The θ parameter may be adjusted dynamically to a very small value with the aid of a very light spin-0 boson a with couplings ≈l/fa, where fa is called the axion decay constant:


where ΛQCD is a typical strong-interaction scale. The absence of axions in accelerator experiments tells us that fa≥1 TeV.

One expects (see, e.g., refs. 42 and 43) coherent waves of axions to have formed in the Universe during the quarkhadron phase transition, yielding


which is ≥1 if ma ≥10−5 eV—i.e., fa≤1012 GeV. There might in addition be a nonnegligible density of axions radiated from cosmic strings or from other sources. If present, these would strengthen the upper bound on fa.

There are many astrophysical constraints on axions by means of their nonemission from the cores of astrophysical objects. For example, the fact that the Sun radiates photons, not axions, tells us that fa≥107 GeV, and a similar limit is obtained from upper limits on the axio-electric effect induced by axions radiated by the Sun. Moreover, the agreement of observations of other astrophysical objects such as Red Giants and White Dwarfs with standard models constrains fa≥few× 109 GeV.

Part of this window may be closed by observations of supernova 1987a (44). According to the standard theory of type II supernovae, 99% of its binding energy should have been radiated in the form of neutrinos with a characteristic energy of a few MeV, and this theory is consistent with the observation of the Irvine-Michigan-Brookhaven and Kamiokande underground experiments. Any extra energy emission by means of axions would have reduced the total energy radiated in neutrinos and would have shortened the pulse. The other astrophysical limits suggest that any axions created in the core would have streamed freely out.

The dominant axion emission process is usually thought to be NN→NNa bremsstrahlung, with a possible contribution from ππ→πa conversion. The axion-nucleon couplings are related to the ∆q introduced earlier:




The values (Eqs. 5) of the ∆q determine the Cap and Can with uncertainties that are smaller than many others in axion emission, which is approximately

We have recently taken a fresh look at axion emission from supernova 1987a (44), incorporating these latest determinations of the ∆q, studying the possible reduction of a emission by many-body effects, and including the possibility of πa conversion. In particular, we found that nucleon spin fluctuations in the nuclear medium could degrade previous limits by a factor ~2, whereas πa conversion could strengthen the limits by a factor ~3 or 4. Overall, we found (44)


corresponding to a lower limit

fa≥1010 to 1011 GeV,

with the precise value depending on nuclear uncertainties. This leaves an interesting window of opportunity for axion search experiments.


Cosmology and the theory of structure formation are going through a (pre-)revolutionary period reminiscent of that leading to the establishment of the Standard Model of particle physics. The observation by Cosmic Background Explorer (COBE) of fluctuations ∆T/T in the microwave background radiation reminds me of the discovery of neutral currents. That was suggestive for the Weinberg-Salam model: COBE is suggestive for inflation. Subsequently, many experiments went on to measure sin2θw very precisely, and the microwave background experiments may go on to map out the inflaton potential. The defining moment of the Standard Model revolution was the discovery of the J/ψ and charm, and it was essentially established by the later discovery of the W± and Z0. For me, the corresponding steps now would be the discovery of a cold dark matter particle and/or the discovery of neutrino masses.

To my mind, no theory of structure formation can be regarded as established unless and until the nature of the dark matter has been identified in a laboratory experiment.

Discovery of the LSP, the axion, or a massive neutrino not only would establish a Standard Model of structure formation but also would reveal to us grand unification, supersymmetry, or some other extension of the Standard Model of particle physics. Interesting years of collaboration among cosmologists, astrophysicists, and particle physicists lie before us.

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