Using Cosmic Droplets to Unlock the Secrets of Nuclear Matter

The Hidden Glue of Matter

Picture a universe where atoms never remained stable––where protons, left to their own devices, would blast apart the atomic nucleus in mutual repulsion. Puzzled by this scenario, physicists in the 1970s realized there must be something far stronger at work deep inside the nucleus. Enter Quantum Chromodynamics (QCD)&emdash;the “colorful” theory of quarks and gluons, the building blocks of protons and neutrons, that give us the recipe to keep matter stable.

Without this strong force, the electric charges of protons would tear each atomic nucleus to bits. At the scale of a nucleus––just a trillionth of a centimeter across––those repulsive forces are immense. Yet quarks and gluons remain bound. These particles possess a type of charge known as color, which must always combine into a neutral (colorless) state. Try to pluck a lone quark out of a proton and the strong force will snap it back, or a new quark will combine with yours to form a lighter particle. In short, the existence of isolated quarks is impossible under normal circumstances. Understanding how isolated quarks nevertheless existed in the early universe has been a key goal of nuclear physics. In recent work, a collaboration involving the Noronha-Hoestler group has taken an important step towards understanding this mystery.

A Flash of Primordial Fire

The conditions in the early Universe, of course, were anything but normal: temperatures hotter than the core of any star and unfathomable densities. Just microseconds after the Big Bang, protons and neutrons melted into a fluid made of quarks and gluons––the quark-gluon plasma (QGP). Understanding the properties of this plasma is key to understanding the cosmic emergence of the elements in the periodic table and thus our own origin. Fortunately, these extreme situations can be replicated in the laboratory. This is done at facilities like the Large Hadron Collider (LHC) in Europe, in the aftermath of reactions known as relativistic heavy-ion collisions, where nuclei are smashed into each other at speeds close to the speed of light.

Scientists leverage sophisticated computational techniques based on relativistic viscous fluid dynamics to replicate these droplets of primordial matter. However, these models often gloss over the details regarding the local behavior of baryon number (B), strangeness (S), and electric charge (Q). The rules of quantum mechanics allow pairs of quarks and antiquarks to be created within this fluid, giving rise to spatial distributions of charge or charge fluctuations. Those fluctuations can leave fingerprints in the particles that emerge when the plasma cools––a clue to the Universe’s earliest moments.

SPH Meets Nuclear Physics

A new collaboration involving Jaki Noronha-Hoestler's group introduces a fluid dynamical approach with a twist: Smoothed Particle Hydrodynamics (SPH), a computational method commonly used in astrophysics, now applied to the study of the QGP. Instead of having a rigid grid, the SPH approach treats the fluid as a swarm of particles––perfect for tracking local charge fluctuations and enforcing exact conservation laws.

“Imagine a cup of water made up of tens of thousands of smaller water droplets”, explains Dr. Travis Dore, one of the paper’s authors and an alumnus of Jaki Noronha-Hoestler's group. “SPH takes advantage of this by simply calculating the position and velocity of each droplet and then averaging over groups of them to calculate thermodynamic properties. When doing computer simulations, this means that the fluid is no longer a prisoner to its container and expands freely.”

By integrating a multi-dimensional lattice-based equation of state (EoS) into the framework––Conserved ChArges hydrodynamiK Evolution (CCAKE)––the authors were the first to probe the QGP in realistic simulations with all (B,S, and Q) conserved charges tracked over time at the LHC. The simulations carried out in the study reveal a more nuanced depiction of the QGP than ever before. Results show that the initial local charge fluctuations do not wash away and remain finite throughout the entire evolution of the plasma, up to the point when the fluid has expanded and its composition has become fixed.

The remnants of the fluid produced in heavy-ion collisions are the particles whose tracks can be measured by experiments. Close comparisons of particle yields and momenta between simulations and experimental observations can then lead to a better understanding of nuclear properties such as deformation, size, and distribution inside the nucleus. One of the study's key findings is how these fluctuations impact the azimuthal anisotropy—or "flow"—of identified particles in Pb+Pb collisions at the LHC.

Behind the Scenes: Computational Feats and Future Perspectives

Writing CCAKE was no easy feat. The SPH approach required the authors to address numerous computational hurdles. An example is the implementation of a multi-dimensional root-finder to flip between temperature and charge chemical potentials and energy and charge densities. Another crucial advancement was the design of fallback equations of state, ready to be used in case another EoS failed to secure a successful evolution, which was necessary since the main, state-of-the-art lattice-based EoS has its own range of validity.

“The equation of state of nuclear matter is one of the holy grails of nuclear physics”, says Dr. Christopher Plumberg, the leading author of the study. “Modeling relativistic nuclear collisions hydrodynamically gives us one of the best available tools for learning about the nuclear EoS, and this new code allows us to do that robustly. By designing the code to handle a wide variety of EoS in a systematic and stable fashion, we maximize the amount we can learn from the physical EoS that we find in nature.”

The researchers are optimistic about the potential applications of CCAKE. Future work could incorporate dissipation effects, study relativistic causality, and be generalized to a 3+1-dimensional framework, providing deeper insights into the transport properties of QGP. Moreover, the open-source release of CCAKE promises to catalyze further innovation in the field.

The study marks a significant leap forward in the quest to understand the QGP. By combining proven computational techniques and applying them to suitable systems, the Noronha-Hoestler group and collaborators have crafted a powerful new tool. As experimental facilities push the boundaries of colliding beam energies, simulations like CCAKE will guide us to refine our understanding of the QGP, ultimately transforming how we comprehend the fundamental fabric of the cosmos.