Brookhaven muon findings

Chuck Grimes cgrimes at tsoft.com
Tue Feb 13 14:44:46 PST 2001


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.]



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