Question: Can anyone briefly explain the muon g-2 experiment?

Susan Cartwright answered on 19 Jun 2015:

Briefly explaining g-2 is hard, because the concepts are not simple, but I’ll do my best…

Elementary particles spin, and this spin together with their electric charge makes them behave like tiny bar magnets. The technical term for something like a bar magnet is a “magnetic dipole” (because it has two magnetic poles, one N and one S). The spin also gives the particle an angular momentum, which is like ordinary momentum except it relates to spinning motion instead of motion in a straight line.

The factor g describes the ratio between the strength of the magnetic dipole (the “magnetic dipole moment”) and the angular momentum. If you do the simplest possible calculation of this ratio in quantum mechanics, then for particles with a spin of half a unit, like the electron and the muon, you get the value 2. However, mare exact calculations, taking into account the Heisenberg uncertainty principle which allows the muon to constantly emit and absorb photons (as long as it does so within the time limit set by the uncertainty principle), predict that the number will differ very slightly from 2 – hence g-2 (pronounced “gee minus 2”). Comparing this calculation with experimental measurements is a very sensitive test of our theory of the electromagnetic force, quantum electrodynamics, QED.

To measure g-2, you put your charged particle in a very precisely known magnetic field. The interaction between the spin and the magnetic field makes the spin direction wobble, or “precess” – this is very like a gyroscope, or an old-fashioned spinning top when it’s running down. If you can measure the rate of precession, you can measure g-2.

Muons are unstable particles, which decay into an electron and two neutrinos. Because of the spins of the particles involved, it turns out that the decay electron (or positron, for a positive muon) comes out along the direction that the muon’s spin axis was pointing in – it’s as if the Earth emitted particles directly upwards from the North Pole. So by measuring the directions and energies of the decay electrons/positrons, we can measure g-2. This has to be done with very great care, because the prediction is extremely precise, and any deviation from it would be very small.

The best measurement of the muon g-2 (from 2004) is
0.0023318416 +/- 0.0000000012
compared with a theoretical calculation of
0.0023318362 +/- 0.0000000016
This is extremely interesting, because the results do not agree within their error bars. The difference is not enough to be sure that it is real, but if it were, it would suggest that the muon g-2 is being affected by particles that are not in the Standard Model (since the Standard Model particles are taken into account in the theoretical calculation). For this reason, a new improved version of the g-2 experiment is being set up at Fermilab, near Chicago, to measure this number to better precision. You can find out much more about g-2 at their website, http://muon-g-2.fnal.gov/

I have a soft spot for this experiment, because the best value prior to 2004 was produced by a CERN experiment that Sheffield physicists played an important part in. It was long before I arrived – the experiment was done in the 1970s – but the leader of the Sheffield group, Fred Combley, was the man who hired me in my present position. He was a lovely man (he died of cancer about 12 years ago) and I have fond memories of him.