Exercises
169
times, thereby reducing the lower bound on the axion mass needed to avoid
overclosure. Of course, if the reheating temperature after inflation is lower than
that of the PQ symmetry breaking, then axion strings and the radiated axions
are washed out and essentially all of the relic axions come from the coherent
oscillations of the zero mode discussed earlier.
Axions produced at a temperature around T '" AQCD when they acquire a
non-zero mass are non-relativistic and they are, therefore, candidates for cold dark
matter (CDM). Studies of large-scale structure formation indicate that CDM is an
important component and, if so, it gets trapped in the gravitational potential and
contributes to the galactic halo. Such axions might be detected experimentally
using a cavity permeated by a strong static magnetic field [39] via the Primakoff
process (5.90). When the cavity frequency is tuned to the axion mass, the galactic
halo axions convert resonantly into photons of that frequency. A cylindrical cavity
of radius 1 m has a lowest TM mode of frequency / = 115 MHz, corresponding
to an axion of mass ma = 0.475 x 10- 6 eV. Experiments using a tunable cavity
of this size have produced exclusion zones in the axion mass versus axion-photon
coupling (ma, gayy) plane. All of these are normalized assuming that the local
halo (CDM) density is entirely in the form ofaxions. The conversion power of the
resonant cavity is proportional to g~yy and, until recently. the power sensitivity
levels were too high to bound theoretically favoured models. However. a recent
experiment at LLNL [40] has excluded KSVZ axions in the range
2.77 x 10- 6 eV < ma < 3.3 x 10- 6 eV
(excluded)
(5.131)
and further experiments are underway at LLNL and Kyoto with sufficient
sensitivity to detect DFSZ axions at even a fraction of the local halo density.
5.4 Exercises
1. Verify the form (5.63) giving the interactions of the axion with the gauge
fields and fermions.
2. Show that axion decay into two photons is described by the Lagrangian
(5.66) with gy given by (5.69).
3. Show that axion decay into an electron-positron pair is proportional to g;u
where gau is given by (5.87).
4. Verify the expression (5.108) for the final axion relic abundance.
5.5 General references
The books and review articles that we have found most useful in preparing this
chapter are:
• Peccei R D 1989 The Strong CP Problem in CP Violation ed C Jarlskog
(Singapore: World Scientific)
169
times, thereby reducing the lower bound on the axion mass needed to avoid
overclosure. Of course, if the reheating temperature after inflation is lower than
that of the PQ symmetry breaking, then axion strings and the radiated axions
are washed out and essentially all of the relic axions come from the coherent
oscillations of the zero mode discussed earlier.
Axions produced at a temperature around T '" AQCD when they acquire a
non-zero mass are non-relativistic and they are, therefore, candidates for cold dark
matter (CDM). Studies of large-scale structure formation indicate that CDM is an
important component and, if so, it gets trapped in the gravitational potential and
contributes to the galactic halo. Such axions might be detected experimentally
using a cavity permeated by a strong static magnetic field [39] via the Primakoff
process (5.90). When the cavity frequency is tuned to the axion mass, the galactic
halo axions convert resonantly into photons of that frequency. A cylindrical cavity
of radius 1 m has a lowest TM mode of frequency / = 115 MHz, corresponding
to an axion of mass ma = 0.475 x 10- 6 eV. Experiments using a tunable cavity
of this size have produced exclusion zones in the axion mass versus axion-photon
coupling (ma, gayy) plane. All of these are normalized assuming that the local
halo (CDM) density is entirely in the form ofaxions. The conversion power of the
resonant cavity is proportional to g~yy and, until recently. the power sensitivity
levels were too high to bound theoretically favoured models. However. a recent
experiment at LLNL [40] has excluded KSVZ axions in the range
2.77 x 10- 6 eV < ma < 3.3 x 10- 6 eV
(excluded)
(5.131)
and further experiments are underway at LLNL and Kyoto with sufficient
sensitivity to detect DFSZ axions at even a fraction of the local halo density.
5.4 Exercises
1. Verify the form (5.63) giving the interactions of the axion with the gauge
fields and fermions.
2. Show that axion decay into two photons is described by the Lagrangian
(5.66) with gy given by (5.69).
3. Show that axion decay into an electron-positron pair is proportional to g;u
where gau is given by (5.87).
4. Verify the expression (5.108) for the final axion relic abundance.
5.5 General references
The books and review articles that we have found most useful in preparing this
chapter are:
• Peccei R D 1989 The Strong CP Problem in CP Violation ed C Jarlskog
(Singapore: World Scientific)