Two Unprecedented Measurements Offer Insight into the Strong Force

Experimental results a decade in the making will help theorists refine their calculations of the strong force

Although the strong force holds together more than 99% of the visible matter around you, it’s the least understood of the four fundamental forces in the universe. Researchers at the U.S. Department of Energy’s Thomas Jefferson National Accelerator Facility want to remedy that.

“On one hand, I am just bloody curious about how it works,” said Karl Slifer, a professor of physics at the University of New Hampshire and co-spokesperson of an experiment conducted in Jefferson Lab’s Hall A to probe the strong force. “On the other hand, the more we understand these forces of nature, the more we can come up with beneficial applications of that understanding.”

Together, Slifer and nearly 100 other physicists published the first results of this experiment, known as g2p, on October 13 in Nature Physics. Their results test a less understood facet of quantum chromodynamics (QCD), the theory of the strong force. QCD attempts to mathematically describe how protons and neutrons in the atom’s nucleus are formed from the interactions of particles called quarks and gluons.

But before the researchers could evaluate this subset of QCD, they first had to obtain two never-before-measured values – the proton’s g2 structure function and a specific spin polarizability of the proton. This challenging mission that took more than 10 years to complete.

First, g2

When quarks and gluons are close together, they don’t interact much, and the strong force is weak. Theorists have figured out the QCD calculations to back this up.

But, when quarks and gluons are pulled further apart, the strong force gets stronger. At these relatively large distances inside subatomic particles, the math gets too complicated, and the shorter-distance QCD calculations fail. To compensate, physicists have developed approximations of QCD. One of these approximations of QCD at longer distances is known as chiral perturbation theory.

“Despite chiral perturbation theory being pretty good, some calculations from the theory have had some major failures,” said David Ruth, a Ph.D. student at the University of New Hampshire and first author of the paper. For example, previous measurements of the neutron have not agreed with some chiral perturbation theory predictions.

Ruth, Slifer, and the many other authors of this paper were curious: How does chiral perturbation theory stand up to measurements of the proton? To find out, they first had to measure the g2 structure function, a previously unmeasured quantity for the proton at long distances.

g2 is a spin structure function, meaning it mathematically describes how the spin behavior of a composite particle, such as a proton, differs from a point particle – an idealized, simple, fundamental particle that doesn't occupy any space.

To get to g2, they needed an electron beam produced by Jefferson Lab’s Continuous Electron Beam Accelerator Facility (CEBAF), a DOE user facility. They shot an electron beam at a target and detected the electrons that scattered off of it. The information carried by these scattered electrons allowed the nuclear physicists to extract g2.

While this sounds pretty simple, it turned out to be a bit more complicated than that. This quantity has remained elusive until now, because it requires both a low-energy beam and a transversely polarized target – a tricky combo.

The electron beam allows the researchers to access strong force interactions occurring over the aforementioned larger distances inside subatomic particles. This 2012 experiment was the last to run during Jefferson Lab’s 6 GeV era, before the beam was upgraded to 12 GeV.

The transversely polarized target, in which the spins of protons are oriented perpendicularly to the incoming electron beam, allows researchers to acquire spin information from the scattered electrons to calculate g2.

However, a low-energy electron beam is deflected by a transversely polarized target (whereas a high energy beam could go right through). To ensure the beam would remain on-target, the team had to install huge, special magnets to steer the low-energy electron beam directly into the target. In addition, other supportive infrastructure for the experiment was installed in Hall A.

“We provide the only data in the world on g2 structure function in this region, because it's such a bear to run these kinds of experiments,” Slifer said. “The experiment wouldn't have happened without the polarized target group and the accelerator staff. It was a technical feat.”

Installation alone took six months, and all of these additions complicated the data analysis, which took more than 10 years.

“Because you’re sort of performing this trick shot on the target rather than just hitting it directly, the resulting scattered electrons have added complexity,” said Ruth.

Two versions of one theory

While g2 carries interesting information about proton spin on its own, the physicists’ main motivation for measuring it was to obtain another value: a spin polarizability. Spin polarizabilities are fundamental properties of a particle, such as charge or mass, that describe how the quarks inside of it align their spin when hit with an electron beam. 

Different mathematical operations can turn g2 into different spin polarizabilities. The researchers of this experiment used g2 to obtain the longitudinal–transverse spin polarizability of the proton, which has never been measured before.

They compared this value to predictions from two different calculations of chiral perturbation theory and found it agrees well with one of them but not with the other.

“Our results show strong support for one calculation, but show the other calculation probably has more room to improve,” said Jian-Ping Chen, senior staff scientist at Jefferson Lab and co-spokesperson of this experiment.

This means some of the assumptions made in the less-right calculation are probably wrong, but the exact differences between these two versions of chiral perturbation theory still need to be pinned down.

“To fully extract the meaning from this data, we need the theorists to figure out where the calculations are different and reconcile their calculations,” Ruth said. “Hopefully, the one that disagrees with our data is fixed and they both agree beautifully.”

Because g2 and this spin polarizability were previously unmeasured for protons, these values will serve as a benchmark for future theory work. If predictions don’t match up with these data, something is probably off. 

This paper was the first to emerge from the g2p experiment.

“After so many people worked on this for so many years, starting to see the fruit of all that labor is wonderful,” Slifer said. “These results take us one step closer to understanding the underlying theory and give us a little peek behind the curtain.”

Next, the authors plan to use g2 to produce more spin polarizabilities for the proton in the hope of continuing to pull back the curtain concealing our understanding of the strongest force in the universe.

Further Reading
Proton spin structure and generalized polarizabilities in the strong quantum chromodynamics regime
Testing the theory of the strong force by measuring proton spin polariz­abilities

Meet Our People: Jian-Ping Chen

By Chris Patrick

Contact: Kandice Carter, Jefferson Lab Communications Office,


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