QCD Phase Transition May Explain Light Nucleus Yield Ratios

Researchers have proposed a theoretical explanation for unusual patterns observed in the production of light nuclei during high-energy heavy-ion collisions. A new study published in the European Physical Journal C suggests that a first-order phase transition in Quantum Chromodynamics (QCD) matter could be responsible for significant enhancements in the yield ratios of tritons, deuterons, and protons. This finding offers a potential link between the fundamental properties of quark matter and observable signatures in experiments conducted at the Relativistic Heavy-Ion Collider (RHIC).

The work utilizes an extended Polyakov-looped Nambu–Jona-Lasinio (PNJL) model to simulate the behavior of baryon density fluctuations as the system evolves through different stages of the collision. The core of the investigation focuses on the yield ratio $N_t \times N_p/N_d^2$, which compares the number of tritons ($N_t$) and protons ($N_p$) to the square of the number of deuterons ($N_d$). Previous measurements by the STAR experiment at RHIC revealed nonmonotonic energy dependencies in this ratio, specifically showing significant enhancements at center-of-mass energies of 19.6 GeV and 27 GeV.

The new study posits that these enhancements are driven by large density fluctuations that occur when the quark-gluon plasma transitions into hadronic matter via a first-order phase transition rather than a smooth crossover. To model this phenomenon, the authors employed an extended PNJL model that incorporates three eight-quark interactions. This theoretical framework allows for the description of the QCD phase diagram, including the region of two-phase coexistence where the first-order transition occurs.

The model includes a Polyakov loop effective potential that accounts for the confinement-deconfinement transition, with parameters tuned to match lattice QCD results at vanishing baryon chemical potential. By adjusting the coupling constants of the eight-quark interactions, the researchers were able to position the critical end point (CEP) and the coexistence region in a way that is accessible to current heavy-ion collision experiments. The study tracks the evolution of the system along isentropic trajectories, which represent paths of constant entropy per baryon ($s/\rho_B$) in the temperature-baryon density plane.

These trajectories correspond to different collision energies ranging from 7.7 to 200 GeV. The key observable used to quantify density fluctuations is the second-order scaled density moment, denoted as $y_2$. In the absence of density fluctuations, $y_2$ equals 1.

However, when the system enters the coexistence region, $y_2$ rapidly increases to form a peak, reflecting the significant inhomogeneities in baryon density caused by the phase separation process. The results indicate that for collision energies below approximately 39 GeV, the isentropic trajectories pass through the coexistence region of the phase diagram. As the system traverses this region, spinodal instability amplifies initial inhomogeneities, leading to clustering of baryons.

This clustering enhances the probability of forming composite light nuclei such as deuterons and tritons. The study finds that the peak value of $y_2$ increases as the entropy per baryon decreases, which corresponds to lower collision energies. This trend aligns with experimental observations that the ratios of deuterons to protons and tritons to protons increase monotonically as the collision energy decreases.

When the researchers calculated the yield ratio $N_t \times N_p/N_d^2$ at chemical freeze-out, they found significant enhancements at 19.6 GeV and 27 GeV. These specific energies match the locations of the anomalies observed in the STAR experiment data. The enhancement occurs because the chemical freeze-out points for these collision energies lie within or near the coexistence region, where density fluctuations are maximal.

In contrast, at kinetic freeze-out, which occurs at later stages of the collision, the system has already exited the coexistence region, and the yield ratios do not show significant enhancements. This distinction highlights the importance of the timing of freeze-out in capturing the signatures of the phase transition. The study acknowledges that the calculated yield ratios are generally lower than the experimental values and the coalescence baseline.

This discrepancy is attributed to the neglect of the density-density correlation length in the simplified thermodynamic calculation. Near the critical end point, the correlation length diverges, which can further enhance the yield ratios. The authors note that recent preliminary data from the STAR Collaboration shows a dip structure in net-proton fluctuations around 19.6 GeV, which is sensitive to the correlation length.

This suggests that the critical region may also contribute to the observed enhancements, and future work will need to integrate the effects of the correlation length into the model. The implications of this study extend beyond the specific yield ratio anomaly. It provides a potential mechanism for identifying the nature of the QCD phase transition in the region probed by the Beam Energy Scan program.

The study suggests that the observed enhancements in light nucleus yields could be explained by the density fluctuations generated in the first-order phase transition region. The study also highlights the role of spinodal instability in amplifying density fluctuations, a process that is crucial for understanding the dynamics of rapidly expanding systems in heavy-ion collisions. Future research will focus on incorporating the extended PNJL model into transport models to simulate the full evolution of heavy-ion collisions.

This will allow for a more detailed investigation of the effects of the critical region and the correlation length on light nucleus production. The combination of theoretical modeling and experimental data will be key to unraveling the complex dynamics of the QCD phase transition and its impact on the production of light nuclei in relativistic heavy-ion collisions.

Subject of Research: Effects of a first-order QCD phase transition on light nuclei production

Article Title: Effects of a first-order QCD phase transition on light nuclei production

Article References: Liu, H., Sun, K.-J., & Chu, P.-C. (2026). Effects of a first-order QCD phase transition on light nuclei production. The European Physical Journal C, 86(10), Article 1228. https://doi.org/10.1140/epjc/s10052-026-16500-7

Image Credits: AI Generated

DOI: 10.1140/epjc/s10052-026-16500-7

Keywords: QCD, phase transition, heavy-ion collisions, light nuclei, baryon density, critical end point, RHIC, STAR experiment, PNJL model, spinodal instability, Effects, first-order