How to test path-length dependence in energy-loss mechanisms: Analysis leading to a new observable

When traversing the QCD medium, high-$p_{\perp }$ partons lose energy, which is typically measured by suppression, and predicted by various energy-loss models. A crucial test of different energy-loss mechanisms is their functional dependence on the length of traversed medium (i.e., path-length dependence). The upcoming experimental measurements will, for the first time, generate data that may allow to clearly assess this dependence, in particular, by comparing results from Pb $+$ Pb collisions with future measurements in smaller systems. However, to perform such a test, it is crucial to choose an optimal observable. To address this, we here use both analytical and numerical analyses to propose a novel—simple, yet accurate and robust—observable for assessing the path-length dependence of the energy loss. Our numerical results show that, by using this observable, different (underlying) energy-loss mechanisms may be directly differentiated from the experimental data, which is, in turn, crucial for understanding the properties of the created QCD medium.

Figure 1

Ratio of $R_{\mathrm{XeXe}}$ and $R_{\mathrm{PbPb}}$ is shown as a function of $p_{\perp }$ for charged hadrons, $D$ and $B$ mesons (full, dashed, and dot-dashed curves, respectively). Centrality regions are denoted in the upper right corners of each panel.

Figure 2

Predictions for $R_L^{\mathrm{XePb}}$ as a function of $p_{\perp }$ are shown for charged hadrons (full curves), $D$ mesons (dashed curves), and $B$ mesons (dot-dashed curves). Upper (lower) dashed gray lines correspond to the case in which energy-loss path-length dependence is linear (quadratic). Centrality regions are denoted in the upper right corners of each panel.

Figure 3

Predictions for $R_L^{AB}$ as a function of $p_{\perp }$ are shown for charged hadrons where the darker sets of curves are obtained by using full dynamical energy loss, whereas upper and lower lighter sets or curves, respectively, correspond to the cases where only collisional or only radiative energy loss is considered. The first to fourth panels correspond to $R_L^{\mathrm{XePb}},R_L^{\mathrm{KrPb}},R_L^{\mathrm{ArPb}}$, and $R_L^{\mathrm{OPb}}$, respectively. In each panel, three centrality regions 30–40%, 40–50%, and 50–60% are marked by blue, orange, and green, respectively.