Below is the Brookhaven DOE announcement on the muon anomolous magnetic moment experiments. Ian Murray posted a clip from the NYT on this last week. There are abstracts and preprints of the technical papers available:
Brown, et. al. (Muon g-2 collaboration), ``Precise Measurement of the Postive Muon Anomalous Magnetic Moment'', at: http://xxx.lanl.gov/abs/hep-ex/0102017
Czarnecki A, Marcinano W, ``The Muon Anomolous Magnetic Moment: A Harbinger for `New Physics''', at: http://xxx.lanl.gov/abs/hep-ph/0102122
[Thanks to Matthew Nobes, Physics Dept, Simon Fraser Univ, B.C. on sci.physics.particle for the above refs.] If anyone is interested in downloading these papers, enter the address without the last number field, then enter the last number in the search engine when the form comes up. They offer pdf under other formats for computers without ps and dvi output readers and printers.
Chuck Grimes
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Background on Brookhaven's g-2 Experiment (E821)
A so-called blind study
The g-2 value is actually a ratio developed by comparing two
different sets of data. To minimize any possible human bias or
error in this extraordinarily precise measurement, the two data
sets were analyzed by separate groups of researchers, who each
deliberately included artificial offsets in their result to conceal
the true value and prevent unconscious bias from intruding during
the analysis process. The offsets were not removed until each
group was certain of the precision and accuracy of its own
analysis.
A total of 68 researchers
The g-2 collaborators hail from Boston University; Brookhaven
National Laboratory; Budker Institute of Technology, Novosibirsk,
Russia; Cornell University; Fairfield University; Heidelberg
University, Germany; KEK Laboratory, Japan; RIKEN/BNL Research
Center; Tokyo Institute of Technology, Japan; University of
Illinois at Urbana-Champaign; University of Minnesota; and Yale
University. A full list of collaborators from these institutions
can be found at: http://www.phy.bnl.gov/g2muon/new_cl4.html
Precision analysis of huge volumes of data
The scientists collected data from more than 1 billion muon decay
events. The new measurement is a factor of 5.6 more precise than
previous measurements made during the 1970s at CERN, the European
laboratory for particle physics near Geneva, Switzerland.
Where? The experiment takes place at the U.S. Department of
Energy's Brookhaven National Laboratory, using the Alternating
Gradient Synchrotron (AGS) to deliver a custom muon beam into the
world's largest superconducting magnet -- the "muon storage ring."
The AGS provides the world's most intense multi-GeV proton beam.
What? A 1.3 parts per million (ppm) precision measurement was made
of the muon's spin anomaly, termed g-2, or the "muon g-factor." The
result is numerically greater than the prediction from the Standard
Model theory of particle physics. The significance of the deviation
is 2.6 standard deviations following standard statistical
analysis. This means that there is a 99 percent probability that
the measurement does not agree with the Standard Model.
Why? The muon g-factor differs from the simple prediction of g=2 by
a small amount, essentially one part in 800. This tiny difference is
due to the muon's interactions with virtual fields. The Heisenberg
uncertainty principle permits the muon to emit and reabsorb
photons, electrons, positrons, and even heavier particles such as
the W and Z bosons, all of which can affect the g-factor. The
electromagnetic, weak, and strong interactions all contribute to
the muon anomaly. Their combined effect is calculated in the
Standard Model to a precision of 0.6 ppm.
A remarkable fact is that the muon g-factor can not only be
predicted to high precision, but also measured to equally high
precision. Thus, a comparison of measurement and theory provides a
sensitive test of the Standard Model. If there is physics not
included in the current theory, and such new physics is of a nature
that will affect the muon's spin, then the measurement at
Brookhaven Lab would differ from the theory. This is what appears
to have been observed, although there are several interpretations
of the result (see below) which must be considered.
How? The measurement is enabled by four important elements:
1) Polarized muons (muons with their spins aligned in one
direction) are injected into a storage ring whose highly uniform
magnetic field is perpendicular to the muon spin
direction. High-precision nuclear magnetic resonance (NMR) probes
measure the strength of the magnetic field. The muons race around
the ring, just like cars going around a racetrack.
2) As the muon circulates around the ring, its spin, which was
initially lined up in the direction of the muon motion, turns a bit
faster than the muon does, so that after about 29 laps around the
ring, the spin has rotated one extra time compared to the muon. The
difference between the rate at which the muon itself turns around
(once per lap of the ring) and the rate at which its spin rotates
(called the precession), is directly proportional to the difference
of the g-factor from 2. Measuring g-2 directly greatly enhances the
precesion with which we can measure g. This is the key idea of
measurement.
3) So that the muons don't spiral up or down and out of the ring,
an electric field is used to confine them. The electric field could
also affect the spin, except at a "magic" speed where the electric
field effect vanishes. This interaction of the muon spin and the
electric field is a specific consequence of Einstein's special
theory of relativity. The experiment is performed with muons at
this magic speed, namely 99.94 percent the speed of light.
4) To follow the precession of the muon spin, a measurement is
required. Each muon is unstable (half have decayed after about 300
revolutions of the ring). When they decay, a positron (a positively
charged electron, the anti-particle to the electron) is emitted
whose energy carries, on average, information about the
instantaneous direction of the muon spin at the time of the decay.A
detector system measures the time and energy of these positrons and
thus produces the experimental data of events versus time. The data
look like any ordinary exponential (radioactive decay) with a
modulation (wiggle) superimposed due to the muon g-factor.
Three valid ways to interpret the finding 1) The Standard Model
theory is right and requires no "new physics" and the experiment is
right. There is approximately one chance in a hundred that the
experimenters would find a deviation as large as reported which is
simply a statistical fluctuation. The E821 (g-2) team has already
obtained an additional body of similar data, having four times as
many events. The analysis of this data, which has just begun, will
yield a result with two times smaller uncertainty and this much
smaller error will eliminate the possibility of a statistical fluke
if the central value of the measurement remains within the present
quoted error limits.
2) The Standard Model theory prediction is right, but new data from
other particle physics experiments used by the model will change
it. Although the uncertainty in the current calculation is smaller
than the experimental measurement, one part of the Standard Model
theory is particularly difficult to determine and involves the
analysis of related data from many experiments at positron-electron
colliders. New data obtained recently at accelerators in Russia ,
China, and the U.S., which has not so far been included in the
Standard Model theory, will soon reduce the Standard Model
uncertainty considerably.
3) Finally, one could conclude that the Standard Model is either
incomplete or wrong. In that case, it would be necessary to revise
the theory. What the E821 measurement does is make a statement that
"there is new physics out there and it affects the muon g-factor at
a certain level." The measurement does not say what that new
physics is likely to be. Of course, many theorists have already
considered this possibility and have suggested that supersymmetry,
muon substructure, or W-boson substructure would very likely affect
the muon g-factor. In any case, the information bodes very well for
the startup of the next run of the Tevatron Collider at the Fermi
National Accelerator Laboratory and, later in the decade, for the
new Large Hadron Collider (LHC) at CERN, as well as for a very high
energy electron-positron collider or a muon collider. These
colliders will be able to make "direct" discoveries of new
particles of high mass that are not now part of the Standard Model
of particle physics.
Some 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 don'st 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 don't 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!
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Material provided by the g-2 collaboration.
[ May 2000 story on g-2 from the Brookhaven Bulletin.]