Spinning muons

Subatomic particles like electrons and muons act like tiny magnets. The strength of the magnet is affected by virtual particles. This effect is well known and can be calculated to a precision better than a part in ten billion. A niggling discrepancy between the prediction and measurement of this quantity has the potential to point to physics beyond the Standard Model. Fermilab’s Muon g-2 experiment is poised to study this vexing question.

If you take an electrical charge and set it in motion, you create a magnet. This is true in both the world of ordinary experience and the quantum world, although the details there are a bit trickier. The simplest quantum system is a single, moving charged particle — say an electron or a muon. While I could select either type of particle for this article, for reasons that will become clear, I concentrate on the muon.

Subatomic particles like the muon have both electrical charge and quantum mechanical spin. Quantum mechanical spin differs a bit from ordinary spin, but it has the same consequence: the spinning muon acts like a magnet. The magnet has a specific strength, determined by the charge of the muon and the fact that it is a spin-1/2 particle. Together, the spin and strength produce an effect that scientists call the magnetic moment.

The prediction of the magnetic moment of the muon (and electron) was first given by Paul Dirac. The measurement involves something called the g factor, and the value of g was predicted to be 2. The way scientists search for deviations from predictions is to measure the quantity (g-2)/2. If the particle had the exact magnetic moment predicted by Dirac, this quantity would be exactly zero. Early measurements of the muon’s g factor showed that it differed from predictions by 0.1 percent.

Such a small difference between theory and measurement could be due to measurement or calculation error. However, the predictions and measurements are now very precise. For muons, the measured value of (g-2)/2 is 0.0011659209, where the measurement uncertainty is only in the last “9.” That means that all the other numbers are meaningful: The measurement is accurate to one part in ten billion. This is equivalent to measuring the circumference of the Earth at the equator to a precision of just under a quarter inch.

So what causes this 0.1 percent difference? There are many names for it, and two such names are virtual particles and quantum foam. In short, empty space isn’t empty space. At the subatomic level, particles are popping in and out of existence like the bubbles in foam. These particles are found in a more concentrated way near particles such as muons. You can think of these virtual particles as bees swarming surrounding a particularly aromatic flower (the muon). These virtual particles alter the strength of the muon’s magnetic field.

Scientists can calculate the effect of these virtual particles, and they agree very well with data to high precision. However, the theory and experiment don’t agree perfectly. Given the precision of the prediction and the measurement, it is possible that this discrepancy might be the signature of physics beyond the Standard Model. The Fermilab Muon g-2 experiment will study the magnetic moment of muons with greater precision than has been possible in the past. If the discrepancy remains and the uncertainty decreases, it may be that research involving spinning muons might yield the measurement that turns a possible crack in the Standard Model into a broken dam through which a new theory rushes and changes everything.

Don Lincoln

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