FR06 · Conditional Bayesian inference

QGP Transport Inference

How much does a viscosity estimate depend on the initial state? A viscosity estimate depends on the initial geometry and on correlations that do not come from collective flow. The same saved synthetic events give different conditional posteriors when those assumptions change, so a narrow interval alone cannot establish an unconditional QGP viscosity.

Fit one fixed synthetic event sample under different initial geometries and pair backgrounds. Watch the viscosity posterior move and widen as the assumptions change.

Model assumptions

The fixed benchmark contains 4,500 synthetic events with exact stored flow-vector statistics. A two-parameter response model predicts pair correlations. The likelihood uses their empirical covariance plus an assigned model discrepancy and uniform bounded priors. Results are conditional teaching posteriors, not a measurement of QGP viscosity.

Reading the fixed synthetic event sample.

Model, units and sources

Natural units are used. The Gaussian density has unit mean squared radius per axis before deformation. Its short-axis direction defines the elliptic emission plane. This is an assigned response calculation, with no transverse fluid solver.

v_n=\kappa_0\varepsilon_n e^{-1.8n^2(\eta/s)/(RT)},\qquad n=2,3

The response coefficient and damping scale are illustrative. Higher harmonics and nonlinear mode coupling are omitted.

Gardim et al. (2012) · Bilandzic et al. (2011) · Bernhard et al. (2019)

Start with the essentials

Focus question: How much does a viscosity estimate depend on the initial state?
One-sentence intuition: The same particle correlations can favor different viscosities when the initial geometry or pair background changes.

Core mathematical model

Distinct-particle pair correlation

C_n=\frac{|Q_n|^2-M}{M(M-1)},\qquad Q_n=\sum_{j=1}^{M}e^{in\phi_j}

Subtracting multiplicity removes each particle paired with itself. The saved event flow vectors determine every plotted correlation.

Four-particle cumulant

c_n\{4\}=\langle\langle4\rangle\rangle-2\langle\langle2\rangle\rangle^2

Four distinct particles contribute to each four-particle term. Cumulants suppress many pair backgrounds; finite samples and clusters that themselves flow still matter.

Conditional posterior

p(\eta/s,\kappa_0\mid D,\mathcal M)\propto\exp\!\left[-\tfrac12\Delta^\mathsf T\Sigma^{-1}\Delta\right]p(\eta/s,\kappa_0)

The residual compares the same six observed pair means with the selected model. Marginalizing the response amplitude gives the viscosity interval.

Common difficulties

What the estimate means

Typical misconceptionA narrow posterior fixes the viscosity of real QGP.

Better mental modelThe displayed interval conditions on the chosen response, geometry, priors, and error model. Real extractions also simulate the full collision and compare many observables.

Run the experiment

01
Keep the sample fixed
Start with Planted assumptions, then download the event records.
What to observe: The benchmark holds 4,500 events. Its seed and generation parameters travel with the records.
02
Change the initial geometry
Choose Larger ellipticity and compare the shaded interval.
What to observe: The data points stay put. The model and conditional posterior move.
03
Test the background
Choose Ignore doublets, then Allow model error.
What to observe: A background change shifts the estimate; a larger discrepancy generally broadens the range compatible with the same sample.

QGP Transport Inference

Conditional posterior

One fixed sample, six pair correlations