Phenomenological Constraints on the Transport Properties of QCD Matter with Data-Driven Model Averaging

Using combined data from the Relativistic Heavy Ion and Large Hadron Colliders, we constrain the shear and bulk viscosities of quark-gluon plasma (QGP) at temperatures of $\sim 150–350\mathrm{MeV}$. We use Bayesian inference to translate experimental and theoretical uncertainties into probabilistic constraints for the viscosities. With Bayesian model averaging we propagate an estimate of the model uncertainty generated by the transition from hydrodynamics to hadron transport in the plasma’s final evolution stage, providing the most reliable phenomenological constraints to date on the QGP viscosities.

Figure 1

The 90% credible intervals for the prior (gray), the posteriors of the Grad (blue), Chapman-Enskog (red), and Pratt-Torrieri-Bernhard (green) models, and their Bayesian model average (orange) for the specific bulk (left) and shear (right) viscosities of QGP.

Figure 2

The 90% credible intervals of the posterior predictive distribution of observables for Pb-Pb collisions at the LHC as functions of centrality, for the Grad (blue), Chapman-Enskog (red), and Pratt-Torrieri-Bernhard (green) particlization models. Plotted is the model discrepancy in units of the experimental standard deviation ${\sigma }_{\exp }$; the vertical axes are labeled with shorthand notation $y\equiv (y_{\text{model}}-y_{\exp })/{\sigma }_{\exp }$, where $y$ stands for the observable whose model discrepancy is shown. The gray bands represent a discrepancy of one ${\sigma }_{\exp }$ above and below zero.

Figure 3

90% credible intervals for the priors (gray) and Bayesian model averaged posteriors for the specific bulk (left) and shear (right) viscosities, along with their corresponding information gain (Kullback-Leibler divergence $D_{\mathrm{KL}}$).