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 cycled muons, known as “heavy electrons”, 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 passed like peaks around their spin axis due to their own magnetic moment.

As they orbited the 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 frequency to the cyclic frequency 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 magnetic moment is the latest in a string dating back to 2006, with the original performed at Brookhaven National Laboratory on Long Island, New York. Each subsequent experiment improved the accuracy of the measurement. The accuracy of the latest measurement is 2.2 times better than the previous determination of the same group based on earlier data. The Muon g-2 Collaboration consists of 181 scientists from seven countries and 33 institutions; their last work was published incl Physical overview D.

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

The determination of lepton magnetic moments, both theoretically and experimentally, represents the pinnacle of scientific achievement. The electron’s magnetic moment is now known to 11 significant figures with a relative accuracy of one part in 10 trillion. Amazingly, the theoretical prediction calculated using Feynman diagrams of quantum electrodynamics (QED) agrees with the measured value to 10 significant figures.

At these levels of muon measurement precision, they hope to sense any deviations from theory that would represent physics beyond the Standard Model.

The lowest-order prediction is based on QED, and obtaining such high accuracy requires computing thousands of complicated Feynman diagrams using computers. (Julian Schwinger made history in 1948 when he hand-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 , which is no longer popular.)

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

The first means to include effects from virtual Higgs bosons and both Z bosons, and the second from virtual hadron loops such as protons, neutrons and mesons. Because of its greater mass, the muon is 43,000 times more sensitive to new particles that may appear in physics beyond the Standard Model. (Possibilities include supersymmetry, string theory, and more.)

Limitations in the theory result from the hadronic sector of the calculation. The collaboration writes: “While QED and electroweak contributions are widely considered uncontroversial, the SM prediction of the g-2 muon is limited by our knowledge of vacuum fluctuations involving strongly interacting particles, which include effects called hadronic vacuum polarization and hadronic light-scattering.” (Here “g-2” is the anomalous magnetic moment).

Inside Fermilab’s storage ring, a burst of eight muon bundles is injected every 1.4 seconds, followed by the same pattern about 267 milliseconds later. In this way, about 100,000 positive muons always enter the storage ring, with 96% of their spins being polarized. The data was compiled between March to July 2019 and November 20190 to March 2020. These second and third series contained more than four times the data compared to the 2018 period, and the data spans a total of three years.

The experimentalists corrected for a number of systematic factors that would otherwise distort the results: several corrections to the dynamics of the beam that orbits the storage ring, such as muon losses due to the finite aperture of the ring, ring muon expansion due to the non-zero electric field, transient disturbances in the magnetic field due to the launch of muon ring injections and more. Muons exposed to occasional sudden changes in the magnetic field had to be separated from the data.

Despite the current data improving accuracy by more than a factor of two, the group ultimately concluded that a comparison with theory was not yet possible. Even for electrons, some previous experimental data are needed to correct the theory of hadronic effects, and the two experiments available for this correction do not agree. Therefore, the high precision value of the muon magnetic moment is also limited.

Three more years of data await analysis, which the team expects will improve the statistical precision — due to the number of muons measured — by another factor of about 2.

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