Nuclear theorists developed a high-resolution map of quark distributions within protons, distinguishing the roles of up and down quarks in proton properties using advanced computational models.
A collaboration of nuclear theorists at the U.S. Department of Energy’s (DOE) Brookhaven National Laboratory, Argonne National Laboratory, Temple University, Adam Mickiewicz University of Poland, and the University of Bonn, Germany, has used supercomputers to predict the spatial distributions of charges, momentum, and other properties of “up” and “down” quarks within protons. The results, published in the journal
To simulate the multiple momentum changes of the proton efficiently, the researchers had to develop a novel theoretical approach, published recently in Physical Review D.
Previously, theorists used the idea that the proton’s change in momentum was shared equally between the proton before the light scattered and afterward. This simplification provided a less accurate representation of reality and also made the simulations computationally expensive.
“Each momentum change value of the proton required a separate simulation, significantly increasing the computational burden to obtain a detailed proton map,” Bhattacharya explained.
“The new method can look at the effect of the momentum transfer as all being on the outgoing proton—the final state. This gives a view that is closer to the actual physical process,” she said.
“Most importantly, the new theoretical approach makes it possible to model numerous momentum transfer values within a single simulation.”
Leveraging the Lattice
The calculations describing quarks and their interactions are spelled out in a theory known as quantum chromodynamics (QCD). But because these equations have many variables, they are very difficult to solve. A technique known as lattice QCD, originally developed at Brookhaven Lab, helps to tackle the challenge.
In this method, physicists “place” the quarks on a discretized 4D spacetime lattice—a sort of 3D grid where quarks are at the nodes that accounts for how the arrangement of quarks changes over time (the fourth dimension). Supercomputers solve the equations of QCD by running through all the possible interactions of each quark with all the others, including how those interactions are affected by the myriad variables.
“The new formalism for modeling the interactions of photons (particles of light) with protons made it possible for us to leverage lattice QCD to simulate a much higher number of momentum transfers to achieve higher resolution imaging about 10 times faster than previous efforts,” said study coauthor Xiang Gao, a research associate at Argonne National Laboratory.
Because the equations of QCD have separate variables for up and down quarks, the method lets the scientists capture separate images of each quark type and calculate their individual GPDs.
Results and Implications
In addition to mapping out the energy-momentum distributions of the up and down quarks, the team also mapped out their charge distributions within protons. They also explored the quarks’ momentum and charge distributions in polarized protons, where the protons’ spins are aligned in a particular direction, to investigate how the inner building blocks contribute to the proton’s spin. Proton spin is a property used every day in magnetic resonance imaging (MRI), allowing doctors to non-invasively see structures inside our bodies. But how this property arises from the proton’s internal building blocks is still a mystery.
“Within a polarized proton, we found that the distribution of the momenta of the down quarks is particularly asymmetric and distorted compared to that of the up quarks,” Gao said. “Since the spatial distribution of momentum tells us about the angular momentum of quarks inside a proton, these findings show that the different contributions of up and down quarks to the proton’s spin arise from their different spatial distributions,” he noted.
According to their calculations, the scientists concluded that up and down quarks can account for less than 70% of the proton’s total spin. This implies that the gluons must contribute significantly as well. How the spin (angular momentum) of the proton is distributed amongst its constituent quarks and gluons provides clues about the proton’s internal structure. This, in turn, helps scientists understand the forces that act within the atomic nucleus.
Experimental findings from Brookhaven Lab’s Relativistic Heavy Ion Collider (RHIC), a DOE Office of Science user facility at Brookhaven Lab, support the idea of a significant gluon contribution to spin. This is one of the central questions that will be explored in great detail at the future EIC.
The new theoretical predictions will be used to provide essential information for comparison with those experiments, and to help scientists interpret their data, noted Joshua Miller, a coauthor carrying out his Ph.D. research at Temple University under the supervision of Constantinou.
“These two complementary things—the theory and experiment—have to be combined to get the complete image of the proton,” Miller said.
References:
“Moments of proton GPDs from the OPE of nonlocal quark bilinears up to NNLO” by Shohini Bhattacharya, Krzysztof Cichy, Martha Constantinou, Xiang Gao, Andreas Metz, Joshua Miller, Swagato Mukherjee, Peter Petreczky, Fernanda Steffens and Yong Zhao, 17 July 2023, Physical Review D.
DOI: 10.1103/PhysRevD.108.014507
“Generalized parton distributions from lattice QCD with asymmetric momentum transfer: Unpolarized quarks” by Shohini Bhattacharya, Krzysztof Cichy, Martha Constantinou, Jack Dodson, Xiang Gao, Andreas Metz, Swagato Mukherjee, Aurora Scapellato, Fernanda Steffens and Yong Zhao, 26 December 2022, Physical Review D.
DOI: 10.1103/PhysRevD.106.114512
This work was supported by the DOE Office of Science (NP) and the National Science Foundation. Computations for this work were carried out in part on facilities of the USQCD Collaboration and the Oak Ridge Leadership Computing Facility—a DOE Office of Science user facility at Oak Ridge National Laboratory. Additional funding and computational resources are listed in the scientific paper.