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

Abstract

The universal dependence of hadron suppression, $R_{\mathrm{AA}}(p_{\perp })$, observed at large-$p_{\perp }$ in heavy ion collisions at RHIC and LHC allows for a systematic determination of the average parton energy loss $⟨ϵ⟩$ in quark-gluon plasma (QGP). A simple relation between $⟨ϵ⟩$ 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 $⟨ϵ⟩\propto L^{\beta }$ with $\beta =1.02{\pm }_{0.06}^{0.09}$, 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, $v_2/\mathrm{e}$, follows the same scaling property as $R_{\mathrm{AA}}$. Finally, a linear relationship between $v_2/\mathrm{e}$ and the logarithmic derivative of $R_{\mathrm{AA}}$ 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.

Comments: 6 pages, 4 figures. Talk given at the 42nd International Conference on High Energy Physics (ICHEP2024)