Unlocking the Secrets of Charm: Exotic Hadrons in Heavy Ion Collisions

Author: Denis Avetisyan

New predictions detail how upcoming experiments at FAIR and the LHC can shed light on the production of rare charmed hadrons and nuclei, offering a window into the strong force.

The study demonstrates a correlation between beam energy and the predicted multiplicities of exotic charmed hadrons in heavy-ion collisions (Au+Au), with differing centrality selections revealing nuanced production rates across a spectrum of energies.

This review presents theoretical predictions for the formation rates of exotic charmed mesons and nuclei in heavy-ion collisions at the CBM experiment at FAIR and the ALICE experiment at the LHC, exploring the potential for observing these states and testing models of hadronization.

Despite established theoretical frameworks, the production and detection of exotic charmed hadrons and nuclei remain a significant challenge in the study of the strong interaction. This work, ‘Charmed nuclei and exotic charmed meson production at CBM@FAIR and ALICE@LHC’, presents predictions for the multiplicities of these states in heavy-ion collisions at the CBM experiment (FAIR) and the ALICE experiment (LHC), leveraging the UrQMD transport model and the Thermal-FIST approach. Calculations suggest both facilities possess comparable potential for observing these rare states, with CBM offering unique sensitivity to charmed nuclei despite lower overall charm production. Will these forthcoming experiments ultimately reveal the existence and properties of these elusive particles, furthering our understanding of quantum chromodynamics in extreme conditions?

Probing the Strong Interaction with Exotic Charmed Hadrons

The strong interaction, fundamental to the stability of atomic nuclei, presents a persistent challenge to physicists due to the complexity arising from the force’s self-interaction. To truly understand its behavior, investigations must extend beyond the familiar realm of ordinary matter and delve into exotic states where the fundamental constituents – quarks and gluons – are no longer confined. These states, like the quark-gluon plasma created in heavy-ion collisions, or the unusual combinations found within exotic hadrons, offer a unique window into the strong force’s dynamics. By meticulously studying these fleeting, high-energy environments, researchers aim to map the intricate phases of quantum chromodynamics, the theory governing the strong interaction, and ultimately, refine models predicting the behavior of matter under extreme conditions. Such explorations are critical not only for advancing fundamental knowledge but also for contextualizing phenomena observed in astrophysical settings, such as neutron stars and the early universe.

Charmed hadrons, composite particles containing the charm quark, offer a particularly insightful window into the extreme conditions of the quark-gluon plasma (QGP), a state of matter thought to have existed shortly after the Big Bang. Unlike lighter hadrons, the presence of the heavy charm quark minimizes the effects of ‘flow’ – the collective motion of particles in the QGP – allowing scientists to more accurately reconstruct the initial conditions and evolution of this primordial soup. Because charmed hadrons decay relatively slowly, they retain information about the plasma’s properties over a larger distance, functioning as sensitive probes of the QGP’s temperature, density, and transport coefficients. Studying their production and characteristics, therefore, provides crucial data for refining theoretical models and deepening the understanding of strong interaction physics at the most fundamental level.

Predicting the creation rate of charmed hadrons in high-energy collisions has long presented a significant hurdle for physicists, as conventional theoretical approaches often fall short due to the intricate dynamics governing these short-lived particles. Existing models frequently struggle to account for the complex interplay of quarks and gluons within the quark-gluon plasma, leading to substantial discrepancies between predictions and experimental observations. However, a novel framework has emerged that demonstrably improves upon these limitations, offering calculations with unprecedented precision. This advancement stems from a refined treatment of fragmentation functions and a more accurate incorporation of heavy-quark mass effects, resulting in production rate predictions that align closely with data from the Large Hadron Collider and other facilities. Consequently, this improved predictive power provides valuable insights into the fundamental properties of the strong interaction and the behavior of matter under extreme conditions.

Charm hadron multiplicities in Au+Au collisions vary predictably with beam energy and centrality, demonstrating a correlation between input symbols and predicted outcomes.

Thermal Equilibrium and Statistical Hadronization

Statistical hadronization models posit that, following a heavy-ion collision, a state is reached – termed ‘chemical freeze-out’ – where inelastic interactions cease and the produced hadrons are in thermal equilibrium. This implies that the hadron species and their relative abundances are determined by maximizing the phase space volume subject to constraints of conserved charges, such as baryon number, strangeness, and electric charge. Essentially, the model treats the hadronization process as a statistical distribution, where the probability of producing a particular hadron is proportional to its multiplicity and determined by the temperature and chemical potential of the system at this freeze-out stage. The observed hadron yields can therefore be used to extract information about the conditions prevailing at chemical freeze-out, providing insights into the strongly coupled matter created in these collisions.

The Thermal-FIST (Thermal-inspired Finite-Source Transport) model predicts hadron yields in high-energy heavy-ion collisions by parameterizing the thermal freeze-out condition with temperature ( $T$ ) and baryochemical potential ( $\mu_B$ ). Unlike strictly thermodynamic calculations, Thermal-FIST incorporates a finite-source size, represented by a space-time volume factor, to account for the limited size and lifetime of the emitting source. The model then calculates hadron densities using the grand canonical ensemble, with the yields determined by phase space integrals and Boltzmann statistics. The accuracy of the predictions relies on precisely determining the values of $T$ and $\mu_B$ , typically fitted to experimental data, but the model’s robustness stems from its ability to simultaneously describe a wide range of hadron species with only these two parameters and the source size.

The maximization of phase space volume is a central tenet of statistical hadronization models, directly impacting predicted hadron multiplicities. Phase space volume, proportional to $\in t d^3p d^3x$ , represents the available states for particles given their momenta and positions. The system, at chemical freeze-out, evolves towards a configuration that maximizes this volume subject to constraints like baryon number, strangeness, and energy conservation. Consequently, hadrons with a larger number of available states – determined by their mass, spin, and degeneracy – are statistically favored, leading to a higher relative abundance in the final state. This principle explains the observed yields of various hadrons, with lighter and more degenerate species generally being more copiously produced.

Multiplicities of charmed nuclei exhibit a baryon number dependence in heavy-ion collisions (Au+Au at 4.0-5.0 GeV and Pb+Pb at 5.02 TeV), which is well-described by exponential fits to Thermal-FIST predictions and indicates a penalty factor influenced by the inclusion of deuteron contributions.

Rigorous Charm Conservation within the Canonical Statistical Hadronization Approach

The canonical statistical hadronization approach (CSHA) rigorously enforces the conservation of charm quantum number during the modeling of hadron production. This is achieved by treating charmed hadron production as a canonical ensemble, where the total number of charm quarks is fixed, and all allowed combinations of charmed hadrons are statistically weighted according to their phase space volume and the charm quark fugacity. The fugacity parameter, determined by overall charm conservation, ensures that the sum of all produced charmed hadrons precisely accounts for the total available charm, preventing violations of this fundamental quantum number. Consequently, CSHA accurately predicts the relative abundances of various charmed hadrons, as it intrinsically satisfies the constraints imposed by charm conservation laws.

Model validation was performed using data obtained from the Large Hadron Collider (LHC). This process assessed the model’s capacity to accurately predict the production rates of a range of charmed hadrons. Specifically, the model successfully predicted the production of the X(3872) meson, the Ds+ meson, the ηc(1S) meson, the χc0(1P) meson, the χc1(1P) meson, the Σc+ baryon, and the Σc++ baryon. Agreement between model predictions and LHC data confirms the model’s reliability in simulating charmed hadron production processes.

Model predictions indicate a production rate of approximately 1 per second for both the $\chi_{c0}(1P)$ and $\chi_{c1}(1P)$ particles at the CBM experiment, based on anticipated collision parameters. Furthermore, the model forecasts a production rate of approximately 1 per minute for the X(3872) particle under the same conditions. These predicted rates allow for validation through comparison with expected event yields, demonstrating the model’s capacity to estimate the abundance of specific charmed hadron states in a high-energy environment.

Predictions indicate that the multiplicity of charmed nuclei in Au+Au collisions varies with beam energy and is sensitive to collision centrality.

Expanding the Horizon: Predicting Exotic Charmed Nuclei

Recent theoretical work demonstrates the successful prediction of several exotic charmed nuclei, extending the known landscape of hadronic matter. The model accurately forecasts the production rates of unusual combinations like the nΛc nucleus, alongside more complex systems including pnnΛc, pnΛc, and αD- nuclei. This capability arises from a sophisticated framework that incorporates both strong and electromagnetic interactions within nuclear collisions, allowing for a detailed accounting of particle production and decay pathways. The ability to reliably predict the formation of these charmed nuclei is a significant step forward, providing crucial benchmarks for experimental investigations into the properties of charmed matter and the strong force in extreme conditions.

Calculations indicate that collisions of gold nuclei – specifically, central Au+Au collisions at an energy of 5 GeV – are predicted to yield approximately $10^{-9}$ pnnΛc nuclei per event. While individually rare, the high event rate anticipated at the CBM (Compressed Baryonic Matter) experiment suggests a potential observational yield of roughly 1000 pnnΛc nuclei per day. This substantial predicted production rate offers a promising avenue for detailed investigation into the properties and interactions of this exotic charmed nuclear system, providing valuable data for understanding the strong force in extreme conditions and validating theoretical models of nuclear structure.

The accurate prediction of charmed nuclear production rates, such as those calculated for nuclei containing charm, is poised to significantly influence the design and execution of experiments at next-generation facilities like the SIS100 accelerator. These projections aren’t merely theoretical exercises; they directly inform crucial parameters including detector acceptance, triggering strategies, and data acquisition timelines. By anticipating the expected yield of rare charmed nuclear species, researchers can optimize experimental setups to maximize the probability of detection and ensure efficient data collection. This proactive approach is essential for unlocking the potential of charmed nuclear systems, enabling detailed investigations into the strong interaction in extreme conditions and furthering understanding of the quark-gluon plasma.

UrQMD simulations of Au+Au collisions, fitted to light hadron multiplicities excluding light nuclei, accurately reproduce the observed input distributions across various centrality selections.

Towards a Complete Picture: Synergistic Modeling and Future Directions

A robust simulation of heavy-ion collisions requires capturing both the initial, dynamic processes and the subsequent evolution towards thermal equilibrium. Researchers are increasingly employing a combined approach, integrating the UrQMD model – which excels at simulating the early, non-equilibrium stages – with a statistical hadronization framework. This framework then accurately predicts the abundance of various particles produced when the system reaches a state resembling a thermalized “hadron gas”. By synergistically linking these two powerful tools, scientists achieve a more complete picture of hadron production, moving beyond the limitations of either model alone. This integrated strategy allows for detailed investigations into how initial collision characteristics influence the final observed particle spectra, ultimately refining understanding of the strong force governing matter at extreme temperatures and densities.

The combined statistical hadronization and UrQMD approach offers a unique window into the evolution of heavy-ion collisions by simultaneously addressing the earliest, dynamic stages and the later, thermalized phases. UrQMD meticulously simulates the initial violent impact of nuclei, charting the rapid production of particles and the complex interplay of colliding nucleons; this detailed dynamic picture then serves as the foundation for the statistical hadronization model. The latter effectively describes the system’s evolution towards chemical equilibrium, predicting the abundance of various hadrons formed in the aftermath. By linking these two processes, researchers can investigate how the initial collision geometry and energy density influence the subsequent thermalization and, ultimately, the observed particle spectra – a crucial step towards fully characterizing the quark-gluon plasma and the strong force at extreme temperatures and densities.

Continued development of theoretical frameworks, such as statistical hadronization and UrQMD, promises a more nuanced comprehension of the strong nuclear force and the exotic states of matter created in high-energy collisions. These advancements are inextricably linked to forthcoming experimental investigations; data from future runs will serve as crucial benchmarks for model validation and refinement, allowing researchers to constrain parameters and test predictions with increasing precision. This iterative process – theory informing experiment, and experiment guiding theory – is expected to reveal subtle features of the quark-gluon plasma and the complex interplay of particles during these extreme events, ultimately pushing the boundaries of knowledge regarding fundamental interactions and the universe’s earliest moments.

UrQMD simulations of Au+Au collisions successfully reproduce experimental light hadron multiplicities <span class="katex-eq" data-katex-display="false"> (symbols) </span> through fitting procedures <span class="katex-eq" data-katex-display="false"> (lines) </span>, including those for deuterons, across various centrality selections. — UrQMD simulations of Au+Au collisions successfully reproduce experimental light hadron multiplicities $(symbols)$ through fitting procedures $(lines)$ , including those for deuterons, across various centrality selections.

The pursuit of understanding exotic charmed hadron production, as detailed within this study, echoes a fundamental principle of mathematical consistency. Predictions utilizing models like Thermal-FIST and UrQMD strive for a provable framework, much like an elegant algorithm. As Albert Einstein once stated, “The most incomprehensible thing about the world is that it is comprehensible.” This notion is vividly exemplified by the effort to predict the yields of these fleeting particles in heavy-ion collisions. The models aren’t merely attempting to fit observed data, but to establish a logically sound and predictive basis for understanding the strong interaction-a testament to the beauty found within consistent boundaries.

The Road Ahead

The presented predictions, while mathematically consistent within the framework of established models – UrQMD and Thermal-FIST – illuminate a persistent ambiguity. The projected production rates of exotic charmed hadrons at CBM and ALICE are not merely numerical outputs; they are statements about the fundamental symmetries governing strong interactions. Should these states remain unobserved, or appear with markedly different abundances, the fault will not lie with experimental limitations, but with the underlying theoretical scaffolding. A discrepancy would demand a re-evaluation of the assumptions embedded within statistical hadronization, and a more rigorous constraint on the parameters governing heavy quark fragmentation.

The true test, of course, lies not in the proliferation of predictions, but in their falsifiability. The field would benefit less from increasingly complex simulations and more from dedicated efforts to quantify the systematic uncertainties inherent in both theoretical models and experimental measurements. A singular observation of an exotic charmed nucleus, however fleeting, would serve as a beacon, guiding refinement of the theoretical landscape. Until then, these predictions remain elegant exercises, poised between possibility and mathematical necessity.

Ultimately, the quest for exotic hadrons at these facilities transcends the mere discovery of new particles. It is a pursuit of mathematical harmony – a validation, or refutation, of the principles that dictate the architecture of matter itself. The elegance of a provable solution, after all, far outweighs the convenience of empirical agreement.

Original article: https://arxiv.org/pdf/2602.22676.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/