Calculation Sharpens Imaging of Protons’ Insides

New theory-based approach gives access to quarks’ tiny transverse motion within protons.

The Science

Nuclear scientists used a new theoretical approach to calculate a value essential for unraveling the three-dimensional motion of quarks within a proton. Employing these new tools, scientists obtained a significantly more accurate picture of these internal building blocks’ transverse motion. This is quarks’ motion around a proton’s spin axis and perpendicular to its direction of motion. The new calculation precisely matches model-based reconstructions from particle collision data. It is particularly effective for quarks with low transverse momenta, where earlier methods fell short. Nuclear physicists will use the new method to predict the 3D motion of quarks — and their binding gluons — for future collider experiments.

The Impact

Unraveling the origin of proton spin is a central goal of the future Collider (EIC). The EIC’s collisions of spin-aligned protons with high-energy electrons will accurately measure the transverse motion of quarks and gluons within protons. This precise 3D imaging will reveal how the transverse motion of quarks and gluons contributes to a proton’s overall spin. This new theory-based approach provides the first accurate calculations of how the distribution of quarks’ transverse momentum within protons changes with collision energy. The approach will provide significantly more accurate theoretical predictions for the small transverse motions of quarks inside protons. This will eliminate the need to model the most complex strong-force governed quark-gluon interactions.

Summary

Nuclear theorists at Brookhaven National Laboratory and Argonne National Laboratory have successfully employed a new theoretical approach to calculate the Collins-Soper kernel, a quantity that describes how the distribution of quarks’ transverse momentum inside a proton changes with the collision energy. The team used lattice quantum chromodynamics (QCD), supercomputer-based simulations that track quark-gluon interactions on a 4D space-time lattice. The new theoretical approach enabled the team to significantly simplify their lattice QCD calculations and obtain precise results for even the small transverse motion of quarks, where the quark-gluon interactions become strong and complex. Such precise descriptions of the small transverse motion of quarks could not be achieved in previous lattice QCD calculations that used more conventional approaches.

The new results for low-transverse-momentum quarks are consistent with previous results but are much more precise and have significantly smaller uncertainties. They also match up with models developed to explain existing experimental data. These achievements demonstrate that the new approach can be used to predict and interpret future experimental results at different collision energies at the EIC, which is being built at Brookhaven National Laboratory, and the European Large Hadron Collider. Physicists will use these predictions and experiments to learn about quarks’ small transverse motion within protons and how that motion contributes to proton spin.

Contact

Funding

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. This research used awards of computer time provided by the INCITE program at Argonne Leadership Computing Facility, the ALCC program at the Oak Ridge Leadership Computing Facility, and the National Energy Research Scientific Computing Center.

Publications

Gao, X., Liu, W.-L., & Zhao, Y., Parton distributions from boosted fields in the Coulomb gauge. Physical Review D 109, 094506 (2024). [DOI: 10.1103/PhysRevD.109.094506].

Bowling, D., Xiang, G., Mukherjee, S., & Zhao, Y., Nonperturbative Collins-Soper kernel from chiral quarks with physical masses. Physics Letters B 852, 138617 (2024). [DOI: 10.1016/j.physletb.2024.138617]

Highlight Categories

Program: NP

Performer: DOE Laboratory