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How Strong is the Weak Nuclear Force?

February 10, 2011

After a decade of experimental development, data-taking, and analysis, an international research team led by scientists from Boston University and the University of Illinois has announced a new value for the muon lifetime. The new lifetime measurement—the most precise ever made of any subatomic particle—makes possible a new determination of the strength of the weak nuclear force. Experiments for this research were conducted using the proton accelerator facility of the Paul Scherrer Institute (PSI) in Villigen, Switzerland. The results were published in the January 25, 2011 issue of the journal Physical Review Letters.

How strong is the weak force?

The weak force is one of the four fundamental forces of nature. Although rarely encountered in everyday life, the weak force is at the heart of many elemental physical processes, including those responsible for making the sun shine. All four of the fundamental forces are characterized by coupling constants, which describe their strength. The famous constant G, in Newton’s law of gravitation, determines the gravitational attraction between any two massive objects. The fine structure constant determines the strength of the electrostatic force between charged particles. The coupling constant for the weak interactions, known as the Fermi constant, is also essential for calculations in the world of elementary particles. Today, physicists regard the weak and the electromagnetic interaction as two aspects of one and the same interaction. Proof of that relationship, established in the 1970s, was an important breakthrough in our understanding of the subatomic world.

Muon lifetime - key to the strength of the weak force

The new value of the Fermi constant was determined by an extremely precise measurement of the muon lifetime. The muon is an unstable subatomic particle which decays with a lifetime of approximately two microseconds (two millionths of a second). This decay is governed by the weak force only, and the muon's lifetime has a relatively simple relationship to the strength of the weak force. "To determine the Fermi constant from the muon lifetime requires elegant and precise theory, but until 1999, the theory was not as good as the experiments," says David Hertzog, professor of physics at the University of Washington. (At the time of the experiment, Hertzog was at the University of Illinois.) “Then, several breakthroughs essentially eliminated the theoretical uncertainty. The largest uncertainty in the Fermi constant determination was now based on how well the muon lifetime had been measured."

Measuring procedure repeated 100 billion times - precision of the measurement two millionths of a millionth of a second

The MuLan (Muon Lifetime Analysis) experiment used muons produced at PSI’s proton accelerator—the most powerful source of muons in the world and the only place where this kind of experiment can be done. "At the heart of the experiment were special targets that caught groups of  positively charged muons during a ‘muon fill period,’" says PSI’s Bernhard Lauss. "The beam was then rapidly switched off, leaving approximately 20 muons in the target. Each muon would eventually decay, typically ejecting an energetic positron—a positively charged electron—to indicate its demise. The positrons were detected using a soccer-ball shaped array of 170 detectors, which surrounded the target." Boston University physics professor Robert Carey adds, "We repeated this procedure for 100 billion muon fills, accumulating trillions of individual decays. By the end, we had recorded more than 100 terabytes of data, far more than we could handle by ourselves. Instead, the data was stored and analyzed at the National Center for Supercomputing Applications (NCSA) in Illinois." A distribution of how long each muon lived before it decayed was created from the raw data and then fit to determine the mean lifetime: 2.1969803 ±0.0000022 microseconds. The uncertainty is approximately 2 millionths of a millionth of a second - a world record.

 

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