Stars as Laboratories for Fundamental Physics - MPP Theory Group

534 Chapter 14
14.3 Fine Points of Axion Properties
14.3.1 The Most Common Axion Models
Axions generically mix with pions so that their mass and their couplings
to photons and nucleons are crudely f π /f a times those of π ◦ . In detail,
however, these properties depend on the specific implementation of
the PQ mechanism. Therefore, it is useful to review briefly the most
common axion models which may serve as generic examples for an
interpretation of the astrophysical evidence.
In the standard model, the would-be Nambu-Goldstone boson from
the spontaneous breakdown of SU(2)×U(1) is interpreted as the third
component of the neutral gauge boson Z ◦ , making it impossible for the
scalar field Φ of which axions are the phase to be the standard Higgs
field. Therefore, one needs to introduce two independent Higgs fields Φ 1
and Φ 2 with vacuum expectation values f 1 / √ 2 and f 2 / √ 2 which must
obey (f 2 1 + f 2 2 ) 1/2 = f weak ≡ ( √ 2 G F ) −1/2 ≈ 250 GeV. In this standard
axion model (Peccei and Quinn 1977a,b; Weinberg 1978; Wilczek 1978)
Φ 1 gives masses to the up- and Φ 2 to the down-quarks and charged
leptons. With x ≡ f 1 /f 2 and 3 families the axion decay constant is
f a = f weak [3 (x + 1/x)] −1 ∼ < 42 GeV. This and related “variant” models
(Peccei, Wu, and Yanagida 1986; Krauss and Wilczek 1986), however,
are ruled out by overwhelming experimental and astrophysical evidence;
for reviews see Kim (1987), Cheng (1988), and Peccei (1989).
Therefore, one is led to introduce an electroweak singlet Higgs field
with a vacuum expectation value f PQ / √ 2 which is not related to the
weak scale. Taking f PQ ≫ f weak , the mass of the axion becomes
very small, its interactions very weak. Such models are generically referred
to as invisible axion models. The first of its kind was the KSVZ
model (Kim 1979; Shifman, Vainshtein, and Zakharov 1980) discussed
in Sect. 14.2.2. It is very simple because the PQ mechanism entirely
decouples from the ordinary particles: at low energies, axions interact
with matter and radiation only by virtue of their two-gluon coupling
which is generic for the PQ scheme. The KSVZ model in its simplest
form is determined by only one free parameter, f a = f PQ , although one
may introduce N > 1 exotic quarks whence f a = f PQ /N.
Also widely discussed is the DFSZ model introduced by Zhitnitskiĭ
(1980) and by Dine, Fischler, and Srednicki (1981). It is a hybrid between
the standard and KSVZ models in that it uses an electroweak
singlet scalar field Φ with a vacuum expectation value f PQ / √ 2 and two
electroweak doublet fields Φ 1 and Φ 2 . There is no need, however, for ex-