Stars as Laboratories for Fundamental Physics - MPP Theory Group

Axions 533
Notably, the Higgs field Φ which gives rise to the axion probably
exhibits effective interactions of dimension 2m + n
V grav (Φ) = g e iδ (ΦΦ† ) m Φ n
m 2m+n−4 , (14.17)
Pl
where g and δ are real numbers. Because such interactions violate the
PQ symmetry for n ≠ 0 they induce an effective potential for the axion
after spontaneous symmetry breaking. The full potential is then of the
form (Kamionkowski and March-Russell 1992)
V (a)
= mQCD[ 2 1 − cos(a/fa ) ] + mgrav[ 2 1 − cos(δ + na/fa ) ] ,(14.18)
fa
2
where m QCD is the usual QCD axion mass while gravity induces
m 2 grav = g m 2 Pl(f a / √ 2 m Pl ) 2m+n−2 . (14.19)
For g of order unity and for low values of m and n one needs a very
small f a for the QCD effect to dominate. Therefore, unless gravity for
some reason favors a minimum at the CP-conserving position for a the
PQ scheme will be ruined entirely. 91
Whatever the ultimate quantum theory of gravitation, no doubt it
will be very special. Therefore, it is by no means obvious that the
above arguments, which do not go far beyond a dimensional analysis,
correctly represent the low-energy effects of Planck-scale physics. Even
then the PQ mechanism still works if the PQ global symmetry is an
“automatic symmetry” of a gauge theory; in this case it is protected
from the assault of quantum gravity. Such models can be constructed
(Holman et al. 1992) and in fact may be quite generic (Barr 1994).
Either way, in order for axions to solve the strong CP problem one
must assume that the PQ scheme is not ruined by quantum gravity.
This discussion illustrates an important feature of axion models,
or any model involving a broken global symmetry and its Nambu-
Goldstone boson. These particles are interlopers in the low-energy
world—axions really belong to the high-energy world at the PQ scale.
These roots make them susceptible to physics at large energy scales,
at the Planck mass, for example. By the same token, if axions were
ever detected, for example by the galactic axion search (Sect. 5.3), they
would be one of the few messengers that we can ever hope to receive
from a high-energy world which is otherwise inaccessible to experimental
enquiry.
91 These issues were studied by Barr and Seckel (1992) and by Kamionkowski and
March-Russell (1992). See also the earlier papers by Georgi, Hall, and Wise (1981),
Lazarides, Panagiotakopoulos, and Shafi (1986), and Dine and Seiberg (1986).