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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!