A simple model to investigate jet quenching and correlated errors for centrality-dependent nuclear-modification factors in relativistic heavy-ion collisions

We apply Bayesian techniques to compare a simple, empirical model for jet-quenching in heavy-ion collisions to centrality-dependent jet-$R_{AA}$ measured by ATLAS for Pb+Pb collisions at $\sqrt{s_{NN}}=5.02$~TeV. We find that the $R_{AA}$ values for central collisions are adequately described with a model for the mean $p_T$-dependent jet energy-loss using only 2-parameters. This model is extended by incorporating 2D initial geometry information from TRENTO and compared to centrality-dependent $R_{AA}$ values. We find that the results are sensitive to value of the jet-quenching formation time, ${\tau }_f$, and that the optimal value of ${\tau }_f$ varies with the assumed path-length dependence of the energy-loss. We construct a covariance error matrix for the data from the $p_T$ dependent contributions to the ATLAS systematic errors and perform Bayesian calibrations for several different assumptions for the systematic error correlations. We show that most-probable functions and ${\chi }^2$ values are sensitive to assumptions made when fitting to correlated errors.