Skip to main content
Particle and nuclear

Particle and nuclear

Muons threaten Standard Model

08 Mar 2001

Precise measurements of the magnetic moment of the muon disagree with theoretical predictions. Katie Pennicott asks if the Standard Model of particle physics has finally cracked.

The Muon (g -2) experiment
In a spin The Muon (g -2) experiment may have found evidence for supersymmetry. (Courtesy: Brookhaven National Laboratory)

For over 30 years particle physicists have been able to explain the results of every high-energy physics experiment in terms of what is called the Standard Model. Now this model has been challenged by new results from the Brookhaven National Laboratory in the US. Precise measurements of the behaviour of muons in a magnetic field disagree with theoretical predictions by about 4 parts in a million and could hint at “new physics” beyond the Standard Model.

The Muon (g – 2) Collaboration – which involves physicists from the US, Russia, Germany and Japan – released its results at a colloquium at Brookhaven on 8 February and submitted a paper to Physical Review Letters the same day. “We are 99% sure that the present Standard Model calculations cannot describe our data,” says Gerry Bunce of Brookhaven, project manager of the experiment. The first theory paper about the new results appeared on the Los Alamos preprint server the day after the announcement.

“There are three possible interpretations of this result,” says Vernon Hughes of Yale University, co-spokesperson for the experiment. “Firstly, new physics beyond the Standard Model, such as supersymmetry, is being seen. Secondly, there is a small statistical probability that the experimental and theoretical values are consistent. Thirdly, although unlikely, there is always the possibility of mistakes in experiments and theories.”

Particle physicists are most excited by the possibility that the Brookhaven team has glimpsed the first evidence for supersymmetry. This theory proposes that every fundamental particle has a companion particle called its superpartner, but to date there has been no firm experimental evidence for supersymmetry. “Many people believe that the discovery of supersymmetry may be just around the corner,” says team member Lee Roberts of Boston University. “We may have opened the first tiny window to that world.”

Closing in on the g-factor

The Standard Model describes how quarks and leptons – a class of particles that includes electrons, muons and neutrinos – interact through three of the four fundamental forces: electromagnetism plus the strong and weak nuclear forces.

However, the model contains 17 parameters that must be inserted “by hand” and physicists believe that it is only an approximation to a more fundamental theory. Moreover, the fourth fundamental force, gravity, has not yet been incorporated into the model.

Since all quarks and leptons have an intrinsic angular momentum or “spin”, they also have a magnetic moment, which is related to the spin by the “g-factor”. Simple quantum theories predict that g = 2 for both the electron and the muon. However, these calculations do not include “radiative corrections” – the continuous emission and re-absorption of short-lived “virtual particles” by the electron or muon. These corrections make the g-factor sensitive to the existence of other particles – both established particles such as electrons and photons, and other, as yet undiscovered, particles that are not part of the Standard Model.

When these radiative corrections are included in calculations, the g-factors for the electron and the muon increase slightly to about 2.0023. Particle physicists work in terms of the so-called anomalous g-factor – which is defined as a = (g – 2)/2. The Standard Model prediction for the anomalous g-factor of the electron agrees with experiment to nine decimal places, which is currently the best agreement between theory and experiment in physics.

The fact that the muon is some 208 times heavier than the electron makes it more difficult to calculate its g-factor because more radiative corrections must be computed, while experiments are more difficult because the muon is unstable and decays with a half-life of about 2 microseconds. However, the muon g-factor is also about 40 000 times more sensitive than the electron to new physics beyond the Standard Model.

The Brookhaven team injected an intense beam of positive muons into a storage ring with a constant magnetic field of 1.45 tesla. The muons were “spin polarized” so that initially all of their spins were pointing in the direction of motion. However, the anomalous magnetic moment caused the spin direction to rotate slightly faster than the actual particles – just like the axis of a spinning top can rotate slowly or “precess” around the vertical as the top itself spins rapidly around its axis. Roughly speaking, the muon spin rotated 30 times for every 29 trips around the storage ring, which had a diameter of 14.2 metres.

To determine the anomalous g-factor for the positive muon, the team had to measure the energy and direction of the positrons emitted when the muons decayed. Based on data from more than one billion decays, they obtained a value of a = 11 659 202 × 10-10, with an error of 1.3 parts per million. This differs from the theoretical prediction by 2.6 standard deviations, which means that there is a 99% probability that the measurement does not agree with the Standard Model.

Cautious reactions

John Ellis, a theoretical physicist at CERN, warns against jumping to conclusions. “We need to be certain that the experimental results are reliable and not subject to a systematic error,” he told Physics World. Ellis added that the statistical error, although small, was not negligible: “The result is very exciting, but even if it is confirmed, we should not tear up 30 years’ worth of experiments that support the Standard Model.”

One possibility is that particle physicists may simply need to supplement the Standard Model. “It is possible that the characteristics of muons are more complex than we first thought,” says Ellis, “but if the data are confirmed, supersymmetry is the most plausible explanation for the results.”

The Brookhaven figure is based on data collected between 1997 and 1999, and the team has still to analyse data taken last year. “When we analyse the data from 2000, we will halve the level of error,” says team member William Morse. The team also hopes that related data from experiments in Novosibirsk, Beijing and Cornell will refine the theoretical predictions. The final analysis is expected within a year.

The last experiment to measure g – 2 for the muon was at CERN in the 1970s. “This experiment is nearly six times more accurate than our set-up,” says John Field, who worked on that experiment. Field eagerly awaits analysis of the remaining data, but is sceptical about supersymmetry. “I don’t think the results represent a real threat to the Standard Model at this stage,” he says, “but it will be extremely interesting to see what the new data reveal.”

Related events

Copyright © 2024 by IOP Publishing Ltd and individual contributors