Charmonium production in p+A collisions at SPS and FAIR energies

Deep within the heart of matter, protons and neutrons are not solid, indivisible spheres but rather bustling cities of even smaller particles called quarks and gluons. Under normal conditions, these particles are bound tightly together, never seen alone. However, when scientists smash heavy atomic nuclei together at incredible speeds, they create a fleeting, super-hot soup where these particles roam freely. This state of matter is known as the quark-gluon plasma, a condition that existed just moments after the Big Bang. To understand how this plasma behaves and how it transitions back into ordinary matter, physicists look for specific "messengers" that can survive the journey through this extreme environment. One of the most important messengers is a particle called charmonium, which is a tiny, tightly bound pair of a charm quark and its antimatter partner. Because charmonium is so heavy and compact, it acts like a sensitive probe; if it disappears or changes as it moves through the hot soup, it tells scientists exactly what the soup is made of and how dense it is.

The challenge lies in separating the effects of this hot soup from the effects of the cold, dense nuclear matter that exists even before the collision happens. To do this, researchers first need a clear baseline: they must understand how charmonium behaves when it passes through ordinary atomic nuclei without the added heat of a plasma. This is the specific question addressed in a new study by a team of physicists working with data from European accelerator facilities. The researchers used a sophisticated computer simulation called the Parton–Hadron–String Dynamics approach to model how these heavy particles form and move. They focused on collisions between protons and various atomic nuclei, ranging from light beryllium to heavy lead and gold, at energies similar to those found at the Super Proton Synchrotron and the upcoming FAIR facility in Germany.

The team's work began by testing their simulation against real-world data from proton collisions with light nuclei. They found that their model could accurately reproduce the number of charmonium particles produced when the collision energy was set to 400 GeV. This success gave them confidence to use the same model to investigate what happens when the proton hits a much heavier nucleus, like lead. In these heavier collisions, the charmonium particle has to travel through a much thicker layer of nuclear matter. The researchers discovered that to match the experimental data, the charmonium must be getting "absorbed" or broken apart by the surrounding protons and neutrons with a specific likelihood. They calculated that for a standard charmonium particle, this absorption probability corresponds to a cross-section of 7 millibarns at the higher energy of 400 GeV. Interestingly, when they lowered the energy to 158 GeV, the model required a larger absorption value of 10 millibarns to match the observations. This suggests that at lower collision speeds, the nuclear matter is more effective at breaking up these heavy particles.

Having established this baseline for ordinary nuclear matter, the team then looked ahead to the future of heavy-ion physics. They extended their simulations to the lower energies expected at the FAIR facility, specifically looking at collisions between protons and gold nuclei at 29 GeV. In this environment, which is rich in baryons (protons and neutrons), the researchers predicted the production rates and survival chances of charmonium. They found that while the particles are still produced, their survival depends heavily on their size and how they interact with the surrounding medium. The study also considered the influence of other particles created during the collision, known as comovers, but determined that in these specific proton-nucleus collisions, their effect is minor compared to the direct absorption by the nucleus.

The ultimate goal of this work is to provide a reliable reference point for future experiments that will smash heavy nuclei together to create the quark-gluon plasma. By precisely knowing how much charmonium is lost just by passing through cold nuclear matter, scientists can better identify how much is lost due to the extreme heat of the plasma itself. The researchers demonstrated that their method, which dynamically models the formation of these particles from their constituent quarks, provides a consistent and quantitative description of the data. This framework is now ready to be applied to the more complex collisions of heavy nuclei, helping to map out the phase structure of the strong force and revealing how the universe transitioned from a hot, free-flowing soup into the structured matter we see today.