The scaling property of large-$p_{\perp }$ hadron suppression, $R_{\mathrm{AA}}(p_{\perp })$, measured in heavy ion collisions at the relativistic heavy ion collider and at the large hadron collider (LHC) leads to the determination of the average parton energy loss $⟨\epsilon ⟩$ in quark-gluon plasma produced in a variety of collision systems and centrality classes. Relating $⟨\epsilon ⟩$ to the particle multiplicity and collision geometry allows for probing the dependence of parton energy loss on the path length $L$. We find that $⟨\epsilon ⟩\propto L^{\beta }$ with $\beta ={1.02}_{-0.06}^{+0.09}$, which is consistent with the perturbative quantum chromodynamics 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, $v_2/\mathrm{e}$, 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 $v_2/\mathrm{e}$ 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.

• Received 6 December 2022
• Revised 27 June 2023
• Accepted 20 February 2024

DOI:https://doi.org/10.1103/PhysRevD.109.L051503

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society