Universal scaling dependence of QCD energy loss from data-driven studies

In this paper we study the energy loss of jets in the Quark Gluon Plasma via the nuclear modification factor $R_{AA}$ for unidentified particles at high $p_{\mathrm{T}}$ ($\gtrsim$$10\mathrm{GeV}/\mathrm{c}$) in and out of the reaction plane of the collision. We argue that at such a high $p_{\mathrm{T}}$ there are no genuine flow effects and, assuming that the energy loss is only sensitive to initial characteristics such as the density and geometry, find that $R_{AA}$ depends linearly on the (rms) length extracted from Glauber simulations. Furthermore, we observe that for different centrality classes the density dependence of the energy loss enters as the square root of the charged-particle multiplicity normalized to the initial overlap area. The energy loss extracted for BNL Relativistic Heavy Ion Collider and CERN Large Hadron Collider data from the $R_{AA}$ is found to exhibit a universal behavior.

Figure 1

The extracted participant distribution for two Glauber samples at $\sqrt{s_{NN}}=2.76\mathrm{TeV}$ [10%–20% centrality (a) and 30%–40% centrality (b)] rotated so that the reaction plane coincides with the $x$ axis. The in-plane rms of the former equals approximately the out of plane of the latter. Comparison of the participant distributions and the $R_{AA}$ for the two cases are shown in (c) and (d), respectively.

Figure 2

Example of scaling relations for LHC data in arbitrary units. $R_{AA}$ vs $L$ (a), ${\rho }^{1/2}L$ (c), ${\rho }^{3/4}{L}^2$ (e) and extracted energy loss $\Delta p_{\mathrm{T}}/p_{\mathrm{T}}$ vs the same scaling variables (b),(d),(f) are shown for $p_{\mathrm{T}}\approx 13\mathrm{GeV}/\mathrm{c}$. We have included the uncertainty arising from the unknown functional form of $\Delta p_{\mathrm{T}}$ as shaded boxes on the points in the right column (see Appendix pp1 for details).

Figure 3

The comparison between $R_{AA}$ in and out of plane for situations where the scaling variable ${\rho }^{1/2}L$ is approximately the same. As can be seen, the good agreement observed in Fig. 2 is reproduced at higher $p_{\mathrm{T}}$.

Figure 4

$R_{AA}$ in and out of plane for $p_{\mathrm{T}}\sim 10–13\mathrm{GeV}/\mathrm{c}$ at $\sqrt{s_{NN}}=2.76\mathrm{TeV}$ (red points) and for $p_{\mathrm{T}}>10\mathrm{GeV}/\mathrm{c}$ at $\sqrt{s_{NN}}=200\mathrm{GeV}$ (blue points) as a function of ${\rho }^{1/2}L$ (a). The corresponding $p_{\mathrm{T}}$ shifts as a function of the same scaling variable are shown in (b). Owing to the different shape of the $p$-$p$ spectrum the energy loss is the same in our model even if the $R_{AA}$ is different.

Figure 5

The $\langle \widehat{q}\rangle$ as a function of centrality for LHC data extracted using Eq. (3).