Topology studies of hydrodynamics using two-particle correlation analysis.

Prior research has shown that relativistic heavy ion collisions create systems with complex dynamics. Established knowledge includes the formation of hot and dense matter during these collisions. However, the role of fluctuating initial conditions in shaping final particle distributions remains unclear. No prior work had resolved how nonsmooth initial states evolve under hydrodynamic conditions. This gap motivated the current investigation into how initial fluctuations impact observable correlations. Existing studies focus on smooth initial conditions, leaving open questions about irregular geometries. The survival of nonsmooth features through hydrodynamic evolution is a novel area of inquiry. This paper contributes by linking topological features in particle correlations to initial state structures.

The aim of this study is to investigate how fluctuating initial conditions affect particle correlations in relativistic heavy ion collisions. Specifically, the problem addressed is understanding how nonsmooth initial states evolve under hydrodynamic conditions. The motivation stems from the need to connect initial geometry to observable signatures in particle distributions. Prior work has not clarified the persistence of nonsmooth features during system evolution. This paper seeks to determine whether such features survive and manifest in final state correlations. The approach involves simulating collisions with fluctuating initial conditions and analyzing the results. The study focuses on angular correlation functions as indicators of topological effects. The goal is to identify signatures of tubular structures in the initial state through collective dynamics.

The study uses the NEXSPHERIO hydrodynamic code to simulate relativistic heavy ion collisions. Initial conditions are generated with fluctuating nonsmooth geometries to model real-world variability. Two-particle correlation analysis is applied to the simulated particle distributions. The analysis focuses on angular correlation functions to detect topological features. Longitudinal and azimuthal correlations are specifically examined for distinct patterns. The code tracks the evolution of the system from initial to final states. The method compares correlation structures before and after hydrodynamic evolution. The results are analyzed to determine if nonsmooth features persist and influence final state correlations.

The results show that nonsmooth initial conditions survive hydrodynamic evolution and appear in final state correlations. A long-range correlation is observed in the longitudinal direction of particle motion. In the azimuthal direction, a double peak structure appears opposite to the trigger particle. These features indicate the presence of tubular structures in the initial state. The correlation patterns are consistent across multiple simulated events. The analysis confirms that the observed features are not artifacts of the simulation setup. The findings suggest a direct link between initial state geometry and final particle distributions. The study provides evidence that topological signatures persist through collective dynamics.

The authors conclude that nonsmooth initial conditions leave detectable topological signatures in particle correlations. These signatures include long-range longitudinal and azimuthal double peak structures. The observed features are attributed to tubular structures in the initial state. The study confirms that such structures survive hydrodynamic evolution. The findings suggest that initial state geometry influences final state correlations. The results support the idea that collective dynamics preserve initial topological features. The authors propose that these signatures can be used to infer initial state configurations. The study provides a framework for connecting initial geometry to observable particle distributions.