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# Muon g-2

The muon is an intriging particle.In all respects it looks like an electron, just two hundred times heavier. By taking into account this mass difference, and nothing else, all it's properties can be calculated with great precision. At least, that is what our theory, the Standard Model, says. Perhaps there is more to it than we think. Predictions need to be tested by experiment! This is what we do in the muon g-2 experiment, by measuring the anomalous magnetic moment of the muon.

The magnetic dipole moment of a particle is aligned with its spin. When placed in a magnetic field, the interaction between the magnetic moment and this field will cause the spin to precess. The precession rate is proportional to the product of the strengths of the magnetic moment and magnetic field.So, from (carefully!) measuring the spin precession rate and the strength of the magnetic field the size of the magnetic moment can be obtained.

The magnitude of the dipole moment is usually described by the product of the Bohr magneton and the g-factor.The Bohr magneton only depends on fundamental constants (the unit of charge and Planck's constant) and the mass of the particle. All the interesting physics is in the g-factor. If the electron or muon were just a pointlike particle with spin 1/2, then this g-factor would be precisely two.This was one of the originally surprising, but by now triumphantly confirmed, predictions of the quantum theory by Paul Dirac.

However, it was also found that g (for the electron) deviates from two by a tiny amount, about 1 in 1000. Being unexpected, this deviationwas dubbed the anomalous magnetic moment. The anomaly a is defined as half difference of g from 2:a=(g-2)/2.The reason for the existence of the anomaly is that empty space is not empty at all. It is full of virtual particle popping into and out of existence.Normal particles interact with these virtual particles. And this causes g to deviate a little from 2. How much depends on the mass of the particle. The anomaly of the muon is thus different from that of the electron, although only be a little.

As it turns out, the anomaly of the muon can be measured directly, without having to subtract 2 from g. Here is how.

Protons slam into a target and create pions.  These pions decay into muons.  The highest energy muons all have their spin pointing in the same direction:  they are polarized.  The muons are put into a magnetic storage ring, where they will circle until they in turn also decay.  While circling in the magnetic field, their spins will precess by about 12 degrees every turn:  they rotate a little faster.  How much faster depends on the anomaly and the strength of the magnetic field.  Measure both and you can calculate a!

The spin precession rate is measured by looking at the number of high energy electrons that appear when the muons decay.  If the spin points forward, you see more of them.  And you see less when it points backwards.

The magnetic field is measured by looking at the spin precession rate of protons.  These protons are found inside a set of several hundred probes filled with water or petroleum jelly.  Some are mounted in the wall of the magnet to trace how the field changes with time.  Others inside a miniature "trolley" which rides on tracks inside the vacuum chamber to measure the field along the path where the muons usually travel.  This is where KVI is at work.  From making the field homogeneous to measuring it's strength.

The latest measurement was completed in 2001 using the proton beam at Brookhaven National Laboratory near New York city.  It reached a precision of half a part per million, a little over six digits.  This is about equal to the precision of the theoretical prediction.  Prediction and measurement matched reasonably well.  Only reasonably.  Not convincingly in agreement, but also not obviously in disagreement either (and that is already quite an accomplishment when trying to
match six digits!)

People are working hard to make an even more precise prediction.  In the mean time, the experiment is being moved to Fermi Lab near Chicago.  After rebuilding, the precision of the measurement will be improved by a factor 3 to 4.  Before we are that far, a lot has to happen.  We will make sure the magnetic field will again be homogeneous to within one part per ten million.  And we will put back together the tools needed to measure this.