Phenomenological constraints on QCD transport with quantified theory uncertainties

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.

💡 Research Summary

This paper presents a state‑of‑the‑art Bayesian analysis of the temperature‑dependent specific shear (η/s) and bulk (ζ/s) viscosities of the quark‑gluon plasma (QGP) created in Pb–Pb collisions at √sNN = 2.76 TeV. The authors employ the JETSCAPE multistage framework, which consists of TRENTo initial conditions, a free‑streaming pre‑equilibrium stage, MUSIC viscous hydrodynamics, a particlization step, and SMASH hadronic transport. Two distinct particlization ansätze are considered: the Grad 14‑moment approximation and the first‑order Chapman‑Enskog (CE) correction. A comprehensive data set of 110 ALICE observables (charged particle multiplicities, transverse energy, identified hadron yields, mean pT, flow coefficients v2, v3, v4, and mean‑pT fluctuations) spanning centralities 0–70 % is used.

A key innovation is the explicit inclusion of model‑theory uncertainty, termed “model discrepancy,” which is introduced at the observable level as an additive term δMD(x). This term is modeled as a Gaussian Process (GP) with a non‑stationary kernel whose variance is allowed to increase with centrality, reflecting the physical expectation that the multistage model becomes less reliable in peripheral collisions. The kernel parameters (baseline variance s, overall scale ċ, centrality‑growth exponent r, and correlation length ℓ) are inferred jointly with the 17 physical model parameters, resulting in a total of 65 unknowns for the discrepancy‑aware analyses.

To make the Bayesian inference tractable, the authors train fast surrogate models using an Automatic Kernel Selection Gaussian Process (AKSGP) emulator, which dramatically reduces the computational cost compared with direct event‑by‑event simulations. Four inference scenarios are performed: Grad without discrepancy (Grad w/o MD), CE without discrepancy (CE w/o MD), Grad with discrepancy (Grad w/MD), and CE with discrepancy (CE w/MD). The “without discrepancy” cases reveal substantial tension: the bulk‑viscosity posterior differs markedly between Grad and CE, and several other parameters (e.g., nucleon width w, free‑streaming time τR, shear‑relaxation factor bπ, and particlization temperature Tsw) shift in opposite directions depending on the particlization choice. This indicates that model imperfections are being absorbed into the physical parameters, compromising their interpretability.

When the GP‑modeled discrepancy is included, the tensions disappear. The posteriors for η/s(T) and ζ/s(T) become statistically indistinguishable between the two particlization schemes, and the remaining 15 model parameters converge to nearly identical distributions. The inferred bulk‑viscosity exhibits a pronounced peak around T ≈ 180–220 MeV with a maximum ζ/s ≈ 0.12–0.15, while lower temperatures are disfavored. The shear‑viscosity posterior favors values in the range η/s ≈ 0.10–0.20, with a modest temperature dependence that shows a slight dip near T ≈ 220 MeV and gradual rise toward both lower and higher temperatures. The particlization temperature is constrained to Tsw ≈ 139 MeV (Grad) and 145 MeV (CE) in the no‑discrepancy analyses, but these values overlap within uncertainties once the discrepancy is accounted for. Other parameters such as the nucleon width, free‑streaming scale, and shear‑relaxation factor also become consistent across the two schemes.

The learned GP discrepancy functions provide diagnostic insight: they are small in the most central bins, confirming that the model is reliable there, but they grow toward peripheral bins, pinpointing where the combination of initial‑state modeling, pre‑equilibrium dynamics, or viscous corrections may be insufficient. This information can guide future improvements of each stage of the simulation chain.

In summary, the paper demonstrates that quantifying theory uncertainties via a centrality‑dependent GP discrepancy is essential for robust extraction of QGP transport coefficients. By doing so, it eliminates model‑dependent biases, yields tighter and more reliable constraints on η/s(T) and ζ/s(T), and offers a systematic way to assess and improve the underlying heavy‑ion collision models. The methodology sets a new standard for Bayesian inference in the field and can be readily extended to other collision systems, energies, and additional observables.