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Backgrounder: Muon g-2

The Muon g-2 Experiment

Where?  |  What?  |  Why?  |  How?

A blind study 

The g-2 value is actually a ratio developed by comparing two different sets of data. To minimize any possible human bias or error in this extraordinarily precise measurement, the two data sets were analyzed by separate groups of researchers, who each deliberately included artificial offsets in their result to conceal the true value and prevent unconscious bias from intruding during the analysis process. The offsets were not removed until each group was certain of the precision and accuracy of its own analysis.

A total of 68 researchers 

The g-2 collaborators hail from Boston University; Brookhaven National Laboratory; Budker Institute of Technology, Novosibirsk, Russia; Cornell University; Fairfield University; Heidelberg University, Germany; KEK Laboratory, Japan; RIKEN/BNL Research Center; Tokyo Institute of Technology, Japan; University of Illinois at Urbana-Champaign; University of Minnesota; and Yale University. See the full list of collaborators from these institutions.

Precision analysis of huge volumes of data 

The scientists collected data from more than 1 billion muon decay events. The new measurement is a factor of 5.6 more precise than previous measurements made during the 1970s at CERN, the European laboratory for particle physics near Geneva, Switzerland.

Where?  The experiment takes place at the U.S. Department of Energyıs Brookhaven National Laboratory, using the Alternating Gradient Synchrotron (AGS) to deliver a custom muon beam into the world's largest superconducting magnet -- the "muon storage ring." The AGS provides the world's most intense multi-GeV proton beam.

What?  A 1.3 parts per million (ppm) precision measurement was made of the muon's spin anomaly, termed g-2, or the "muon g-factor." The result is numerically greater than the prediction from the Standard Model theory of particle physics. The significance of the deviation is 2.6 standard deviations following standard statistical analysis. This means that there is a 99 percent probability that the measurement does not agree with the Standard Model.

Why?  The muon g-factor differs from the simple prediction of g=2 by a small amount, essentiallyone part in 800. This tiny difference is due to the muon's interactions with virtual fields. The Heisenberg uncertainty principle permits the muon to emit and reabsorb photons, electrons, positrons, and even heavier particles such as the W and Z bosons, all of which can affect the g-factor. The electromagnetic, weak, and strong interactions all contribute to the muon anomaly. Their combined effect is calculated in the Standard Model to a precision of 0.6 ppm.

A remarkable fact is that the muon g-factor can not only be predicted to high precision, but also measured to equally high precision. Thus, a comparison of measurement and theory provides a sensitive test of the Standard Model. If there is physics not included in the current theory, and such new physics is of a nature that will affect the muon's spin, then the measurement at Brookhaven Lab would differ from the theory. This is what appears to have been observed, although there are several interpretations of the result (see below) which must be considered.

How?  The measurement is enabled by four important elements:

1) Polarized muons (muons with their spins aligned in one direction) are injected into a storage ring whose highly uniform magnetic field is perpendicular to the muon spin direction. High-precision nuclear magnetic resonance (NMR) probes measure the strength of the magnetic field. The muons race around the ring, just like cars going around a racetrack.

2) As the muon circulates around the ring, its spin, which was initially lined up in the direction of the muon motion, turns a bit faster than the muon does, so that after about 29 laps around the ring, the spin has rotated one extra time compared to the muon. The difference between the rate at which the muon itself turns around (once per lap of the ring) and the rate at which its spin rotates (called the precession), is directly proportional to the difference of the g-factor from 2. Measuring g-2 directly greatly enhances the precesion with which we can measure g. This is the key idea of measurement.

3) So that the muons don't spiral up or down and out of the ring, an electric field is used to confine them. The electric field could also affect the spin, except at a "magic" speed where the electric field effect vanishes. This interaction of the muon spin and the electric field is a specific consequence of Einstein's special theory of relativity. The experiment is performed with muons at this magic speed, namely 99.94 percent the speed of light.

4) To follow the precession of the muon spin, a measurement is required. Each muon is unstable (half have decayed after about 300 revolutions of the ring). When they decay, a positron (a positively charged electron, the anti-particle to the electron) is emitted whose energy carries, on average, information about the instantaneous direction of the muon spin at the time of the decay.A detector system measures the time and energy of these positrons and thus produces the experimental data of events versus time. The data look like any ordinary exponential (radioactive decay) with a modulation (wiggle) superimposed due to the muon g-factor.

Three valid ways to interpret the finding:

(1) The Standard Model theory is right and requires no "new physics" and the experiment is right. There is approximately one chance in a hundred that the experimenters would find a deviation as large as reported which is simply a statistical fluctuation. The E821 (g-2) team has already obtained an additional body of similar data, having four times as many events. The analysis of this data, which has just begun, will yield a result with two times smaller uncertainty and this much smaller error will eliminate the possibility of a statistical fluke if the central value of the measurement remains within the present quoted error limits.

(2) The Standard Model theory prediction is right, but new data from other particle physics experiments used by the model will change it. Although the uncertainty in the current calculation is smaller than the experimental measurement, one part of the Standard Model theory is particularly difficult to determine and involves the analysis of related data from many experiments at positron-electron colliders. New data obtained recently at accelerators in Russia , China, and the U.S., which has not so far been included in the Standard Model theory, will soon reduce the Standard Model uncertainty considerably.

(3) Finally, one could conclude that the Standard Model is either incomplete or wrong. In that case, it would be necessary to revise the theory. What the E821 measurement does is make a statement that "there is new physics out there and it affects the muon g-factor at a certain level." The measurement does not say what that new physics is likely to be. Of course, many theorists have already considered this possibility and have suggested that supersymmetry, muon substructure, or W-boson substructure would very likely affect the muon g-factor. In any case, the information bodes very well for the startup of the next run of the Tevatron Collider at the Fermi National Accelerator Laboratory and, later in the decade, for the new Large Hadron Collider (LHC) at CERN, as well as for a very high energy electron-positron collider or a muon collider. These colliders will be able to make "direct" discoveries of new particles of high mass that are not now part of the Standard Model of particle physics.

For a link to the Physical Review Letters paper and more information on g-2, see these links: