The magnetic dipole moment of the muon is a measure of the strength of its interaction with a magnetic field. The g-factor relates the magnetic dipole moment of a charged particle to its intrinsic spin. According to the Dirac equation this will be g=2. However a more detailed analysis predicts a value slightly away from 2 due to the interactions involving virtual particles. The first order QED correction predicts an anomalous magnetic dipole moment g−2=α/π. There will then be further corrections due to higher order QED corrections; then electroweak processes; hadron interactions; and anything else which can couple in some way to the muon.

This means the precise value of g−2 is potentially sensitive to new particles. As it can be both calculated, and measured, to sub-ppm precision, this provides a way to search for a signature of new interactions beyond the standard model of particle physics.

The g-2 factor for the electron has been measured to 0.28ppt and found to agree with that calculated using 12672 Feynman diagrams. This demonstrates the phenomenal success of QED theory in predicting particle properties.

The g-2 factor for the muon cannot be calculated to such high precision, as it is sensitive to heavier particles, with greater uncertainties on these interactions. But this also means it is more sensitive to potential new particles predicted by theories such as supersymmetry, just beyond the reach of collider experiments. Not so useful to test QED, but much more sensitive as a probe of new physics.

The latest experimental result, measured by the Brookhaven g−2 experiment is:

a_μ = (g−2)/2 = 116 592 080(63)×10^-11
while the theoretical value is 116 591 785(51)×10^-11

The small difference between these values is a 3.6σ discrepancy. With the aim of clarifying if this is a sign of new physics, or a statistical fluctuation, the new g−2 collaboration will repeat this measurement improving the precision by a factor of four. This will be done using the same muon storage ring (transported from Brookhaven to Fermilab), a higher intensity muon beam, and upgraded instrumentation.

The muon g−2 factor, or anomalous magnetic dipole moment, is measured using muons stored in a magnetic storage ring. As the muons orbit the 7m radius ring, the direction of their spin will precess about the direction of travel at the anomalous spin precession frequency. When the muons decay, this direction can be inferred from direction of the resulting positron. The precession frequency is measured by counting the oscillations in the event rate of an array of detectors around the ring.

At the same time the magnetic field around the ring is tracked using several hundred magnetometer probes, which determine the strength of the field from the NMR frequency of protons in water samples.

Both these quantities must be measured to 70ppb precision.

The magnetometer probes must all be calibrated against a standard probe to account for ppm shifts introduced by the probe materials. The standard calibration probe uses a precision made spherical water sample and controlled materials to reduce the uncertainty for this probe to 35ppb. At Oxford we have now investigating a new calibration standard using a ³He gas sample.