Longitudinal Dynamics of Large and Small Systems from a 3D Bayesian Calibration of RHIC Top-energy Collision Data

TL;DR

This work develops and applies a comprehensive (3+1)D Bayesian calibration of high-energy nuclear collisions at RHIC, combining a 3D Glauber initial state, 3+1D viscous hydrodynamics, and a hadronic afterburner to analyze a wide set of rapidity-dependent observables from Au–Au and d–Au (with extensions to p–Au and ^3He–Au). By building Gaussian process emulators of a 20-parameter model and performing MCMC Bayesian inference on rapidity- and p_T-differential data, the study constrains both the longitudinal energy deposition profile and the temperature-dependent transport coefficients η/s(T) and ζ/s(T). The results reveal that including forward/backward rapidity data tightens constraints and shifts inferred viscosities, while exposing tensions among certain observables (notably STAR v_2(η) and Au–Au v_2(p_T)) and some inter-system differences between Au–Au and d–Au calibrations. The calibrated model then makes predictions for small-system observables and for p–Au and ^3He–Au, highlighting a consistent longitudinal structure of collectivity and offering a robust baseline for future 3D heavy-ion studies and jet–medium investigations.

Abstract

A comprehensive Bayesian analysis of the 3D dynamics of high-energy nuclear collisions is presented. We perform a systematic model-to-data comparison using simulations of large and small collision systems, and a broad range of measurements from the PHENIX, STAR, PHOBOS, and BRAHMS collaborations spanning nearly two decades of RHIC operations. In particular, we perform fully 3D multi-stage simulations including rapidity-dependent energy deposition with global energy conservation using the 3D Glauber model, along with relativistic viscous hydrodynamics with MUSIC. We calibrate the model on rapidity- and $p_T$-differential observables and analyze the respective constraints on initial state and transport properties they provide. We emphasize the additional constraints provided by rapidity-dependent measurements, the differences in large and small system calibrations, and the tension exhibited by particular observables. We use our calibrated model to make predictions of observables in p-Au and $^3$He-Au collisions. Furthermore, we facilitate direct comparison of experimental measurements by highlighting the dependence of flow measurements on the rapidity of the regions of interest and reference, as well as the importance of the centrality selection. In particular, we examine the apparent differences between the STAR and PHENIX $v_2$ and $v_3$ measurements in small systems.

Figures (36)

• Figure 1: Viscosity parametrization as a function of temperature for the specific shear viscosity given by Eq. \ref{['eq:etaparam']} (top) and specific bulk viscosity given by Eq. \ref{['eq:zetaparam']} (bottom).
• Figure 2: The observable prior for the data included in the calibration as well as some not included. The solid markers are the experimental data, while the bands show a 90% interval of the prior calculated using the full model at the design points. Each plot is labeled with the number of data bins corresponding to each observable in a given plot.
• Figure 3: Comparison of experimental and emulation uncertainties for all observables in the calibration. Each point represents one observable bin, with coordinates given by the scaled experimental variance (horizontal axis) and scaled emulation variance (vertical axis). The variances (diagonal elements of the covariance matrices) are scaled by the product of the mean experimental measurement $y_{exp}$ and the mean emulator prediction $y_{emu}$. The emulation uncertainties combine interpolation and statistical uncertainties, evaluated at the maximum a posteriori (MAP) parameter point. Points near the diagonal indicate balanced contributions from experimental and emulation uncertainties, while points above the diagonal are dominated by a combination of interpolation and statistical uncertainty from the emulator. The three observables shown in Figs. \ref{['covariance_ratio']} and \ref{['covariance_emu']} are indicated in color and labeled.
• Figure 4: The observable posterior for the data included in the calibration, plotted in green, as well as predictions for some not included, plotted in olive. The solid markers are the experimental data, while the bands show a 90% interval of the posterior calculated using the emulator. Each plot is labeled with the number of data bins corresponding to each observable in a given plot.
• Figure 5: The posterior for the specific shear (top) and bulk (bottom) viscosity as a function of temperature for the default calibration (in green) and the calibration using only the mid-rapidity data (in orange).