Parton and nuclear dynamics at large $x$: the CJ26 global QCD analysis

To understand the matter that makes up our world, physicists often look at the proton, the tiny, positively charged particle found in the center of every atom. For decades, scientists have treated the proton as a simple bag containing three fundamental particles called quarks, held together by a force field. When researchers smash electrons into protons at high speeds, they can map out how these quarks are distributed inside. This map is known as a parton distribution function. It tells us not just how many quarks are there, but how much momentum each one carries. In the high-energy collisions that happen in massive machines around the world, these maps are usually very clear. The rules of physics that govern these interactions are well understood, and the data fits neatly into a standard picture.

However, the picture becomes blurry when scientists look at the quarks that carry a very large share of the proton's momentum. In this extreme region, the simple rules start to break down. The data comes from lower-energy experiments where the effects of the proton's own mass and the complex interactions between its internal parts become significant. Furthermore, to see the difference between the two main types of quarks inside the proton, scientists must also study the deuteron, a heavier nucleus made of one proton and one neutron bound together. This introduces a new layer of complexity: the neutron is not just a free particle, but a bound one, and its behavior is altered by its partner. Untangling the true nature of the quarks from the effects of this binding and the lower energy of the experiment has been a persistent challenge.

A new analysis called CJ26, led by researchers at Jefferson Lab and other institutions, has taken a major step forward in solving this puzzle. The team performed a massive global fit, a statistical method that combines thousands of measurements from different experiments to find the most likely description of the proton's interior. For the first time, this analysis included the complete set of data from the 6 GeV electron beam at Jefferson Lab, along with the very first published results from the upgraded 12 GeV beam. By bringing in this wealth of new information, the researchers were able to separate the genuine structure of the quarks from the distortions caused by the lower energy of the experiment and the binding of the neutron.

The core of the problem lies in distinguishing between two different types of effects that appear in the data. One effect is the fundamental structure of the quarks themselves, which follows the standard laws of physics. The other is a collection of "power corrections," which are small deviations that become noticeable when the energy is not high enough to ignore the mass of the particles or the complexity of their interactions. In the past, scientists often had to throw away the lower-energy data to avoid these messy corrections, but that meant losing valuable information about the high-momentum quarks. The CJ26 team chose a different path. Instead of discarding the data, they built a model that accounts for these corrections directly within the analysis. They treated the corrections as a flexible, fitted component, allowing the data itself to determine how large these effects are, rather than guessing beforehand.

A critical part of this work involved the deuteron. Because the neutron is hard to isolate, scientists use the deuteron as a proxy, but the neutron inside it is slightly different from a free neutron. It is "off-shell," meaning its internal energy is shifted by the binding force. The researchers had to model this shift carefully, as it can look very similar to the power corrections mentioned earlier. If they assumed the wrong shape for this shift, it would distort the picture of the quarks. The new analysis used the wide range of energies provided by the 6 GeV and 12 GeV data to tell these two effects apart. The 6 GeV data, with its dense collection of points, helped pin down the size of the power corrections, while the 12 GeV data extended the reach to higher energies, providing the leverage needed to separate those corrections from the off-shell effects.

The results of this effort are a more precise and stable map of the proton's interior. The analysis confirmed that the ratio of down quarks to up quarks, a key quantity that had been difficult to pin down at high momentum, is more stable than previously thought. The uncertainty in this ratio has been reduced significantly, particularly in the region where the quarks carry between 20 and 60 percent of the proton's momentum. Perhaps more importantly, the team found that their results for the fundamental quark structure remain consistent even when they changed how they modeled the complex corrections. This stability suggests that the extraction of the quark distribution is robust and not an artifact of a specific mathematical choice.

The researchers also addressed a long-standing question about whether the differences seen in the data between protons and neutrons could be a sign of a deeper violation of symmetry in the laws of physics. The analysis showed that these differences are not evidence of a new fundamental force or a breakdown of symmetry. Instead, they are simply the result of the different ways the power corrections and off-shell effects manifest for the two types of particles. The model successfully absorbed these differences without needing to invent new physics, clarifying that the observed variations are a consequence of the environment in which the particles are found, not a change in the particles themselves.

The study also highlighted the importance of how experimental errors are handled. In many previous analyses, systematic errors—those that affect many data points in the same way—were treated as if they were independent random fluctuations. The CJ26 team found that this approach distorted the results. By correctly accounting for the correlations between these errors, they were able to produce a more accurate picture. This attention to detail ensured that the final map of the proton was not skewed by the way the data was processed.

Looking ahead, the authors note that while the current analysis has significantly reduced the uncertainties, the job is not entirely finished. The separation between the fundamental quark structure and the complex corrections is now much cleaner, but future data from even higher-energy experiments will be needed to make the distinction absolute. The team points to upcoming measurements from the Electron-Ion Collider and new tagged-neutron experiments as the next steps that will further refine our understanding. For now, the CJ26 analysis stands as a comprehensive and careful re-examination of the proton, proving that by embracing the complexity of the data rather than avoiding it, scientists can reveal a clearer view of the building blocks of matter.