A team of nuclear theorists from several institutions, including Brookhaven National Laboratory, Argonne National Laboratory, Temple University, Adam Mickiewicz University of Poland, and the University of Bonn in Germany, collaborated to predict the spatial distributions of charges and momentum of “up” and “down” quarks within protons using supercomputers. Their findings, recently published in Physical Review D, highlighted significant differences between the characteristics of up and down quarks. The calculations indicated that up quarks are more symmetrically distributed over a smaller distance compared to down quarks, implying distinct contributions to the proton's properties, such as internal energy and spin.
Swagato Mukherjee from Brookhaven Lab's nuclear theory group emphasized that this work is the first to employ a new theoretical approach, resulting in a high-resolution map of quarks within a proton. The team's calculations are crucial for interpreting data from nuclear physics experiments that investigate the distribution of quarks and gluons within the proton, affecting its overall properties.
Experiments exploring these quark and gluon distributions are already happening at the Continuous Electron Beam Accelerator Facility (CEBAF) at Thomas Jefferson National Accelerator Facility, a DOE Office of Science user facility. Additionally, more detailed experiments are planned for the future Electron-Ion Collider (EIC) at Brookhaven Lab. These experiments utilize high-energy electrons to emit virtual particles of light, which scatter off the proton without breaking it apart. The resulting changes in proton momentum reveal crucial details about the inner components, akin to an X-ray imaging technique for understanding the building blocks of matter on a fundamental level.
New theoretical approach to GPD
Researchers studying the Generalized Parton Distribution (GPD) of the proton, which encompasses quarks and gluons, gain valuable insights into how energy-momentum and other characteristics are distributed within the proton. Imagine the proton as a bag filled with marbles representing these particles, and the GPD provides a map indicating the likelihood of finding a marble with specific energy-momentum at various positions inside the bag, especially when the bag is shaken and the marbles move around.
Analyzing multiple scattering interactions involving different momentum changes of the proton is crucial to creating a detailed map. To achieve this efficiently, the team developed a novel theoretical approach, published in Physical Review D, which differs from previous methods. In the past, theorists assumed the proton's momentum change was equally shared before and after scattering, leading to less accurate representations and computationally expensive simulations.
The new method focuses on the effect of momentum transfer solely on the outgoing proton (final state), which provides a more realistic view of the physical process. The advantage is that numerous momentum transfer values can now be modeled within a single simulation, significantly reducing the computational burden and opening doors to deeper understanding and potential applications of this knowledge.
Leveraging the lattice
Quantum chromodynamics (QCD) is the theory used to describe quarks and their interactions, but solving its equations is challenging due to numerous variables. To tackle this, physicists employ lattice QCD, a technique originally developed at Brookhaven Lab.
In lattice QCD, quarks are placed on a discretized 4D spacetime lattice—a 3D grid considering quark arrangement over time (the fourth dimension). Supercomputers then calculate all possible interactions among the quarks, considering various variables.
A new formalism for modeling photon-proton interactions enabled researchers to leverage lattice QCD and achieve higher-resolution imaging about 10 times faster than before. This breakthrough allows scientists to capture separate images of up and down quarks and calculate their individual Generalized Parton Distributions (GPDs). The method provides valuable insights into the inner workings of protons and the distribution of quark characteristics within them.
Results and implications
In addition to mapping the energy-momentum distributions of up and down quarks within protons, the research team also explored their charge distributions. They went further to investigate the momentum and charge distributions of quarks within polarized protons, where the proton spins align in a specific direction. Understanding how the internal building blocks contribute to the proton's spin is crucial, as proton spin plays a significant role in magnetic resonance imaging (MRI) used in medical diagnostics.
The team found that the momentum distribution of down quarks within polarized protons is notably asymmetric and distorted compared to up quarks. This asymmetry provides insights into the angular momentum of quarks within the proton and reveals that the different contributions of up and down quarks to the proton's spin arise from their distinct spatial distributions.
Their calculations led them to the conclusion that up and down quarks alone cannot account for more than 70% of the proton's total spin, indicating that gluons must significantly contribute to it as well. Understanding how the proton's spin is distributed among its constituent quarks and gluons is vital for comprehending the forces at work within the atomic nucleus.
Experimental results from Brookhaven Lab's Relativistic Heavy Ion Collider (RHIC) support the idea of a significant gluon contribution to the proton's spin. The future Electron-Ion Collider (EIC) will delve deeper into this central question.
The theoretical predictions derived from this research will be crucial for comparison with experimental data, helping scientists interpret the results. Combining theory and experimentation will provide a comprehensive understanding of the proton's inner structure and contribute to our knowledge of fundamental forces in nature.
Source: Brookhaven National Laboratory