BeAGLE++: A modern modular framework for eA physics at the EIC

Deep inside the heart of every atom lies a world governed by forces so powerful they bind the smallest building blocks of matter together. This realm is described by a theory called quantum chromodynamics, which explains how particles known as quarks and gluons stick together to form protons and neutrons. While scientists have long understood how these particles behave when floating freely, their behavior when packed tightly inside an atomic nucleus remains one of the great mysteries of modern physics. When a high-speed electron smashes into a heavy nucleus, it does not just bounce off a single particle; it triggers a complex chain reaction that ripples through the entire nuclear structure. Understanding exactly how this energy spreads, how new particles are born, and how the nucleus shatters or reshapes itself is crucial for mapping the fundamental rules of our universe. To study these violent collisions, researchers rely on powerful machines called colliders, but to make sense of the data they collect, they need sophisticated computer programs that can simulate these events with extreme precision.

For years, a computer program known as BeAGLE served as the primary tool for simulating these electron-nucleus collisions. It allowed scientists to predict what would happen when a beam of electrons hit a target made of heavy atoms. However, the original software was built on older technology that made it difficult to update or test new ideas about how particles interact inside the nucleus. To address this, a team of physicists has developed a next-generation successor called BeAGLE++. This new framework is not just a minor update; it is a complete reimagining of how the simulation handles the chaotic aftermath of a collision. The researchers rebuilt the program from the ground up using modern coding standards, allowing them to introduce a more realistic way of tracking how particles move and collide within the dense environment of an atomic nucleus.

The core of this new approach lies in how the program handles the split-second moments after an electron strikes a nucleon inside the nucleus. In the old model, the simulation treated the nucleus as a static snapshot, like a frozen photograph, where particles moved in a rigid, pre-determined order. The new BeAGLE++ treats the nucleus as a living, breathing system. In this updated view, the particles inside the nucleus are constantly moving and interacting in a dynamic environment. When a collision occurs, the program tracks every single interaction in the exact order it happens in time, rather than grouping them by generation. This means that if a particle created in the first split-second of a collision is fast enough to hit another particle before a second collision even finishes forming, the simulation accounts for that. This time-ordered approach, combined with a more detailed list of possible particle interactions, creates a much richer and more accurate picture of the nuclear breakup.

One of the most significant improvements involves how the program handles the formation of new particles. When a collision creates a new particle, it does not instantly become a solid object that can bounce off other things; it takes a tiny amount of time to "form." The new model carefully tracks this formation time, ensuring that particles are only allowed to interact once they have fully materialized. This subtle but critical detail changes the outcome of the simulation, particularly for how energy is deposited inside the nucleus. To verify the model's parameters, the researchers calibrated the formation time using forward neutron multiplicity data from muon-lead (µ–Pb) collisions measured by the Fermilab E665 experiment. They found that their new model predicts a higher number of neutrons being ejected from the nucleus after a collision compared to the old version. This increase is not an error; rather, it suggests that the new model captures more of the energy transfer that happens during the crash, leading to a more excited nucleus that sheds more particles as it cools down.

To verify that their new model was working correctly for other observables, the team compared its predictions against real data from the same E665 experiment, this time using muon-xenon (µXe) collisions. They looked at how many charged particles were produced and how they were distributed in space. The results showed that BeAGLE++ matched the experimental data very well, particularly in the region where the nucleus itself breaks apart. In the old model, the simulation often underestimated the number of particles coming from the shattered nucleus. The new version corrected this, providing a much closer match to reality. However, the researchers also noted that in the region where the original struck particle flies away, the new model still slightly underestimates the number of particles produced. This suggests that while the new framework has solved many problems regarding the nuclear debris, there are still some complex interactions involving the initial collision that need further study.

The team also discovered that the new model handles the creation of light nuclear clusters differently than its predecessor. In the old simulation, protons knocked out of the nucleus usually flew away as individual particles. In the new simulation, some of these protons stick together to form small, stable groups of particles, such as helium or deuterium. This change affects the total count of free protons detected, shifting the distribution of particles in a way that aligns better with what the E665 experiment actually observed. This finding highlights a key strength of the new framework: it can now distinguish between individual particles and small clusters, offering a more nuanced view of how matter reorganizes itself after a high-energy impact.

Looking ahead, the authors emphasize that BeAGLE++ is designed to be a flexible foundation for future discoveries. It is built to be easily updated as new physics theories are developed, making it an essential tool for the upcoming Electron-Ion Collider, a massive new facility currently under construction. This new machine will allow scientists to probe the nucleus with unprecedented clarity, and having a simulation tool that can accurately model the complex dance of particles inside the nucleus is vital for interpreting the data. While the current version focuses on the most common types of collisions, the framework is ready to incorporate more exotic scenarios, such as those involving the saturation of gluons or the effects of nuclear deformation. By providing a modular and transparent way to test different ideas, BeAGLE++ ensures that when the new collider begins its work, scientists will have a reliable map to navigate the strange and powerful world of the atomic nucleus.