Supercomputer illuminates subatomic particle that helps hold matter together

A team of researchers has leveraged a supercomputer at the U.S. Department of Energy’s (DOE) Argonne National Laboratory to reveal the internal structure of a pion in unprecedented detail. The findings are published in the Journal of High Energy Physics.

Pions are subatomic particles that help bind matter at some of the smallest scales in nature. They are closely connected to the strong nuclear force, the fundamental force that holds protons and neutrons together inside atomic nuclei. Understanding how pions work can help scientists explain how matter forms at its most fundamental level.

“Pions mediate the strong force that binds nucleons—that is, the protons and neutrons that account for an atom’s mass,” said Yong Zhao, an Argonne physicist and principal investigator on the project.

Scientists have long been interested in understanding how quarks are distributed within composite particles held together by the strong nuclear force. For the lightest of these particles, the pion, there are few experimental results available, so scientists rely on large-scale simulations to reveal its internal 3D structure.

The research helps resolve a fundamental mystery in nuclear physics: how visible matter forms from elementary particles such as quarks and gluons.

“Pion structure can be addressed at a profound level by quantifying its multidimensional structure,” Zhao said. “By probing the pion’s internal structure, we gain a deeper understanding of how quarks and gluons are confined to creating visible matter.”

To investigate the pion’s structure, the team, which included scientists from DOE’s Brookhaven National Laboratory, used the Polaris supercomputer at the Argonne Leadership Computing Facility (ALCF) in combination with advanced theoretical frameworks to simulate the physics of the strong force.

Their simulations produced high-resolution 3D images of the pion, showing how quarks are arranged inside the particle. The ALCF is a DOE Office of Science user facility.

“Polaris allowed us to simulate how quarks move and correlate inside the pion, both along its direction of motion and across it,” Zhao said.

“The simulation captures hundreds of snapshots of our 4D spacetime, represented on a lattice with millions of grid points. This is a task possible only with large-scale parallel computing power like that of ALCF supercomputers. We thereby obtained high-resolution images of the quark structure inside a moving pion. These images reveal the transverse spatial distributions of quarks carrying different fractions of the pion’s momentum.”

The Polaris calculations revealed the quark generalized parton distribution (GPD) of the pion, which helped the team generate a detailed 3D image of it. The pion GPD is determined with controlled systematic uncertainties across different quark longitudinal momentum values. These values are measured both along the direction of the pion’s motion and perpendicular to it.

“Our results reveal that the transverse size of the pion decreases as the momentum in the direction of the pion increases—a pattern also seen in the proton—and that the effective size of the pion is smaller than that of the proton at moderate parallel pion momentum values,” Zhao said.

Because there currently are no experimental measurements of the pion GPD, the team’s theoretical results provide valuable guidance and support for upcoming experiments, including those at DOE’s Thomas Jefferson National Accelerator Facility and the future Electron-Ion Collider at Brookhaven.

“Our next step is to use the ALCF’s Aurora supercomputer to map the proton in three dimensions,” Zhao said. “Protons, together with neutrons, make up all the atomic nuclei that compose the visible matter in our universe.”

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