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g-2 Backgrounder

Muon g-2 Vocabulary and Terms

Muon: Essentially, a "heavy" electron. The muon g-2 test is 40,000 times more sensitive to the Standard Model extensions compared to the electron. However, the electron g-factor has been measured to about 4 parts per billion (ppb ) already. The muon, electron, and tau are generically referred to as charged leptons, and they have the remarkable property that they are believed to be point particles. That is, they donšt have any root physical structure and they are not made out of any smaller building blocks, although the presence of electric and other fields do give them some dimension. Contrast this with, say, a proton, which is made up of quarks. The electron is a stable particle, while the muon and tau are radioactive and decay after some period of time. Electrons are all around us, and some muons (and even taus) are produced by cosmic rays. To obtain the number of muons necessary to measure the muon g-2, however, they must be produced by collisions of high-energy particles in a laboratory.

Spin: All muons spin on their axes like a toy top or the earth on its polar axis. All muons spin at the same rate. When we speak of spin direction we mean the direction of the axis of rotation.Polarization: In a collection of a large number of muons, if the spin directions are random, we would say that they are "unpolarized." On the other hand, if their spins tend to be in one particular direction on average, we say that they are "polarized." In the muon g-2 experiment, when the muons are first injected into the storage ring, they are polarized along their direction of motion.

Magnetic moment: The muon has a magnetic moment, which is equivalent to saying it has a north and south pole just like a bar magnet or a compass. The north and south poles of the muon magnet are aligned along the direction of the spin. The strength of the magnet is indicated by the magnitude of the magnetic moment. Its value is sensitive to detailed properties of the muon, and its measurement is an excellent test of models which predict these properties.

Spin precession: The familiar toy top kit consists of a gyroscope and a stand to support it. Suppose that the top's axis is in the horizontal plane. The support point of the top is on the axis of rotation, but away from the center of mass, so that gravity will exert a torque which tends to align the axis with the direction of gravity (the top will fall down). If the top is not spinning, this is exactly what happens -- the top falls down. On the other hand, if the top is spinning, the axis of the top precesses slowly in the horizontal plane instead of aligning with the gravitational force. The rate of precession will depend on the force of gravity (its torque) and on how fast the top is spinning.

In the g-2 experiment, the magnetic field in the storage ring is vertically oriented. When the muons are injected into the storage ring, their spin axes are in the horizontal plane (in fact they are aligned with their direction of motion). The north-south poles of the muon magnet are aligned with the spin direction, so themagnetic field will exert a torque which tends to align the spin axis with the direction of the field, just like a compass or bar magnet would align along the field. If the muon were not spinning, this would be exactly what happens. On the other hand, the muon is spinning, so the axis of the muon precesses slowly in the horizontal plane instead of aligning with the magnetic field. The rate of precession will depend on the force of the magnetic field (its torque), the size of its magnetic moment, and on how fast the muon is spinning.

g-factor: The magnetic moment is proportional to the dimensionless quantity g and fundamental constants, including the inverse of its mass.

g-2: The most rudimentary theory would predict that the value of g for the muon would be 2 (Dirac theory). More complete treatments, using more advanced theories, predict that g-2 is on the order of one part in 800, and experiments have confirmed this to high precision. The quantity a_mu =(g-2)/2 is called the "anomaly." If g were exactly 2, then the muon spin, if initially directed along the muon's momentum, will turn at the same rate as the muon around the ring, and will remain aligned with the muon momentum. In the muon g-2 experiment we measure the rate at which the muon spin changes direction compared to the rate at which the muon momentum changes direction -- in other words, we measure g-2, not g. If we measure g-2 to 1.3 parts per million of itself, then we measure g, and therefore the size of the magnetic moment, to about 2.6 parts per billion!

Standard Model: The Standard Model is a model of the basic building blocks of matter (quarks, leptons) together with the particles that mediate the electromagnetic force (gauge bosons, e.g. W, Z, photons, gluons), the strong force (the powerful force which holds nuclei together), and the weak force (much weaker than either the strong or electromagnetic force, and responsible, for example, for the decay of the muon). Gravity is the fourth force, but has not yet been incorporated into the Standard Model, and is so much weaker than the other forces that it is not believed to be of any consequence in the muon g-2. The Standard Model predicts virtually all known experimental results. But in many ways, the Standard Model is considered unsatisfying, since we donšt really know why we have the basic particles, and the model is not able to predict such things as their masses (the masses are believed to come from the so-called Higgs mechanism, the subject of study of many high-energy experiments, yet to be demonstrated).

Beyond the Standard Model: There are a number of potential theories which modify the Standard Model. For example, there is supersymmetry, which predicts a partner for every known particle. Every fermion would have a boson partner, and every boson would have a fermion partner. So far, none of these hypothesized partners have been seen. Under certain scenarios, the existence of such particles would have a slight effect on g-2. If the measured value of g-2 differs from the Standard Model prediction, then supersymmetry is one of the possible explanations. Another possibility is that the muon is not a point particle after all, but is in fact constructed of as yet unkown smaller particles. Or, the W gauge boson may have a g value which differs from 2. These are usually listed as the most likely explanations for any discrepancy between the Standard Model and the measured value of g-2, but perhaps none of them is right!