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 $\mathrm{Pb}+\mathrm{Pb}$ 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 two parameters. This model is extended by incorporating two-dimensional initial geometry information from TRENTo and compared to centrality-dependent ${R}_{AA}$ values. We find that the results are sensitive to the value of the jet-quenching formation time, ${\ensuremath{\tau}}_{f}$, and that the optimal value of ${\ensuremath{\tau}}_{f}$ 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 the most-probable functions and ${\ensuremath{\chi}}_{d}^{2}$ values are sensitive to assumptions made when fitting to correlated errors. This work demonstrates the utility of a simple model that can quickly demonstrate the constraining power of jet-quenching observables with corresponding uncertainties and guide future studies using more sophisticated models.