Stars as Laboratories for Fundamental Physics - MPP Theory Group

532 Chapter 14
Fig. 14.3. Nucleon-nucleon bremsstrahlung emission of axions or pions.
with the axion example Eq. (14.15) where only one Nambu-Goldstone
boson was present as opposed to the pion isotriplet. However, this additional
term does not contribute to the bremsstrahlung process in the
limit of nonrelativistic nucleons so that the above conclusion regarding
the derivative coupling remains valid.
In the process NN → NNa (Fig. 14.3) axions and pions appear so
that again two Nambu-Goldstone bosons are attached to one fermion
line. It is then necessary to use a derivative coupling for at least one
of them (Raffelt and Seckel 1988). For other bremsstrahlung processes
such as e − p → pe − a, where the particles interact through a virtual
photon (a gauge boson) the pseudoscalar coupling causes no trouble.
Also for the Compton process γe − → e − a one may use either the pseudoscalar
or the derivative axion coupling: both yield the same result.
Because it is not always a priori obvious whether the pseudoscalar and
derivative couplings yield the same result it is a safe strategy to use the
derivative coupling in all calculations.
14.2.4 The Onslaught of Quantum Gravity
A heavy critique was levied against the PQ mechanism by quantumgravity
inspired phenomenological considerations. The main idea is
that generally the PQ symmetry, like any other global symmetry, will
not be respected by gravity (Georgi, Hall, and Wise 1981). For example,
a black hole can “swallow” any amount of PQ charge without a
trace, while a swallowed electric charge remains visible by its Coulomb
force. At energy scales exceeding the Planck mass m Pl = 1.2×10 19 GeV
quantum gravitational effects are expected and so m Pl is a phenomenological
cutoff for any quantum theory which does not fundamentally
include gravitation. In the “low-energy” world it should manifest itself
by all sorts of effective interactions which are not forbidden by a symmetry
and which likely involve inverse powers of the cutoff scale m Pl .