Muon conundrum

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Figure 1. The g-2 storage-ring magnet at Fermilab for experiment E989. Originally designed for the Brookhaven g-2 experiment (E821), it was moved to Fermilab. The geometry allows for a very uniform magnetic field to be established in the ring.

The discrepancy between SM predictions and experiment for anomalous muon magnetic moment: Compilation of recent published results for a(mu) (in units of 10−11), subtracted by the central value of the experimental average. The shaded band indicates the size of the experimental uncertainty. The SM predictions are taken from four different published papers in 2009, 2011 and 2017. (The plot does not include the results from the latest calculation (2018) discussed in the article.)

Figure 3. The barge transporting the muon g-2 electromagnet goes through locks on the Illinois river in Joliet, Illinois, on July 20, 2013.

The muon g-2 electromagnet rolls towards Wilson Hall at Fermilab in Batavia, Illinois, on July 26. Photo: Fermilab

Some representative diagrams of processes contributing to the magnetic moment, or the g-factor, of the muon. When a charged particle such as the muon (µ) enters an electromagnetic field, the carrier particle of electromagnetism, photon (γ), shown schematically by a wavy line, couples with the particle. At the basic level of quantum theory, the interaction is described by the Dirac equation and represented by the simple vertex diagram (Fig. a). At higher orders of quantum theory, virtual quantum processes, or “radiative corrections”, come into play. In the framework of the Standard Model, virtual processes due to the electromagnetic (Fig. b), the electroweak (Fig. c & d) and the strong or the hadronic (Fig. e) sectors contribute to the muon g-factor. The yellow blob in the centre of Fig. e represents the polarisation of the vacuum when hadronic particles emerge from the vacuum for a fleeting instant and quickly disappear back into the vacuum. The contributions of (Fig. b), (Fig. c) and Fig. (d), and Fig. (e) can be respectively calculated in the frameworks of quantum electrodynamics (QED), the unified electroweak theory and quantum chromodynamics (QCD), which together constitute the Standard Model. Figures b-e represent the lowest order contributions of the respective sectors. Higher order approximations to the g-factor can be obtained by calculating the contributions from the next higher processes, and so on, and each higher order process would involve addition of one more virtual quantum loop. (Legend: µ: muon; γ: photon; ν: neutrino; W: W-boson; Z: Z-boson)

An experiment being carried out at Fermilab to measure the magnetic property of the muon has the potential to show the way to new physics.
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