Stars as Laboratories for Fundamental Physics - MPP Theory Group

528 Chapter 14
Because of the mixing with π ◦ , axions share not only their mass, but
also their couplings to photons and nucleons with a strength reduced
by about f π /f a . Therefore, they generically couple to photons so that
the general discussion of Chapter 5 applies directly except for those
aspects which required massless pseudoscalars.
The effective axion mass is a low-energy phenomenon below Λ QCD ≈
200 MeV. Above this energy pions and other hadrons dissociate in
favor of a quark-gluon plasma. Then a = 0 is no longer singled out so
that any value in the interval 0 ≤ a < 2πf a is physically equivalent.
Because the universe is believed to begin with a hot and dense “big
bang,” any initial value for a is equally plausible, or different initial
conditions in different regions of space. As the universe expands and
cools below Λ QCD , however, the axion field must relax to its newly
singled-out ground state at a = 0. This relaxation process produces a
population of cosmic background axions which is, in units of the cosmic
critical density (e.g. Kolb and Turner 1990),
Ω a h 2 ≈ (f a /10 12 GeV) 1.175 . (14.5)
The exact value depends on details of the cosmic scenario and of the
relaxation process. Modulo this uncertainty, values exceeding f a ≈
10 12 GeV are excluded as axions would overdominate the dynamics of
the universe. With Eq. (14.4) this corresponds to m a ∼ < 10 −5 eV; axions
near this bound would be the cosmic dark matter. A search strategy
for galactic axions in this mass range was discussed in Sect. 5.3.
14.2.2 Axions as Nambu-Goldstone Bosons
The invariance of L Θ in Eq. (14.1) against transformations of the form
Θ → Θ+2π, and the corresponding invariance of the axion Lagrangian
against transformations a → a + 2πf a , calls for a very simple interpretation
of the axion field as the phase of a new scalar field.
A transparent illustration is provided by the KSVZ axion model
(Kim 1979; Shifman, Vainshtein, and Zakharov 1980) where one introduces
a new complex scalar field Φ which does not participate in
the weak interactions, i.e. an SU(2)×U(1) singlet. There is also a new
massless fermion field Ψ and one considers a Lagrangian with the usual
kinetic terms, a potential V for the scalar field, and an interaction term,
L = ( i
2 Ψ∂ µγ µ Ψ + h.c. ) + ∂ µ Φ † ∂ µ Φ − V (|Φ|)
− h ( Ψ L Ψ R Φ + h.c. ) . (14.6)