According to the Standard Model of elementary particles, the strong interactions are described by quantum chromodynamics (QCD). QCD is similar to quantum electrodynamics (QED), except that electrons are replaced by quarks, photons by gluons, and the U(1) gauge group by SU(3). The physics of QCD and QED differ significantly, however. One important difference is that the coupling constant of QCD becomes stronger at long distances. Another is that QCD depends on an extra parameter θ that arises because of nonperturbative effects associated with QCD instantons. The dependence of QCD on θ causes a difficulty that the existence of an axion solves.
When θ differs from zero, QCD violates the discrete symmetries P and CP. P stands for parity and CP for the product of charge conjugation invariance and parity. Because the strong interactions obey P and CP in the laboratory, QCD can only describe them well if θ is very small, of order 10-9 or less. However, in the Standard Model, there is no reason why θ should be small. The theory must violate P and CP because these symmetries are broken by the weak interactions. The P and CP violation in the weak interactions feeds into the strong interactions in such a manner that θ is expected to be of order unity. The inability of the Standard Model to account for P and CP conservation by the strong interactions is called the strong CP problem.
A solution to the strong CP problem can be achieved by modifying the theory in such a way that becomes a dynamical field. In these models, the previously mentioned nonperturbative QCD instanton effects produce an effective potential for the θ field. Because the minimum energy state occurs at θ = 0, the θ field relaxes to zero, and the strong CP problem is solved. This solution predicts the existence of a new particle, called the axion. The axion is the quantum of oscillation of the θ field. It has zero spin, zero electric charge, and negative intrinsic parity. It is coupled to all other particles with a strength proportional to its mass.
The mass ma of the axion is not known a priori . Indeed, the axion solves the strong CP problem regardless of the value of its mass. However, masses larger than 50 keV are ruled out by searches for the axion in high-energy and nuclear physics experiments. Also, the masses between 300 keV and 3 milli-eV are ruled out by stellar evolution considerations, specifically the ages of red giants and the duration of the observed neutrino pulse from Supernova 1987a. Finally, masses less than approximately 1 micro-eV are ruled out because axions that light are so abundantly produced in the early universe, they would exceed the closure density. The only remaining window of allowed axion masses is 10-6 < ma < 3 × 10-3 eV.
In that window, axions make an important contribution to the present cosmological energy density. In fact, axions are one of the leading candidates to constitute the dark matter that appears clustered in halos around galaxies and also appears to be present on a larger scale within galactic clusters and the universe as a whole. Dark matter axions can be searched for on Earth by stimulating their conversion to microwave photons in an electromagnetic cavity permeated by a strong magnetic field. Searches of this type are presently underway in the United States and in Japan. Existing detectors are able to detect dark matter axions if axions constitute all of the halo matter and if their coupling is favorable. Future detectors will be sensitive to even a fraction of the halo density in a model-independent way.
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