photon coupling of pions or other pseudoscalars allows for the
conversion a ↔ γ in an external electric or magnetic field by virtue of
the amplitude shown in Fig. 5.2. This process was first proposed by
Primakoff (1951) to study the π ◦ -γ-coupling which is experimentally
difficult to measure in free decays π ◦ → 2γ. In stars, this process
allows for the production of low-mass pseudoscalars in the electric fields
of nuclei and electrons (Dicus et al. 1978).
Fig. 5.2. Primakoff conversion between axions or other pseudoscalars and
photons in an external electromagnetic field.
The Primakoff process turns out to be important for nonrelativistic
conditions where T ≪ m e so that both electrons and nuclei can be
treated as “heavy” relative to typical energies of the ambient photons.
Therefore, ignoring recoil effects one finds for the differential cross section
in this limit (target charge Ze)
dσ γ→a
dΩ
= g2 aγZ 2 α
8π
|k γ × k a | 2
q 4 , (5.6)
where q = k γ − k a is the momentum transfer; the axion and photon
energies are the same.