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Bayesian Model Selection and Uncertainty Propagation for Beam Energy Scan Heavy-Ion Collisions

Syed Afrid Jahan, Hendrik Roch, Chun Shen

Abstract

We apply the Bayesian model selection method (based on the Bayes factor) to optimize $\sqrt{s_\mathrm{NN}}$-dependence in the phenomenological parameters of the (3+1)-dimensional hybrid framework for describing relativistic heavy-ion collisions within the Beam Energy Scan program at the Relativistic Heavy-Ion Collider. The effects of various experimental measurements on the posterior distribution are investigated. We also make model predictions for longitudinal flow decorrelation, rapidity-dependent anisotropic flow and identified particle $v_0(p_\mathrm{T})$ in Au+Au collisions, as well as anisotropic flow coefficients in small systems. Systematic uncertainties in the model predictions are estimated using the variance of the simulation results with a few parameter sets sampled from the posterior distributions.

Bayesian Model Selection and Uncertainty Propagation for Beam Energy Scan Heavy-Ion Collisions

Abstract

We apply the Bayesian model selection method (based on the Bayes factor) to optimize -dependence in the phenomenological parameters of the (3+1)-dimensional hybrid framework for describing relativistic heavy-ion collisions within the Beam Energy Scan program at the Relativistic Heavy-Ion Collider. The effects of various experimental measurements on the posterior distribution are investigated. We also make model predictions for longitudinal flow decorrelation, rapidity-dependent anisotropic flow and identified particle in Au+Au collisions, as well as anisotropic flow coefficients in small systems. Systematic uncertainties in the model predictions are estimated using the variance of the simulation results with a few parameter sets sampled from the posterior distributions.

Paper Structure

This paper contains 16 sections, 22 equations, 22 figures, 8 tables.

Table of Contents

  1. Introduction
  2. The Theoretical Framework
  3. Bayesian Model Selection
  4. Identify $\sqrt{s_{\rm NN}}$-dependent parameters
  5. Bayesian model selection
  6. $\mu_B$ dependence of shear and bulk viscosities
  7. Progressive constraints from different experimental data sets
  8. Model predictions with uncertainty propagation
  9. Longitudinal flow decorrelation
  10. Collision energy dependence of $v_2(\eta)$
  11. Anisotropic flow in small systems
  12. Identified particle $v_0(p_T)$ at RHIC BES
  13. Conclusion
  14. Cluster Sampling of Posterior Distributions
  15. Comparisons of different $\delta f$ corrections at particlization
  16. ...and 1 more sections

Figures (22)

  • Figure 1: Marginal posterior distributions of the 20 model parameters obtained from separate Bayesian analyses at $\sqrt{s_\mathrm{NN}}=200$, 19.6, and 7.7 GeV. The values above each panel indicate the median and $90\%$ credible intervals of the corresponding posterior distributions. The horizontal axes reflect the ranges of the uniform prior distributions used in the analyses.
  • Figure 2: Marginal posterior distributions of the 24 model parameters obtained from separate Bayesian analyses with three different experimental datasets. The values above each panel indicate the median and $90\%$ credible intervals of the corresponding posterior distributions. The horizontal axes reflect the ranges of the uniform prior distributions used in the analyses.
  • Figure 3: Centrality dependence of identified particle yields from simulations with Posterior distributions 1 and 2 compared with the STAR measurements for Au+Au collisions at 200 (panel (a)), 19.6 (panel (b)), and 7.7 (panel (c)) GeV. The shaded bands represent systematic uncertainty in the theoretical results.
  • Figure 4: Charged hadron $v_2(p_\mathrm{T})$ from simulations with three Posterior distributions compared with the STAR measurements for 20-30% Au+Au collisions at 200 (panel (a)), 19.6 (panel (b)), and 7.7 (panel (c)) GeV. The shaded bands represent systematic uncertainty in the theoretical results.
  • Figure 5: The longitudinal decorrelation for elliptic flow $r_2(\eta)$ in 10-40% Au+Au collisions at RHIC BES program scaled by the corresponding beam rapidity. The preliminary STAR measurements are compared with model results from Posterior 1 (Panel (a)) and Posterior 2 (Panel (b)). The shaded bands represent systematic uncertainty in the theoretical results. The STAR preliminary data are extracted from the STAR talks STAR_rn_QMtalks.
  • ...and 17 more figures