Fundamental magnetic property of the muon measured with unprecedented precision

Scientists have measured the muon’s magnetic moment with unprecedented precision, more than doubling the previous record.

Physicists from the Muon g-2 collaboration sent muons, known as “heavy electrons,” spinning around in a particle storage ring at Fermilab in the United States at nearly the speed of light. By applying a magnetic field about 30,000 times stronger than Earth’s, the muons precessed like tops around their axis of rotation due to their own magnetic moment.

As they orbited a 7.1-meter-diameter storage ring, the muon’s magnetic moment, influenced by virtual particles in the vacuum, interacted with the external magnetic field. By comparing this precession rate to the cycling rate around the ring, the collaboration was able to determine the muon’s “anomalous magnetic moment” to within 0.2 parts per million.

This measurement of the muon’s magnetic moment is the latest in a series of measurements dating back to 2006, the first being made at Brookhaven National Laboratory on Long Island, New York. Each subsequent experiment has improved the precision of the measurement. The precision of the latest measurement is 2.2 times better than the previous determination by the same group based on earlier data. The Muon g-2 collaboration consists of 181 scientists from seven countries and 33 institutions; their latest work was published in Physical examination D.

Muons are 207 times more massive than an electron, but otherwise identical, with the same electric charge and spin. (“Who ordered this?” exclaimed physicist and future Nobel laureate Isidor Isaac Rabi when the muon was discovered in 1936. An even more massive cousin of this lepton family was discovered in 1975, called the tau, with a mass 3,477 times that of the electron.)

The determination of the magnetic moments of leptons, both theoretically and experimentally, represents a pinnacle of science. The magnetic moment of the electron is now known to 11 significant digits, with a relative accuracy of one part in 10 trillion. Surprisingly, the theoretical prediction calculated using the Feynman diagrams of quantum electrodynamics (QED) agrees with the measured value to within 10 significant digits.

At these levels of precision, muon measurements hope to detect any deviations from theory that represent physics beyond the Standard Model.

The lowest-order prediction is based on QED, and achieving such high accuracy requires computing thousands of complicated Feynman diagrams using computers. (Julian Schwinger made history in 1948 when he manually calculated the lowest-order correction to the electron’s anomalous magnetic moment, α/2π, which appears on his tombstone. He used QED, but not Feynman diagrams, using his own highly analytical technique that is no longer popular.)

Compared to the electron, the theory that predicts the anomalous magnetic moment of the muon is different and more difficult to predict. The QED result applies exactly as for the electron (but with a different mass, of course), with two additional considerations: the contribution of the electroweak theory and that of hadrons in the Standard Model.

The first involves including the effects of virtual Higgs bosons and the two Z bosons, and the second involves virtual hadronic loops like the proton, neutron, and mesons. Because of its heavier mass, the muon is 43,000 times more sensitive to new particles that might appear in physics beyond the Standard Model. (Possibilities include supersymmetry, string theory, and many others.)

The limitations of the theory come from the hadronic sector of computation. The collaboration writes: “While contributions from quantum electrodynamics and the electroweak are widely considered uncontroversial, the Standard Model prediction of the g-2 muon is limited by our knowledge of vacuum fluctuations involving strongly interacting particles, including effects called hadronic vacuum polarization and hadronic light-light scattering.” (Here, “g-2” is the anomalous magnetic moment.)

Inside Fermilab’s storage ring, a burst of eight muon bunches is injected every 1.4 seconds, followed by the same pattern about 267 milliseconds later. In this way, about 100,000 positive muons are delivered to the storage ring each time, 96% with their spin polarized. The data were compiled between March and July 2019 and between November 2019 and March 2020. These second and third rounds of collections included more than four times as much data as the 2018 round, and in total, the data spans three years.

The experimenters corrected for a multitude of systematic factors that could have distorted the results: several corrections for the dynamics of the beam surrounding the storage ring, such as muon losses due to the finite opening of the ring, a scattering of muons from the ring due to a non-zero electric field, transient perturbations of the magnetic field due to the start of muon injections into the ring, etc. Muons subjected to occasional sudden changes in the magnetic field had to be excluded from the data.

Despite current data improving the accuracy by a factor of more than two, the group ultimately concluded that no comparison with theory was yet possible. Even for electrons, some preliminary experimental data are needed to correct the theory for hadronic effects, and the two experiments available for this correction disagree. Thus, the high-precision value for the muon magnetic moment is also limited.

Three more years of data await analysis, which the group says should improve statistical precision – due to the number of muons measured – by another factor of about 2.

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