Theory Offers a High-Resolution View of Quarks Inside Protons

Theorists predict differential distribution of 'up' and 'down' quarks within protons—and differential contributions to the proton's properties.

Image courtesy of Brookhaven National Laboratory
A view inside a proton moving at nearly the speed of light toward the viewer with its spin pointing horizontally shows differences in the spatial distributions of the momentum of up (left) and down (right) quarks—white is high; violet is low.

The Science

Protons contain two up quarks and one down quark. New calculations predicting the spatial distributions of the charges, momentum, and other properties of the quarks within protons revealed key differences between the up and down quarks. The calculations show that the up quarks are more symmetrically distributed and spread over a smaller distance within the proton than the down quark. In polarized protons, where the spin (angular momentum) of the proton is aligned in a particular direction, the distribution of the momenta of the down quarks is particularly asymmetrical and distorted compared to the up quarks. The results imply that these two types of quarks contribute differently to a proton’s properties.

The Impact

Scientists studying atomic nuclei want to understand how quarks and gluons—the particles that make up protons and neutrons—contribute to a proton’s overall properties. The new calculations are the first to use a new theoretical approach to obtain a high-resolution map of quarks in a proton. The predictions provide insight into how the inner building blocks contribute to proton properties such as spin. Physicians use proton spin every day in magnetic resonance imaging, but its origins are a mystery. Calculations resulting from this new theoretical approach will also aid in interpreting data from nuclear physics experiments.


Experiments exploring proton structure take place at the Continuous Electron Beam Accelerator Facility, a Department of Energy Office of Science user facility at the Thomas Jefferson National Accelerator Facility, and are planned for the future Electron-Ion Collider at Brookhaven National Laboratory. In these experiments, high-energy electrons emit virtual photons that scatter off and change the overall momentum of a proton. The scatterings give scientists access to the Generalized Parton Distribution (GPD) — how the energy-momentum and other characteristics of quarks and gluons are distributed within the proton. It’s like an x-ray imaging technique for the building blocks of bulk matter. Theoretical models provide a basis for analyzing and predicting results from these experiments. To that end, a collaboration of nuclear theorists at Brookhaven National Laboratory, Argonne National Laboratory, Temple University, Adam Mickiewicz University of Poland, and the University of Bonn, Germany, has employed a new theoretical formalism for calculating GPDs. Their approach made it possible to simulate very large numbers of these scattering interactions to produce detailed maps of the distribution of momenta, charge, and other characteristics of up and down quarks within unpolarized and polarized protons. The results show key differences between up and down quarks and imply that these two quark types contribute differently to proton properties.


Martha Constantinou
Department of Physics, Temple University

Swagato Mukherjee
Nuclear Theory Group, Brookhaven National Laboratory


This work was supported by the Department of Energy (DOE) Office of Science, Office of Nuclear Physics, within the frameworks of the Scientific Discovery through Advanced Computing (SciDAC) award “Fundamental Nuclear Physics at the Exascale and Beyond,” by the Quark-Gluon Tomography Topical Collaboration, by a DOE Office of Science Early Career Award, and by the National Science Foundation.


Bhattacharya, S., et al., Moments of proton GPDs from the OPE of nonlocal quark bilinears up to NNLO. Physical Review D 108, 014507 (2023). [DOI: 10.1103/PhysRevD.108.014507]

Bhattacharya, S., et al., Generalized parton distributions from lattice QCD with asymmetric momentum transfer: Unpolarized quarks. Physical Review D 106, 114512 (2022). [DOI: 10.1103/PhysRevD.106.114512]

Related Links

Calculations Reveal High-Resolution View of Quarks Inside Protons, Brookhaven National Laboratory news release

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