Axions for amateurs

ABSTRACT

Axions are an increasingly popular topic in theoretical physics, and are sparking a global experimental effort. In the following I review the motivations for the existence of axions, the theories underlying them, and the methods to search for them. The target audience is an interested amateur, physics undergraduate, or scientist in another field, and so I use no complicated mathematics or advanced theoretical topics, and instead use lots of analogies.

KEYWORDS:

• Axions
• dark matter
• haloscope
• superradiance
• axion electrodynamics
• strong cp problem

Acknowledgments

I am supported by an Ernest Rutherford Fellowship from the Science and Technologies Facilities Council (ST/T004037/1).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Nomenclature/ notation

The gradient operator in three dimensions is ∇, and in this context × is the vector cross product. The speed of light is c, Planck's constant is h. Particle masses are quoted in units of electronvolts, eV, where $1\text{ eV}=1.78\times {10}^{-36}\text{ kg}$, and an atom of hydrogen is approximately ${10}^9\text{ eV}$. Particle physicists often used units where $\hslash =c=1$, and while I have tried my best to restore these factors, as well as those of ${ϵ}_0$ and ${\mu }_0$, I cannot guarantee I caught every one.

Notes

1 For further reading on GR I recommend the introductory book by Schutz [70] for practical purposes, while the ‘first track’ in Misner, Thorne, and Wheeler [71] contains lots of thought experiments and intuition. For those keen to do research, I enjoy Carroll [72].

2 We focused on evidence for DM from the CMB because it is impossible to explain the CMB any other way. Modifying gravity doesn't work without also introducing new dark degrees of freedom, i.e. without introducing DM.

3 The constant of proportionality can be estimated by dimensional analysis. An EDM has units charge times distance. The charge we have to play with is the quark charge, e/3, and the distance is the size of the neutron, ${10}^{-15}\text{ m}$. So we estimate the constant as the product of these numbers, about $3\times {10}^{-14}e\text{ m}$. The value of the neutron EDM computed using quantum field theory [73] is $d=5\times {10}^{-14}\theta e\text{ m}$: very close to our naive estimate.

4 The name ‘axion’ is due to Frank Wilczek. It was Weinberg and Wilczek who, independently later in 1977 (published in 1978) [74,75] first realised that Peccei and Quinn's theory predicted the existence of a particle, and computed its mass. Wilczek coined the phrase ‘axion’ after the American detergent. The ‘axi’ comes from the left/right-handed necessity of the interaction between axions and quarks, which physicists call ‘axial’, while the ‘on’ just sounds like a particle name (think ‘boson’, ‘neutron’ etc.). The axion ‘cleans up the mess’ of the strong-CP problem. Weinberg's name for the particle was the ‘Higglet’, since it is a bit like a Higgs boson, only lighter.

5 The actual computation requires a graduate course in quantum field theory. You can find it in these references [76,77].

6 You can read about Kaluza–Klein theory on Wikipedia.

7 In the weakly coupled limit. In the strong coupling limit, degrees of freedom on the strings reorganise themselves into an ‘emergent’ 11th dimension or even a 12th ‘half’ dimension in so-called M-theory and F-theory.

8 For a Contemporary Physics article on related and parallel topic, the use of atom interferometers to search for ultralight scalar dark matter, see Ref. [78].

9 In a remarkable coincidence, some of the first searches for another dark matter candidate, the supersymmetric weakly interacting massive particle (WIMP), were also carried out in this year [79]. The theory of WIMP DM production, like that of axions, was also developed in 1983 [80,81], after major theoretical breakthroughs in 1981 [82]. The futures of these two models, WIMPs and axions, were very different though, with WIMPs very much in the ascendancy throughout the 1990s and early 2000s. This was due, in part, to technology: WIMP DM direct searches developed sensitivity rapidly, and indirect searches piggybacked off the Higgs search at Cern. Axion searches were much more limited by technology, and ideas, until the 2010s and later. Now, the fortunes of axions and WIMPs have largely reversed.

10 There are some subtleties if the axion clumps into ‘miniclusters’, but this is not expected to be relevant at the mass scale probed by ADMX, see Refs. [83–87]

Additional information

Notes on contributors

David J. E. Marsh

David J. E. Marsh obtained his DPhil from the University of Oxford, and has since held posts at Perimeter Institute, King's College London, and University of Goettingen. He is currently an Ernest Rutherford Fellow and Lecturer in Theoretical Particle Physics and Cosmology at King's College London, Strand, London, WC2R 2LS.