Probing the path-length dependence of parton energy loss via scaling properties in heavy ion collisions

Abstract

The scaling property of large-$p_{\perp }$ hadron suppression, $R_{\mathrm{AA}}(p_{\perp })$, measured in heavy ion collisions at RHIC and LHC leads to the determination of the average parton energy loss $⟨ϵ⟩$ in quark-gluon plasma produced in a variety of collision systems and centrality classes. Relating $⟨ϵ⟩$ to the particle multiplicity and collision geometry allows for probing the dependence of parton energy loss on the path-length $L$. We find that $⟨ϵ⟩\propto L^{\beta }$ with $\beta =1.02_{-0.06}^{+0.09}$, consistent with the pQCD expectation of parton energy loss in a longitudinally expanding quark-gluon plasma. We then demonstrate that the azimuthal anisotropy coefficient divided by the collision eccentricity, $v_2/\text{e}$, follows the same scaling property as $R_{\mathrm{AA}}$. This scaling is observed in data, which are reproduced by the model at large $p_{\perp }$. Finally, a linear relationship between $v_2/\text{e}$ and the logarithmic derivative of $R_{\mathrm{AA}}$ is found and confirmed in data, offering an additional way to probe the $L$ dependence of parton energy loss using coming measurements from LHC Run 3.

Comments: 6 pages, 4 figures