New Insights into Quark Dynamics Within Protons

Scientists from Brookhaven National Laboratory and Argonne National Laboratory developed a new theoretical method for calculating the Collins-Soper kernel, which characterizes how the three-dimensional motion of quarks within a proton varies with collision energy. The study was published in Physical Review D.

The Science

Nuclear scientists developed a new theoretical approach to determine a key value essential for understanding the three-dimensional motion of quarks within a proton. Using this method, researchers were able to achieve a much clearer image of the transverse motion of these fundamental particles.

This refers to the motion of quarks perpendicular to the proton's direction of motion and around its spin axis. The new computation aligns precisely with reconstructions from particle collision data based on models.

The method is particularly effective for quarks with low transverse momenta, where previous techniques had limitations. Nuclear physicists will use it to predict the three-dimensional motion of quarks and their binding gluons in preparation for upcoming collider experiments.

The Impact

One of the main goals of the upcoming Electron-Ion Collider (EIC) is to uncover the origin of proton spin. The EIC will measure the transverse motion of quarks and gluons within protons through collisions of spin-aligned protons with high-energy electrons.

This precise three-dimensional imaging will reveal how a proton's overall spin is influenced by the transverse motion of its quarks and gluons. The new theory-based method provides the first accurate computations of the relationship between collision energy and the distribution of quarks' transverse momentum within protons.

The method will enable more accurate theoretical predictions of the small transverse motions of quarks inside protons. It will eliminate the need for complex modeling of the intricate quark-gluon interactions governed by the strong force.

Summary

The team employed lattice quantum chromodynamics (QCD), which simulates quark-gluon interactions on a 4D space-time lattice using supercomputers. With the new theoretical approach, the team achieved accurate results for the small transverse motion of quarks, where quark-gluon interactions are strong and complex. This method greatly simplified their lattice QCD calculations, allowing for improved precision in these challenging scenarios.

Earlier lattice QCD calculations using more traditional methods could not describe the small transverse motion of quarks with such precision.

The new results for low-transverse-momentum quarks are more accurate and have significantly fewer uncertainties, while remaining consistent with previous findings. They also align with models designed to match current experimental data.

These advancements demonstrate that the new method can be applied to both the European Large Hadron Collider and the upcoming EIC at Brookhaven National Laboratory, enabling more precise predictions and interpretations of future experimental results across a range of collision energies.

These experiments and predictions will help physicists understand the small transverse motion of quarks within protons and how that motion affects proton spin.

This research was supported by the Department of Energy (DOE) Office of Science, Office of Nuclear Physics, through the Scientific Discovery through Advanced Computing (SciDAC) award "Fundamental Nuclear Physics at the Exascale and Beyond," the Quark-Gluon Tomography Topical Collaboration, a DOE Office of Science Early Career Award, and the National Science Foundation. Computational resources were provided through awards of computer time from the INCITE program at the Argonne Leadership Computing Facility, the ALCC program at the Oak Ridge Leadership Computing Facility, and the National Energy Research Scientific Computing Center.

Journal Reference:

‌Gao, X., et al. (2024). Parton distributions from boosted fields in the Coulomb gauge. Physical Review. D. doi.org/10.1103/physrevd.109.094506.