Within what we think of as solid matter, the reality is not so simple. The core of atoms, which consists of particles called hadrons—commonly known as protons and neutrons—is actually a turbulent environment filled with quarks and gluons that interact constantly, collectively referred to as partons.
A group of physicists, known as the HadStruc Collaboration, has recently unified their efforts to map these partons and clarify how they interact to create hadrons. This team operates out of the Thomas Jefferson National Accelerator Facility, part of the U.S. Department of Energy, and focuses on developing a mathematical framework for understanding parton interactions. Their most recent research has been published in the Journal of High Energy Physics.
“The HadStruc Collaboration is centered at the Jefferson Lab Theory Center along with some partner universities,” said Joseph Karpie, a postdoctoral researcher at the Jefferson Lab’s Center for Theoretical and Computational Physics. “We have members from William & Mary and Old Dominion University involved as well.”
The paper also includes contributions from fellow researchers at Jefferson Lab, such as Robert Edwards, Colin Egerer, Eloy Romero, and David Richards. From William & Mary, Hervé Dutrieux, Christopher Monahan, and Kostas Orginos—who also holds a position at Jefferson Lab—are co-authors. Anatoly Radyushkin belongs to both Jefferson Lab and Old Dominion University, while Savvas Zafeiropoulos represents Université de Toulon in France.
A Strong Theory
Partons, which are the constituents of hadrons, are held together by the strong interaction, one of nature’s four fundamental forces alongside gravity, electromagnetism, and the weak force that is seen in particle decay.
Karpie mentioned that the HadStruc Collaboration, like numerous theoretical physicists around the globe, is investigating how quarks and gluons are arranged within the proton. To achieve this, they employ a mathematical method known as lattice quantum chromodynamics (QCD), which helps in understanding the construction of the proton.
Dutrieux, who is a postdoctoral researcher at William & Mary, explained that their paper presents a three-dimensional perspective for analyzing hadronic structure using QCD. This perspective was validated through supercomputer calculations.
The 3D approach is built on a concept called generalized parton distributions (GPDs), which provide theoretical benefits over the older one-dimensional parton distribution functions (PDFs).
“The GPD is far superior because it helps answer one of our primary questions about the proton: how does its spin come about?” Dutrieux explained. “In contrast, the one-dimensional PDF offers a very limited understanding.”
He clarified that, in a basic sense, a proton is composed of two up quarks and one down quark—termed valence quarks. These valence quarks interact with an ever-changing array of gluons that emerge from the strong force, holding the quarks together. Additionally, pairs of quarks and antiquarks—which are referred to as the sea of quarks-antiquarks—continuously appear and vanish due to strong force dynamics.
A notable discovery regarding the spin of the proton occurred in 1987 when experimental results indicated that quark spins contribute to less than half of the proton’s total spin. A significant portion of this spin may originate from gluon spin and the orbital motion of partons. Extensive experimental and computational work is still required for further insights.
“GPDs provide an exciting opportunity to access the orbital angular contributions and to clarify how the proton’s spin is distributed among its quarks and gluons,” noted Dutrieux.
He added that another related focus for the collaboration involves analyzing something known as the energy momentum tensor.
“The energy momentum tensor illustrates how energy and momentum are allocated within the proton,” Dutrieux shared. “It also details how the proton responds to gravity, but at this point, our concentration is on understanding its matter distribution.”
Simulating the Data
Acquiring this type of information necessitates advanced calculations on supercomputers. After formulating their new approach, the theorists executed around 65,000 simulations to validate their concepts.
This extensive computational task was performed on Frontera at the Texas Advanced Computer Center, along with the Frontier supercomputer at the Oak Ridge Leadership Computing Facility, which is part of the DOE Office of Science user facilities at Oak Ridge National Laboratory. These simulations included 186 proton momentum variations within a backdrop of 350 randomly generated gluon configurations, requiring millions of collective processing hours. The final assessments of these results were conducted on smaller supercomputers at Jefferson Lab.
The outcome was a solid evaluation of the 3D framework created by the theorists, proving to be a significant achievement for DOE’s Quark-Gluon Tomography (QGT) Topical Collaboration.
“This was our proof of concept. We aimed to see if the results from these simulations matched what we know about these particles,” Karpie stated. “Our next step will be to enhance the approximations used in these calculations, which will be computationally about 100 times more resource-intensive,” he added.
New Data on the Horizon
Karpie emphasized that the HadStruc Collaboration’s GPD research is already under investigation in experiments at high-energy facilities worldwide. Two methods for analyzing hadron structure using GPDs—deeply virtual Compton scattering (DVCS) and deeply virtual meson production (DVMP)—are currently being explored at Jefferson Lab and other institutions.
Both Karpie and Dutrieux anticipate that their team’s findings will be part of the Electron-Ion Collider (EIC) experiments, a particle accelerator under construction at the DOE’s Brookhaven National Laboratory on Long Island. Jefferson Lab is collaboratively involved with Brookhaven on this project.
The EIC is expected to possess the capabilities to investigate hadrons beyond the limits of current instruments, yet research on hadron assembly will not wait for the EIC to launch.
“We have several new experiments underway at Jefferson Lab. They’re currently gathering data that will assist us in comparing with our calculations,” Karpie noted. “And we are looking forward to obtaining even better insights at the EIC. This all contributes to a progressive development chain.”
Members of the HadStruc Collaboration are also eyeing additional experimental applications of their QCD theory research at Jefferson Lab and elsewhere. One example includes using supercomputers to generate more precise results from decades-old data.
Karpie aims to stay ahead of the experimental efforts. “QCD has traditionally trailed behind experiments. We’ve generally been in a situation of post-dicting outcomes rather than pre-dicting events,” Karpie expressed. “Thus, if we can manage to accomplish something that experimenters have not yet undertaken, that would indeed be impressive.”
Some of this research was supported by Jefferson Lab’s Lab Directed Research & Development (LDRD) program, which allocates a portion of its research efforts to support cutting-edge initiatives relevant to the DOE’s mission.
