Path-length dependence of parton and jet energy loss from universal scaling laws

TL;DR

This paper demonstrates that the suppression of high-momentum particles in heavy ion collisions follows a universal scaling law, revealing a linear path-length dependence of parton and jet energy loss consistent with pQCD predictions.

Contribution

It establishes a universal scaling law linking parton energy loss to medium path-length and shows that both hadron and jet energy losses follow the same parametric dependence.

Findings

Energy loss scales approximately linearly with path-length (L^1.02).

Azimuthal anisotropy follows the same scaling as suppression.

Hadron and jet energy losses share the same path-length dependence.

Abstract

The universal dependence of hadron suppression, $R_{\rm{AA}}(p_\perp)$, observed at large-$p_\perp$ in heavy ion collisions at RHIC and LHC allows for a systematic determination of the average parton energy loss $\langle \epsilon \rangle$ in quark-gluon plasma (QGP). A simple relation between $\langle \epsilon \rangle$ and the soft particle multiplicity allows for probing the dependence of parton energy loss on the medium path-length. We find that all the available measurements are consistent with $\langle \epsilon \rangle \propto L^\beta$ with $\beta=1.02\pm^{0.09}_{0.06}$, consistent with the pQCD expectation of parton energy loss in a longitudinally expanding QGP. We then show, based on the model predictions, that the data on the azimuthal anisotropy coefficient divided by the collision eccentricity, $v_2/\rm{e}$, follows the same scaling property as $R_{\rm{AA}}$. Finally, a linear relationship between $v_2/\rm{e}$ and the logarithmic derivative of $R_{\rm{AA}}$ at large $p_\perp$ offers a purely data-driven access to the $L$ dependence of parton energy loss. Quite remarkably, both hadron and jet measurements obey this latter relationship, moreover with consistent values of $\beta$. This points to the same parametric path-length dependence of parton and jet energy loss in QGP.