I’m sure you know the tale of the police officer who spots a drunk person looking for their wallet beneath a streetlight. The officer asks if the drunkard is sure that’s where it’s lost. “No, I’m not,” the drunkard replies. “It’s just the only place I can see.” Psychologists refer to this observational bias, in which you study something where you can conveniently look, the “streetlight effect”. For experimental high-energy physicists, however, it’s all they can ever do.

Consider the muon – a “fatter” version of an electron – onto which huge resources have been devoted to measuring the way it wobbles. Physicists have been pursuing this quest almost continuously since the 1950s when they began building the theoretical edifice known as quantum electrodynamics (QED). In QED, which describes how light interacts with matter, particles are conceived as spinning magnets, with the ratio of their magnetic moment to spin being a value called g.

The difference between g and 2 is an indication of whether QED is comprehensive enough – or whether there is physics “beyond” it

In QED’s basic versions, g is exactly equal to 2. But when muons whirl around in a magnetic field, they encounter traces of all particles and forces “out there” in nature, and how they wobble depends on the total value of such traces. The experimental value of the difference between g and 2, called the anomalous magnetic moment or g–2, is therefore an indication of whether QED is comprehensive enough – whether there is physics “beyond” it.

To determine a value for g–2, physicists soon realized they’d have to align the spin axes of muons, send them through a magnetic field, and then see how they scatter. Unfortunately, that proved too difficult and it was not until the discovery of “parity violation” in the weak interaction in 1957 that things radically changed. Nature, it turned out, had bestowed a wonderful gift upon particle physicists. Among other things, parity violation meant that muons emit their decay products – electrons – only in certain directions with respect to their spin axis. Complex and difficult polarization and scattering procedures were no longer needed to determine the frequency of muon wobble. Instead, you could just study patterns of electrons.

Changing times

The first “g–2 experiment” began at CERN in 1959. Apart from potentially revealing that QED might be defective, experimentalists hoped that the project might reveal something about the difference between muons and electrons. The experiment also provided an important use for CERN’s first accelerator, the synchrocyclotron, whose value was already in doubt given the new generation of machines called synchrotrons.

Running in spurts for several years, with a final report issued in 1965, that first g–2 experiment was ultimately disappointing. It revealed no breakdown of QED, and heralded nothing new about the muon. As far as one could tell, the QED edifice was solid.

But then CERN’s new accelerator, the Proton Synchrotron, came into operation. Various experimental developments, coupled with a more precise theoretical value, suddenly made another experiment worthwhile. The second CERN g–2 experiment, which began in 1966, arrived at a measurement 25 times more precise than before. This result disagreed with theory by 1.7σ, a sign of a defect in the QED edifice jarring enough to inspire more work from both theorists and experimentalists.

By the time the second CERN g–2 experiment ended, yet more ways to beat back systematic errors had been uncovered, leading to a third version at CERN starting in 1969. One interesting feature was that this experiment was a highly sensitive test of general relativity. Debate was still ongoing about the physical reality of time dilation (i.e. the slowing down of a clock with respect to an observer) and now the measure of time dilation of the muon lifetime in the storage ring ended the debate. The results, which confirmed the QED prediction to a precision of 0.0007%, were published in 1979.

By that year, what was becoming known as the Standard Model of particle physics had come together, linking the known particles and almost all the known forces in a single theoretical package. Predicted particles were discovered, and measurements of various processes turned out to be in accord with theory. The QED edifice looked sounder than ever. Strangely, this attracted renewed attention to g–2, for now physicists sought some way – any way – to look for defects.

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The muon’s theory-defying magnetism is confirmed by new experiment

Another experiment was duly embarked upon, this time at the Brookhaven National Laboratory in the US. Using a 15 m-diameter storage ring fitted with superconducting magnets providing a vertical 1.45 T magnetic field, it sought to push the measurement down from seven parts per million to just one part per million, testing the limits of the Standard Model. With data collection complete in 2001, the result was published in 2004 and disagreed with theory by around 2.5σ, with an accuracy of 0.5 parts per million in the anomaly (Phys. Rev. Lett. 92 1618102).

Science is not a simple sequence of theoretical test and experimental confirmation or refutation

This was a suggestive, but not definitive, indication of physics beyond the Standard Model. A fifth g–2 experiment duly began at Fermilab in 2013, after Brookhaven bequeathed its magnet to the Illinois lab. Now consisting of about 200 people, the experiment announced its latest findings in April showing a discrepancy of 4.2σ (Phys. Rev. Lett. 126 141801). Despite being a little shy of the 5σ now considered necessary to achieve consensus for a claim, the new result was derived from only the first of several runs.

The critical point

The sequence of five g–2 experiments is an intriguing lesson in the history of physics. Each was undertaken for a different motive, each involved a different set of technologies, and each gave rise to results that had different implications. The story shows that science is not a simple sequence of theoretical test and experimental confirmation or refutation. Rather, many different theoretical and experimental factors come into play in making such a time-consuming and expensive experiment worthwhile.

Ultimately, experimentalists may very well find what they are looking for under the streetlight after all.