On $Ω_{3c}NN$ and $Ω_{3c} Ω_{3c} N$ systems with HAL QCD potentials

Deep within the heart of matter, protons and neutrons are not the smallest building blocks; they are themselves made of even tinier particles called quarks. Usually, these quarks stick together in groups of three to form the familiar particles that make up our world. However, physicists have long wondered what happens when we swap the usual ingredients for heavier, stranger ones, such as the "charm" quark. By mixing these heavy quarks with ordinary ones, scientists can create exotic versions of atomic nuclei that have never been seen in nature. The question driving this research is whether these heavy, strange combinations can hold together tightly enough to form stable new forms of matter, or if they simply fly apart. This inquiry touches on the fundamental forces that bind the universe together, testing our understanding of how particles interact when pushed to the very limits of their mass and complexity.

A team of researchers set out to explore this question by simulating a specific, highly unusual type of atomic cluster. They focused on systems containing a rare particle known as the triply charmed Omega baryon, which is made of three heavy charm quarks, paired with ordinary protons and neutrons. Using powerful computer simulations based on the laws of quantum mechanics, they modeled how these particles would behave when brought close together. The team employed a sophisticated mathematical framework to calculate the forces between the particles, relying on recent data from lattice quantum chromodynamics—a method that treats space and time as a grid to solve complex particle interactions. Their goal was to determine if the attraction between these heavy and light particles was strong enough to create a bound state, a stable cluster where the particles remain stuck together, or if they would only form fleeting, unstable arrangements.

The results of their investigation revealed that nature is not quite ready to form these heavy clusters into stable objects. When the researchers modeled a system containing one triply charmed Omega baryon, one proton, and one neutron, they found that the particles did not stick together to form a permanent bond. The attractive forces between them were simply not strong enough to overcome the tendency of the particles to drift apart. However, the story did not end with a simple "no." While no stable particle was found, the simulations suggested that these systems might briefly hover on the edge of existence. The researchers identified what are known as near-threshold resonances, which are like fleeting echoes of a bound state. In one specific arrangement where the spins of the particles were aligned in a particular way, the system appeared to exist just 1.1 million electron volts below the point where it would break apart. In another arrangement with the lowest possible spin, the system sat exactly at the breaking point, suggesting it might form a very short-lived resonance that barely clings to existence before dissolving.

The team also examined an even more exotic scenario involving two triply charmed Omega baryons and one nucleon. In this case, the heavy particles were even more reluctant to form a stable group. The simulations showed no evidence of a bound state here either. Instead, the data pointed toward a resonance that would exist at a much higher energy level, roughly 9.5 million electron volts above the point where the system would break apart. This suggests that if such a cluster were to form, it would be highly unstable and short-lived, existing far from the conditions where stable matter usually resides. The researchers noted that these findings depend on the specific details of the interaction models used, and the exact energy values could shift slightly depending on how the calculations were refined, but the overall picture of instability remained consistent.

A crucial part of this study involved looking closely at what happens when these heavy particles get extremely close to one another. The simulations indicated that at very short distances, the interaction between the triply charmed Omega baryon and a nucleon becomes strongly repulsive. This repulsion acts as a barrier, preventing the heavy particle from sinking inside the nucleon. While one might imagine a heavy particle nesting inside a lighter one, the laws of physics governing the strong force make this impossible. The quarks inside each particle are confined in a way that creates a hard core of repulsion when the particles try to overlap significantly. This ensures that the heavy baryon remains a distinct entity interacting with the nucleon from the outside, rather than merging into a single, confused mass of six quarks.

Ultimately, this work provides a clear, albeit sobering, map of the landscape for these heavy nuclear systems. It confirms that while the forces between these exotic particles are attractive, they are not strong enough to create stable, permanent clusters of this specific type. The existence of these systems is limited to the realm of fleeting, near-threshold resonances rather than the formation of new, stable forms of matter. By ruling out the possibility of stable bound states for these specific combinations, the study helps physicists narrow down where to look for new forms of matter and deepens our understanding of the delicate balance of forces that govern the subatomic world. The findings serve as a rigorous test of our current theories, showing that even with the heavy pull of charm quarks, the universe maintains a strict limit on how tightly these exotic ingredients can be packed together.