The Muon Magnetic Moment: What is the “g−2” factor and why is it interesting?

The Muon g−2 magnet arrives at Fermilab. Credit: Fermilab.

The Fermilab particle physics laboratory, an hour’s drive west of Chicago, is the home of an experiment with the wonderfully nerdy three-character name of g−2 (“gee minus two). It is built with a single purpose, to measure the g−2 factor. As the name implies, this is the result of the simple arithmetic of subtracting two from g. When scaled up, this gives 116 591 802. At least that’s the theory. The last experimental measurement, carried out at the Brookhaven laboratory near New York over ten years ago, gave 116 592 089. The different in the last few figures could provide a clue to new phenomena still to be discovered, and hint at what undiscovered particles may be found in particle collider experiments in the next few decades.

The g factor is the muon magnetic dipole moment. The muon is one of the dozen fundamental particles of matter in the Standard Model of Particle Physics. It is heavier than the electron, but lighter than the tau. Enormous numbers of them are produced every day when high energy cosmic rays hit the upper atmosphere, but they only live for a few millionths of a second. It is a nice particle to study as they are easy to make in a particle accelerator laboratory by shooting a high energy proton beam into a target, and they live long enough to let us take precision measurements, but the muon is also sufficiently exotic to provide some exciting clues about the fundamental properties of matter.

Its magnetic dipole moment is a measure of how it interacts with the magnetic field. This can be calculated using the formidable mathematics of Quantum Field Theory. The simple calculation gives g=2. But it is influenced by every other particle. Clouds of virtual particles and antiparticles appear and disappear in the vacuum surrounding the muon, and shift its g-factor away from two. To calculate this we must consider the contribution of every known particle in the Standard Model, an effort which has taken an international team of theoretical physicists many years. If the difference between the calculated and measured value turns out to be real, this would be a sign of a new unknown particle, and the measured value would give a hint to their character of this yet-to-be-discovered entity.

Measuring the magnetic dipole moment is even harder than calculating it. This is done by throwing the muons into a magnetic field and counting the frequency with which they whirl about their direction of travel in an elaborate dance. The first measurements were done in the 1970s at CERN, the European laboratory for particle physics in Geneva, Switzerland. The challenge was then taken up by the Department of Energy’s Brookhaven National Laboratory on Long Island. A muon beam was passed into a specially constructed muon storage ring, a fourteen metre diameter superconducting magnet. The high magnetic field bends the beam into a circle, the individual muons whizzing around the loop at a little less than the speed of light. As they each traverse this orbit, their orientation—or spin axis—precesses about this direction at rate set by the interaction with the magnetic field. When the short-lived muons die, they turn into electrons, which curve away from the ring and hit an array of particle detectors inside. With all particles dancing in unison, the detector count rate will rise and fall with the precessing muon spins—at over sixty million times a second.

The Brookhaven experiment took the best-ever measurement of the muon dipole moment in 1995, and to the great excitement of the research community, it was a little different from the value predicted by the theory. A close study of the possible errors on the measurements and the uncertainty of the calculation concluded the possibility that this was just a chance fluctuation was less than one percent. Yet that was not enough to declare a discovery of New Physics. In the world of particle physics research, where teams of physicists conduct hundreds of similar analyses searching for possible anomalies, we would expect a few chance fluctuations to crop up. The convention is that to declare a discovery, the probability of such a signal being a random fluctuation must be less than one in a million.

The Brookhaven experiment came to an end without a conclusive answer. For years the g−2 result was seen as an interesting anomaly. Plenty of theoretical physicists published papers speculating about the possible New Physics which could cause such an anomaly. Yet it was never satisfactorily shown that it was real.

It was time for a new experiment. The aim of the new muon g−2 experiment is simply to measure the g−2 factor to an even better precision. To do this it needs more muons. The Fermilab laboratory had a suitable accelerator, which could be configured to produce a brighter beam of muons. To link this up to the apparatus, it was just necessary to ship a fourteen-metre electromagnet from New York to Illinois.

The story of how that was done, and how I came to work on this project is a tale for another time.

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