Probing the Dependence of Partonic Energy Loss on the Initial Energy Density of the Quark Gluon Plasma

TL;DR

This work investigates how partonic energy loss in the quark-gluon plasma depends on the initial energy density created in heavy-ion collisions. By introducing a spectrum-shift proxy, $Δp_{ m T}$, they quantify average energy loss from high-$p_{ m T}$ hadron spectra and relate it to Bjorken-like initial energy density, $\varepsilon_{\mathrm{Bj}}$, computed via Glauber-based transverse areas and mid-rapidity multiplicities. The study identifies two robust area classes, $A_W$ and $A_\cup$, that yield a strong, linear $Δp_{ m T}$–$\varepsilon_{\mathrm{Bj}}$ correlation across RHIC and LHC energies, while an outlier $A_\cap$ is disfavored. Extending the framework, high-$p_T$ elliptic flow, $v_2$, is modeled from geometric path-lengths and $Δp_{\rm T}$, showing reasonable agreement at high $p_T$ but indicating additional physics at lower $p_T$; overall, the results suggest initial energy density as the dominant driver of average partonic energy loss in the explored regimes.

Abstract

Considerable evidence now exists for partonic energy loss due to interaction with the hot, dense medium created in ultra-relativistic heavy-ion collisions. A primary signal of this energy loss is the suppression of high transverse momentum $p_{\mathrm{T}}$ hadron yields in A-A collisions relative to appropriately scaled $pp$ collisions at the same energy. Measuring the collision energy dependence of this energy loss is vital to understanding the medium, but it is difficult to disentangle the medium-driven energy loss from the natural kinematic variance of the steeply-falling $p_{\mathrm{T}}$ spectra across different $\sqrt{s_{\mathrm{NN}}}$. To decouple these effects, we utilize a phenomenologically motivated spectrum shift model to estimate the average transverse momentum loss $Δp_{\mathrm{T}}$ imparted on high $p_{\mathrm{T}}$ partons in A-A collisions, a proxy for the medium induced energy loss. We observe a striking correlation between $Δp_{\mathrm{T}}$ and Glauber-derived estimates of initial state energy density $\varepsilon_{\mathrm{Bj}}$, consistent across two orders of magnitude in collision energy for a variety of nuclear species. To access the path-length dependence of energy loss, we couple our model to geometric event shape estimates extracted from Glauber calculations to produce predictions for high-$p_{\mathrm{T}}$ hadron elliptic flow $v_2$ that agree reasonably with data.

Figures (12)

• Figure 1: (a.) Computed transverse areas as a function of the event centrality for Pb– Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV. Ratios of certain methods against (b.) $A_\cup$ and (c.) $A_W$. The blue and orange markers denote the class of methods that scale like $A_\cup$ and $A_W$ respectively. The EBE exclusive calculations are shown as the black cross markers. See text for details.
• Figure 2: Cartoon illustrating the procedure used to determine $\Delta p_{\rm T}$.
• Figure 3: Cartoon illustrating the steps of the $v_2$ estimation process.
• Figure 4: Energy density using $A_\cup$ for a variety of collision species and beam energies, as a function of $\langle N_{\text{part}} \rangle$ (upper) and centrality (lower).
• Figure 5: Energy density using $A_W$ for a variety of collision species and beam energies, as a function of $\langle N_{\text{part}} \rangle$ (upper) and centrality (lower).