Towards Precision-Controlled Partonic Structures from First Principles
This dissertation advances the first-principles understanding of hadron structure by presenting state-of-the-art lattice QCD calculations of pion and nucleon partonic observables, including transverse-momentum-dependent distributions and the Collins-Soper kernel, while also exploring machine-learning techniques to accelerate lattice simulations.
Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer
To understand the matter that makes up our visible universe, physicists look past the atoms and nuclei to the protons and neutrons that form them. Inside these particles, a chaotic sea of smaller constituents called quarks and gluons whips around, bound together by the strong force. For decades, scientists have mapped how these particles share momentum when moving in a straight line, creating a one-dimensional picture of the proton's interior. However, this view is incomplete. To truly grasp the structure of matter, researchers need to see how these particles move side-to-side as well, creating a three-dimensional map of the proton's inner life. This is the frontier of modern particle physics, a quest to move from a flat sketch to a full, detailed portrait of the building blocks of reality.
The challenge lies in the fact that the strong force becomes incredibly powerful at the low energies found inside a proton, making standard mathematical tools useless. To bypass this, a researcher led by Jinchen He at the University of Maryland has turned to a different approach: using massive supercomputers to simulate the laws of physics directly. They built a digital version of space and time, a grid where they could watch quarks and gluons interact according to the rules of quantum chromodynamics. By running these simulations, they calculated the probability of finding a quark with a specific speed and direction inside a proton and a pion, a lighter cousin of the proton. This work represents a significant leap forward, moving from theoretical concepts to concrete, first-principles calculations that can be compared directly with experiments at facilities like the upcoming Electron-Ion Collider.
The researcher focused on two main types of particles: the pion, which is made of a quark and an antiquark, and the nucleon, which is the proton or neutron made of three quarks. For the pion, they calculated how the momentum is shared between its two constituents. Their results showed that the distribution is much broader than the simplest theoretical predictions suggested, indicating that the internal dynamics are more complex and energetic than previously thought. For the nucleon, the task was far more difficult due to the presence of three quarks and a dense spectrum of excited states that can muddy the data. By using advanced techniques to isolate the true signal from this noise, the researcher successfully mapped the transverse momentum-dependent distributions. These maps show not just how fast the quarks are moving, but also how their motion is correlated with the spin of the proton, revealing a rich, three-dimensional structure that had never been seen from first principles before.
A critical part of this success was the development of new methods to handle the mathematical difficulties that arise when simulating these particles on a computer grid. The researcher introduced a specific way of fixing the orientation of the fields in their simulation, known as the Coulomb gauge, which simplified the calculations and removed certain types of mathematical errors that had plagued previous attempts. They also rigorously tested whether the choice of how to fix these orientations introduced any hidden biases. Their analysis showed that any such bias was so small it was invisible compared to the statistical noise of the simulation, confirming that their method was robust and reliable. This validation is essential, as it ensures that the detailed maps they produced are genuine reflections of nature rather than artifacts of the computer code.
To push these calculations even further, the researcher also explored the use of artificial intelligence to speed up the simulation process. They trained neural networks to act as a kind of intelligent filter that could rearrange the digital space before the main calculation began. In tests using a simplified two-dimensional version of the theory, this approach significantly reduced the time the computer spent wandering aimlessly between different states, allowing it to explore the most important configurations much faster. While this was a preliminary test, it demonstrated that machine learning could become a powerful tool for making these complex simulations more efficient, potentially allowing for even finer grids and more precise results in the future.
The findings presented in this work provide a new, independent way to understand the internal structure of hadrons, free from the assumptions often required in other methods. The calculated distributions for both the pion and the nucleon agree well with existing experimental data where comparisons are possible, but they also reveal specific details in the middle range of momentum that were previously uncertain. The researcher noted that their results are less reliable at the very edges of the momentum range, where the mathematical approximations used in the method begin to break down, and they identified this as a key area for future improvement. By combining rigorous lattice calculations with modern effective field theory and machine learning, this study has established a clear path toward a precision-controlled understanding of the proton's three-dimensional architecture, bringing us closer to a complete picture of how the visible universe is built from its smallest parts.
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