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Non-Standard Muon

May 24, 2021

Readers of this blog are likely familiar with the spherical cow parable about a physicist who was assigned the task of finding ways to increase milk production on a dairy farm. After completing his study, he began the presentation of his research results with the phrase, "Consider a spherical cow." I just read another physics-themed cow joke that describes a cow's favorite elementary particle as the muon. Unfortunately, the joke is based on the mispronunciation of the Greek letter, mu (μ). It would have been funnier if it was a cat's favorite elementary particle.

Physicists love the Greek alphabet at least as much as mathematicians. The muon is just one of the many Greek letter named subatomic particles, the most famous example of which is the Omega-minus (Ω-) particle that was discovered at Brookhaven National Laboratory in 1964 (see figure). This discovery confirmed a 1961 theory of the quark model by American physicist Murray Gell-Mann (1929-2019) and Israeli physicist Yuval Ne'eman (1925-2006).

Omega minus particle and the Eightfold Way

On the left, a baryon decuplet of Delta (Δ), Sigma (Σ), Xi (Ξ), and Omega (Ω) baryons. In this illustration, Q is electric charge and S is strangeness. On the right is a tracing of the bubble chamber photograph of the discovery of the Omega minus particle. (Left, a modified Wikimedia Commons image. Right, a Wikimedia Commons image. Click for larger image.)

The muon has been in the news recently as the result of an experiment on its magnetic moment that shows a 4.2 standard deviation difference from the Standard Model.[1-11] The Standard Model is the theory that adequately describes three of the four known fundamental forces and classifies all known elementary particles. Since 4.2 sigma is still short of the accepted gold standard of 5 sigma in particle physics experiments, this finding is said to be compelling evidence of new physics and not an actual discovery.[3] The research team for this experiment was composed of more than 200 scientists from 35 institutions in seven countries.[3]

American physicist, Albert Michelson (1852-1931), who conceived the Michelson–Morley experiment that demonstrated the absence of a luminiferous aether, famously said that "the future truths of physical science are to be looked for in the sixth place of decimals." The accepted theoretical value for the muon g-factor is 2.00233183620(86), while the experiment gives 2.00233184122(82).[3] This means that the discrepancy lies at the eighth decimal place.

Albert Michelson and Aristotle

Albert Michelson (1852-1931) (left) and Aristotle (384-322 BC). In his Physics, Aristotle wrote about an aether that surrounds the celestial bodies. In this illustration from the 1493 Nuremberg Chronicle, Aristotle is clothed in the manner of a medieval scholar. This would be a good meme for a thinking cap, the supposed headwear designed to improve thinking. (Left, a Wikimedia Commons image by AstroLab, modified for artistic effect. Right, a Wikimedia Commons image from the Nuremberg Chronicle.)

The muon has the same charge and spin as an electron, and it's also an elementary particle with no known sub-structure; that is, it's not a composite of other, simpler particles. The muon is the electron's fat cousin, and not by just a little. A muon has a mass that's 206.768 times as large. A muon can replace an electron in an atom; so, a hydrogen atom can be constructed from a muon and a proton. Since a muon is more massive than an electron, its atomic orbitals are closer to the nucleus, and this enables some experimental tests of quantum electrodynamics that I wrote about in a previous article (The Proton Size Problem, November 3, 2016).

The Standard Model has endured all tests since its conception in the 1970s, but physicists are still looking for cracks in its edifice, and that's the purpose of the Muon g−2 Experiment at the Fermi National Accelerator Laboratory (Fermilab). This experiment is named after the magnetic g-factor that it probes.[1] This same type of experiment was conducted at Brookhaven National Laboratory twenty years ago, and it showed a 2.7-sigma discrepancy between the experimental and theoretical value.[2-3]. In fact, the superconducting magnet of the Brookhaven measurement was shipped to Fermilab for its experiment.[3] This new statistic of a 4.2-sigma discrepancy combines the Brookhaven and Fermilab data.[1]

Muon experiment statistics.

Experimental values of The muon anomaly aμ from the Brookhaven National Laboratory experiment, the Fermilab experiment, and their combined average. The value for the Standard Model is also shown.

(Fig. 4 of Ref. 1, licensed under a Creative Commons Attribution 4.0 International license. Click for larger image.)

This magnet is a 50-foot-diameter superconducting magnetic storage ring that creates a uniform vertical magnetic field in which the muons circulate.[2-3] The magnet was tweaked using 8000 hand-cut strips of iron foil glued onto it to give a threefold improvement in uniformity above what was achieved at Brookhaven.[2,8] The magnet is sensitive to environmental conditions, such as temperature, so it is monitored by an array of 378 nuclear magnetic resonance probes based on proton spin precession in water.[1,8]

The measurement is based on the idea that the g -factor, which is exactly 2 for an ideal point particle with spin 1/2, has a slightly different g-factor as it interacts with the quantum foam of virtual particles. The deviation from 2 is what's important, and that's why the experiment is called Muon g−2.[2-3] The Standard Model predicts this effect with extreme precision, and that's why measuring the g-factor is a good test.[3]

The Fermilab results vindicate the Brookhaven data. The published results are based on a experimental run done in 2018, but further data taken in 2019 and 2020 are now being analyzed, two additional runs are planned, and there's a potential of achieving 7-sigma significance in the statistics.[2,3] Other groups have different g-factor experiments planned.[2] Says Chris Polly, a Fermilab scientist and a co-spokesperson for the current experiment,
"So far we have analyzed less than 6% of the data that the experiment will eventually collect. Although these first results are telling us that there is an intriguing difference with the Standard Model, we will learn much more in the next couple of years."[3]
Alexey Petrov, a theorist at Wayne State University says that development of a model beyond the Standard Model "... is going to be a field day for theorists.[7] The Muon g-2 experiment was funded by the US Department of Energy, the National Science Foundation, and the German Research Foundation, among other sources.[1]


  1. B. Abi et al. (Muon g−2 Collaboration), "Measurement of the Positive Muon Anomalous Magnetic Moment to 0.46 ppm," Physical Review Letters, vol. 126 (April 7, 2021), Article 141801, DOI:https://doi.org/10.1103/PhysRevLett.126.141801. This is an open source article with a PDF file here.
  2. Priscilla Cushman, "Muon's Escalating Challenge to the Standard Model," Physics, vol. 14, no. 54, April 7, 2021.
  3. Tracy Marc, "First results from Fermilab’s Muon g-2 experiment strengthen evidence of new physics, Fermilab Press Release, April 7, 2021.
  4. Fact Sheet: Muon g-2 Experiment (PDF file), Fermilab
  5. Muon g-2 experiment finds strong evidence for new physics, Fermilab YouTube Video, April 7, 2021.
  6. Davide Castelvecchi, "Is the standard model broken? Physicists cheer major muon result," Nature, April 7, 2021, doi: https://doi.org/10.1038/d41586-021-00898-z.
  7. Adrian Cho, "Particle mystery deepens, as physicists confirm that the muon is more magnetic than predicted," Science, April 7, 2021, doi:10.1126/science.abi8829.
  8. Michael Schirber, "Measuring the Magnet that Measures the Muon," Physics, vol. 14, no. 53 (April 7, 2021).
  9. Mounting hope for new physics, Johannes Gutenberg-Universität Mainz Press Release, April 7, 2021.
  10. Savannah Mitchem, "Field guides: Argonne scientists bolster evidence of undiscovered particles or forces in Muon g-2 experiment," Argonne National Laboratory Press Release, April 7, 2021
  11. Particle physics: will muons lead us towards a new physics?, CNRS Press Release, April 7, 2021.

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