Nuclear theorists turn to supercomputers to map the building blocks of matter in 3D

Deep within what we perceive as solid matter, the landscape is anything but stationary. Inside the building blocks of the atom’s nucleus—particles called hadrons that a high school student would recognize as protons and neutrons—is a bubbling mix of interacting quarks and gluons, known collectively as partons.

A group of physicists has come together to map these partons and unravel how they interact to form hadrons. Based at the U.S. Department of Energy’s Thomas Jefferson National Accelerator Facility and known as the HadStruc Collaboration, the nuclear physicists have been working on a mathematical description of the parton interactions. Their latest findings were recently published in the journal Journal of High Energy Physics.

“The HadStruc collaboration is a group based at Jefferson Lab Theory Center and some nearby universities,” said Joseph Karpie, a HadStruc member and postdoctoral researcher at Jefferson Lab’s Center for Theoretical and Computational Physics. “We have people at William & Mary and Old Dominion University.”

Other members of the collaboration who are co-authors on the paper are Jefferson Lab scientists Robert Edwards, Colin Egerer, Eloy Romero and David Richards. William & Mary’s physics department is represented by Hervé Dutrieux, Christopher Monahan and Kostas Orginos, who also holds a joint appointment at Jefferson Lab. Anatoly Radyushkin is also a joint faculty member at Jefferson Lab affiliated with Old Dominion University, while Savvas Zafeiropoulos is at the University of Toulon in France.

A solid theory

The components of hadrons, called partons, are bound together by the strong force, one of the four fundamental forces of nature, along with gravity, electromagnetism and the weak force, observed in particle decay.

Karpie explained that the HadStruc collaboration members, like many theoretical physicists around the world, are trying to figure out where and how quarks and gluons are distributed in the proton. The group uses a mathematical approach known as lattice quantum chromodynamics (QCD) to calculate how the proton is built.

Dutrieux, a postdoctoral researcher at William & Mary, explained that the group’s paper describes a three-dimensional approach to understanding hadronic structure through QCD lensing. This approach was then carried out via supercomputer calculations.

The 3D concept is based on the notion of generalized parton distributions (GPDs). GPDs offer theoretical advantages over structures visualized by one-dimensional parton distribution functions (PDFs), an older QCD approach.

“The GPD is much better in the sense that it can elucidate one of the big questions we have about the proton, which is how its spin arises,” Dutrieux said. “The one-dimensional PDF gives only a very, very limited picture of this phenomenon.”

He explained that the proton consists, to a first approximation, of two up quarks and one down quark, called valence quarks. The valence quarks are held together by a changing list of gluons from the strong force interactions, which act to glue the quarks together. These gluons, along with quark-antiquark pairs, commonly referred to as the quark-antiquark sea to distinguish them from valence quarks, are continually being created and dissolved in the strong force.

One of the most surprising discoveries about proton spin came in 1987, when experimental measurements showed that quark spin contributed less than half of the overall proton spin. In fact, a large part of the proton spin may come from gluon spin and parton motion in the form of orbital angular momentum. Much experimental and computational effort is still needed to clarify this situation.

“GPDs represent a promising opportunity to access this orbital angular part and produce a well-founded explanation of how the proton spin is distributed between quarks and gluons,” Dutrieux noted.

He went on to say that another aspect the collaboration hopes to address through GPDs is a concept known as the energy momentum tensor.

“The energy-momentum tensor actually tells us how energy and momentum are distributed inside your proton,” Dutrieux explained. “They also tell us how your proton interacts with gravity. But right now, we’re just looking at its matter distribution.”

Data simulation

As we mentioned earlier, accessing this information requires sophisticated calculations on supercomputers. After developing their new approach, the theorists then ran 65,000 simulations of the theory and its hypotheses to test it.

This massive number of calculations was performed on Frontera at the Texas Advanced Computer Center and on the Frontier supercomputer at the Oak Ridge Leadership Computing Facility, a DOE Office of Science user facility at Oak Ridge National Laboratory. This included 186 simulations of protons moving with different momenta, performed against the backdrop of 350 randomly generated collections of gluons. This computation required the processors at these facilities to run collectively for millions of hours. The final analysis of these results is being performed on the smaller supercomputers at Jefferson Lab.

The result of this work was a robust test of the 3D approach developed by the theorists. This test represents an important milestone for the DOE thematic collaboration on quark-gluon tomography (QGT).

“This was our proof of principle. We wanted to know if the results of these simulations would be reasonable given what we already know about these particles,” Karpie said. “Our next step is to improve the approximations we used in these calculations. This costs 100 times more in terms of computational time.”

New data on the horizon

Karpie noted that the HadStruc collaboration’s GPD theory is already being studied in experiments at high-energy facilities around the world. Two methods for examining hadron structure using GPD, deep virtual Compton scattering (DVCS) and deep virtual meson production (DVMP), are currently being implemented at Jefferson Lab and other facilities.

Karpie and Dutrieux expect the group’s work to be integrated into experiments at the Electron-Ion Collider (EIC), a particle accelerator under construction at DOE’s Brookhaven National Laboratory on Long Island. Jefferson Lab is partnering with Brookhaven National Laboratory on the project.

The EIC is expected to be powerful enough to probe hadrons beyond the point at which current instruments begin to lose signal, but exploration of the structure of the hadron assembly will not wait until the EIC is commissioned.

“We’re doing new experiments at Jefferson Lab. They’re collecting data right now and giving us information that we can compare to our calculations,” Karpie said. “Then we hope to expand and get even better information at EIC. It’s all part of that chain of progress.”

Members of the HadStruc collaboration are considering further experimental applications of their work on QCD theory at Jefferson Lab and other facilities. One example is using supercomputers to calculate more precise results from data that have been available for decades.

Karpie added that he hopes to be a few steps ahead of the experimenters.

“QCD has always lagged behind experiments. We were usually doing ‘post-dictations’ instead of ‘predicting’ what was happening,” Karpie said. “So if we could actually move forward, if we could do something that experimentalists can’t do yet, that would be pretty cool.”