A joint Fermilab/SLAC publication

Building a mystery with the g-2 experiment


Experimental physicists love a mystery. When an experiment does not turn out the way theorists predict, it can mean the discovery of new physics.

So it might seem contradictory that one thing a physicist simply cannot tolerate is uncertainty.

Experiments studying subatomic particles called muons recently illustrated the difference between the two and spurred experimentalists to call for further study.

The trouble with uncertainty

g-2 experiment at Brookhaven National Laboratory / BNL

g-2 experiment at Brookhaven National Laboratory / BNL

Muons are the heavy cousins of electrons. Both muons and electrons have a property called a magnetic moment, which determines how they act in a magnetic field. The equation to calculate the magnetic moment of a muon depends on a number represented by the letter g, which early theory had predicted was equal to 2. Subsequent experiments found a different value for g.

In 2004, an experiment called g-2 (g minus two) at Brookhaven National Laboratory on Long Island in New York made the most precise measurement of g-2 until that point.

But the results were uncertain. The theoretical prediction had an amount of uncertainty. The experimental result had an amount of uncertainty. Both amounts were smaller than one part in a million.

The difference between the two numbers and the combined uncertainty just barely left scientists without a clear answer as to whether they had actually discovered a difference between theory and experiment.

"The goal of the experimentalist is to be able to say something meaningful, so we hate these small-significance deviations," said Denis Bernard, experimental physicist at Ecole Polytechnique in France. "Each time we have a small-significance deviation, we work to improve the precision and eliminate a mere statistical fluctuation--or better, discover the next big thing."

In a lecture at the Physics in Collision conference in Kobe, Japan, this week, Bernard presented the results of a new method of determining the theoretical measure of g-2.

Physicists in the BaBar collaboration at SLAC National Accelerator Laboratory submitted the results of the new measurement to Physical Review Letters last week.

The new measurement was more precise, and the result brought the theoretical prediction for g-2 and its experimental measurement closer together.

However, the significance of the difference between the two numbers remains maddeningly the same.

It works like a poll. If Candidate A is predicted to earn 60 percent of the vote and Candidate B is predicted to earn 40 percent, but the margin of error is 11 percentage points, the poll does not actually predict a winner.

But if the two percentages are closer together--say, 51 percent to 49 percent--the margin of error can be lower--say, 2 percentage points--and still render the prediction of who will win just as meaningless.

Bernard said a new g-2 experiment, which some physicists hope might take place at Fermi National Accelerator Laboratory in Illinois or at High Energy Accelerator Research oragnization (KEK) laboratory in Japan, could finally put an end to the frustration.

Either the theory and experimental results correspond or the numbers are far enough apart that scientists can officially declare a discrepancy. If theory and experiment do not match, physicists may have their mystery.

“Theory could be incomplete,” Bernard said. “We might be seeing new physics. Who knows?”

Theory through experiment

The least precisely understood ingredient of the theoretical prediction for g-2 is related to the strong force. Physicists cannot compute this number using quantum chromodynamics, the study of how quarks and gluons interact through the strong force. So they must find it through experiment.

Physicists from the BaBar collaboration at SLAC made this measurement by studying the production of a pair of subatomic particles called pions in collisions of electrons and their antiparticles, positrons, at a wide range of energies.

The physicists used a new technique to study collisions at different energies. They focused on electron-positron collisions in which the electron or positron released a high-energy photon, a particle of light, before colliding. The photons took different amounts of energy with them and therefore reduced the energy of the collisions by different amounts. So researchers were able to study different kinds of collisions without changing the energy at which they ran the accelerator.

The number of pion pairs created in these collisions depended on the energy of the collisions. Determining the relationship between the energy level and the number of events that resulted in pion pairs helped the physicists predict the value of g-2.

g-2, part II

Explanation of g-2 experiment / BNL

Explanation of g-2 experiment / BNL

In the old g-2 experiment at Brookhaven, physicists fed spinning muons into a ring-shaped magnetic field almost 46 feet in circumference.

A muon’s spin axis changed by a set number of degrees at each turn as it circulated around the ring, like a horse on a merry-go-round that spins on its pole as the entire ride moves in a circle.

Eventually the muon would decay, breaking apart into an electron and neutrinos. The speed at which the escaping subatomic particles moved depended upon the direction in which the muon had been spinning.

Imagine you are about to fling yourself dramatically from a speeding car as it jumps the gap between two sides of an opening drawbridge. Do you try to jump backward to land on the near side of the bridge? Or do you try to jump forward onto the far side?

Even if you try to jump backward, the momentum you have from traveling in the speeding car will pull you forward. The force of flinging yourself backward will only slow your forward momentum, not reverse it, so you will probably land in the water below.

If you try to jump forward, however, your effort will combine with the forward momentum you already have, and you may just make it to the other side.

Similarly, a muon with a backward spin will not fling its electron as far forward as a muon with a forward spin.

Using this knowledge, scientists measured the energy of electrons to determine the direction in which their parent muons were spinning. Electrons with higher energy, the ones that made it to the other side of the metaphorical bridge, came from muons with forward spins. And electrons with lower energy, the ones that wound up in the water, came from muons with backward spins.

Some researchers have suggested physically moving the g-2 experiment from Brookhaven National Laboratory to Fermilab, in Batavia, Illinois, where facilities could produce a larger number of muons. Others have suggested designing a new g-2 experiment at KEK laboratory in Tsukuba, Japan. Both laboratories could be capable of finding more precise results.

Then, Bernard said, physicists could finally solve the mystery. Or create a new one.

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