Stars as Laboratories for Fundamental Physics - MPP Theory Group

536 Chapter 14
By their generic coupling to gluons, axions necessarily mix with
pions and hence couple to photons according to
L int = − 1 4 g aγF µν ˜F µν a = g aγ E · B a, (14.22)
where F is the electromagnetic field strength tensor and ˜F its dual. In
models where the quarks and leptons which carry PQ charges also carry
electric charges, there is a contribution from a triangle loop diagram as
in Fig. 14.2, replacing g s with the electric charge Q j e of the lepton. It
yields an axion-photon coupling proportional to
E ≡ 2 ∑ j X jQ 2 j D j , (14.23)
where D j = 3 for color triplets (quarks) and 1 for color singlets (charged
leptons). The total axion-photon coupling strength is then (Kaplan
1985; Srednicki 1985)
g aγ = −
α 3
2πf a 4 ξ = m eV
ξ, (14.24)
0.69×10 10 GeV
where
ξ ≡ 4 ( E
3 N − 2 )
4 + z + w
= 4 ( )
E
3 1 + z + w 3 N − 1.92 ± 0.08 (14.25)
and m eV ≡ m a /eV.
In the DFSZ or grand unified models one has for a given family
of quarks and leptons E/N = 8/3. Neglecting w this yields ξ ≈
(8/3) z/(1 + z) ≈ 1. However, one may equally consider models where
E/N = 2 so that ξ = 0.1±0.1, i.e. the axion-photon coupling is strongly
suppressed and may actually vanish (Kaplan 1985).
14.3.3 Model-Dependent Axion-Fermion Coupling
The discussion in Sect. 14.2.3 implies that axions interact with a given
fermion j (mass m j ) according to a pseudoscalar or a derivative axialvector
interaction,
L int = −i C jm j
f a
Ψ j γ 5 Ψ j a or
C j
2f a
Ψ j γ µ γ 5 Ψ j ∂ µ a , (14.26)
where C j is an effective PQ charge of order unity to be defined below.
Evidently g aj ≡ C j m j /f a plays the role of a Yukawa coupling and
α aj = g 2 aj/4π that of an “axionic fine structure constant.” Numerically,
g ae = C e m e /f a = C e 0.85×10 −10 m eV ,
g aN = C N m N /f a = C N 1.56×10 −7 m eV (14.27)
for electrons and nucleons.