Phenomenological constraints on QCD transport with quantified theory uncertainties

TL;DR

The paper addresses the challenge of extracting QCD transport coefficients from heavy-ion data when theoretical model uncertainties are non-negligible. It introduces a Bayesian calibration framework for a multistage heavy-ion model (JETSCAPE) that includes Grad and CE particlization and a Gaussian-process model discrepancy $\delta_{MD}(x)$ to quantify theory uncertainty. When theory uncertainties are accounted for, Grad and CE posteriors converge, yielding robust, uncertainty-aware constraints on $(\eta/s)(T)$ and $(\zeta/s)(T)$ over $T \sim 150$–$350$ MeV, with a notable enhancement of $\left(\zeta/s\right)(T)$ around $T \approx 180$–$220$ MeV and a particlization temperature $T_{sw} \approx 144$ MeV. The inferred discrepancy map highlights observables and centralities where the model underperforms, guiding future improvements, and the approach provides a broadly applicable framework for uncertainty-aware Bayesian model–data comparisons in complex multistage simulations.

Abstract

We present data-driven, state-of-the-art constraints on the temperature-dependent specific shear and bulk viscosities of the quark-gluon plasma from Pb-Pb collisions at $\sqrt{s_{\mathrm{NN}}}=2.76\,\mathrm{TeV}$. We perform global Bayesian calibration using the JETSCAPE multistage framework with two particlization ansätze, Grad 14-moment and first-order Chapman-Enskog, and quantify theoretical uncertainties via a centrality-dependent model discrepancy term. When theoretical uncertainties are neglected, the specific bulk viscosity and some model parameters inferred using the two ansätze exhibit clear tension. Once theoretical uncertainties are quantified, the Grad and Chapman-Enskog posteriors for all model parameters become almost statistically indistinguishable and yield reliable, uncertainty-aware constraints. Furthermore, the learned discrepancy identifies where each model falls short for specific observables and centrality classes, providing insight into model limitations.

Figures (7)

• Figure 1: Parameter inference without accounting for model discrepancy (w/o MD). Top row: Posteriors for the specific bulk and shear viscosities, with central $90\%$ and $60\%$ credible interval (CI) bands. The shaded gray regions denote the $90\%$ prior intervals. Bottom rows: Solid and dashed curves show the posterior distributions for the remaining model parameters. Colored shaded regions show the central $60\%$ CI, and shaded gray regions indicate the uniform prior range. In each subplot, a dotted vertical line marks the posterior median, and the printed value reports $\text{median} \pm 60\%\, \mathrm{CI}$.
• Figure 2: Parameter inference accounting for model discrepancy (w/ MD). The plot layouts and legends are identical to those in Fig. \ref{['fig:param_woMD']}.
• Figure 3: Model predictions, obtained using the parameter posteriors shown in Figs. \ref{['fig:param_woMD']} and \ref{['fig:param_wMD']}, are compared with ALICE data (black). Panels below each observable show the normalized discrepancies $(y_{\rm exp}-\eta_{\rm mod})/|\langle y_{\rm exp}\rangle|$ from the w/ MD predictions.
• Figure 4: Observable predictions of $\eta_{\rm mod}+\delta_{\rm MD}$ obtained using the full parameter posteriors shown in Figs. \ref{['fig:param_woMD']} and \ref{['fig:param_wMD']} together with the inferred hyperparameters of $\delta_{\rm MD}$ (not shown), compared with ALICE data. Panels below each observable show the normalized error $(y_{\rm exp}-\eta_{\rm mod}-\delta_{\rm MD})/|\langle y_{\rm exp}\rangle|$, with the horizontal line at $0$ indicating exact agreement with the mean experimental value.
• Figure 5: Parameter posteriors from calibration to ALICE measurements using only $dN_{\text{ch}}/d\eta$, $dE_T/d\eta$, and $v_n\{2\}$ ($n=2,3,4$), without accounting for model discrepancy (w/o MD). The plot layout and legend are identical to those in Fig. \ref{['fig:param_woMD']}. Good agreement between Grad and CE is observed for the specific viscosities and model parameters. However, the posteriors for $\zeta/s$, $d^3_{\min}$, $\alpha$, and (for Grad) $T_{\rm sw}$ shift significantly when all measurements are included in the inference (see Fig. \ref{['fig:param_woMD']}), indicating a lack of robustness of the parameter estimates. For $\zeta/s$, posterior at low temperatures in Fig. \ref{['fig:param_woMD']} shifts well outside the posterior band seen here.