Parton distribution functions and strong coupling constant: MSHT

Inside every atom, protons and neutrons are not solid, indivisible spheres but rather bustling cities of smaller particles called quarks and gluons. These constituents are constantly zipping around, colliding, and transforming, held together by the strong nuclear force. To understand how the universe works at its most fundamental level, from the birth of stars to the collisions in massive particle accelerators, physicists need a precise map of how these particles are distributed inside a proton. This map is known as the parton distribution function. Without it, scientists cannot accurately predict what happens when protons smash into each other at near-light speeds, making it impossible to test the laws of physics or search for new particles. The challenge lies in the fact that these internal arrangements are not fixed; they change depending on how hard you probe them, and the forces involved are so complex that they cannot be calculated from first principles alone. Instead, researchers must build these maps by combining the best available theories with a vast amount of experimental data collected over decades.

A team of researchers known as the MSHT group has recently updated this essential map with their MSHT20 set, refining the picture of the proton's interior with unprecedented detail. Their work represents the latest step in a long lineage of studies that began in the 1990s, evolving alongside improvements in both theoretical physics and the quality of data from particle colliders. The team analyzed a massive collection of experimental results, including data from the Large Hadron Collider, the Tevatron, and the HERA electron-proton collider. By feeding this data into sophisticated computer models that simulate the behavior of quarks and gluons, they adjusted their mathematical descriptions until the predictions matched the observed reality as closely as possible. The result is a new set of parameters that describes the probability of finding a specific type of quark or a gluon carrying a certain amount of momentum within the proton.

One of the most significant findings in this update concerns the strange quark, a heavier and less common cousin of the up and down quarks that make up most of the proton's mass. Previous maps suggested a certain amount of these strange particles, but the new analysis, incorporating high-precision data from the Large Hadron Collider, indicates that there are more strange quarks inside the proton than previously thought, particularly at lower momentum levels. This adjustment helps resolve a long-standing tension between different types of experimental data, bringing the theoretical predictions for the production of W and Z bosons into better agreement with what detectors actually see. The team also refined the description of the gluon, the particle responsible for holding the quarks together. While the central value of the gluon distribution remained stable, the uncertainty around it was reduced, giving scientists a clearer view of how this force carrier behaves at different energy scales.

The researchers did not stop at simply updating the numbers; they also tested the robustness of their methods to ensure the map was not just a lucky guess. They performed what are known as closure tests, a rigorous procedure where they generated fake data based on a known theoretical model and then tried to reconstruct that model using their fitting techniques. They found that their mathematical framework was flexible enough to perfectly recover the input model, proving that their method is not the bottleneck limiting the precision of the map. However, when they applied their method to real experimental data, they found that the uncertainties in the final map were larger than the raw statistical errors of the data would suggest. This led them to investigate the nature of experimental errors themselves, concluding that the way scientists currently handle systematic uncertainties—errors caused by the measurement tools rather than random chance—might be too optimistic. They suggest that a more realistic treatment of these errors, acknowledging that we do not know the exact size of every uncertainty, is necessary to produce truly reliable maps.

Beyond the structure of the proton, the study also tackled the value of the strong coupling constant, a fundamental number that dictates the strength of the force holding the proton together. By treating this constant as a variable rather than a fixed input, the team was able to determine its most likely value directly from the data. They found that the best fit at the highest level of theoretical precision points to a value of 0.1174, with a small margin of error. This result is consistent with the global average accepted by the physics community, but the path to this number revealed interesting disagreements between different types of experiments. For instance, data from older fixed-target experiments tended to prefer a slightly weaker force, while data from the Large Hadron Collider often favored a stronger one. These tensions highlight that while the overall picture is consistent, there are still subtle details in how different experiments see the proton that need to be reconciled.

The MSHT20 update also ventured into the realm of higher-order corrections, pushing the theoretical calculations to a level of precision that includes effects previously considered too small to matter. This allowed them to produce an approximate version of the map at a next-to-next-to-next-to-leading order, a technical term for a level of calculation that is incredibly close to the theoretical limit of what can be computed. They found that including these higher-order effects changed the predicted behavior of the gluon distribution, particularly at very low momentum fractions, and improved the stability of the predictions. Furthermore, they incorporated the effects of electromagnetism, treating the proton as if it also contains a photon, a particle of light. This addition, while small, is crucial for the most precise calculations of future experiments, ensuring that the map remains accurate as the field moves toward even higher energies.

Ultimately, this work serves as a critical foundation for the future of particle physics. The maps produced by the MSHT group are not just static pictures; they are dynamic tools that evolve as new data arrives. The team has made their results publicly available, allowing other scientists to use these updated distributions to interpret their own experiments. By refining our understanding of the proton's internal landscape and the strength of the forces within it, this research ensures that when the next generation of particle colliders comes online, physicists will have the most accurate guide possible to navigate the subatomic world. The journey to understand the proton is far from over, but with each iteration of these maps, the blurry edges of the quantum world become a little sharper, bringing us closer to a complete understanding of the building blocks of our universe.