Statistical analysis of pQCD energy loss across system size, flavor, $\sqrt{s_{NN}}$, and $p_T$

TL;DR

This work develops a comprehensive, perturbative QCD energy-loss framework that includes radiative and collisional mechanisms with small-system corrections, calibrated against central heavy-ion data to extract an effective strong coupling $\alpha_s^{\text{eff.}}$. The model propagates through realistic geometry, fluctuations, and hadronization to predict $R_{AB}$ across system sizes, flavors, and collision energies, then tests robustness with data subsets and extrapolates to peripheral large systems and central small systems. Key findings include stable $\alpha_s^{\text{eff.}}$ across flavor and centrality but tensions with some small-system measurements that are attributed to centrality biases and potential missing physics such as medium-modified hadronization or running coupling effects; the analysis also yields estimates of $\hat q/T^3$ and highlights the need for photon- or $Z$-normalized baselines to disentangle initial- vs final-state effects. The results underscore the potential of high-$p_T$ observables to constrain energy-loss dynamics and running coupling scales, while pointing to future measurements in very small systems (e.g., O+O, Ne+Ne) and double ratios to separate competing mechanisms.

Abstract

We present suppression predictions from our pQCD-based energy loss model, which receives small system size corrections, for high-$p_T$ $π$, $D$ and $B$ meson $R_{AB}$ as a function of centrality, flavor, $\sqrt{s_{NN}}$, and $p_T$ from large to small collision systems at RHIC and LHC. A statistical analysis is used to constrain the effective strong coupling in our model to available high-$p_T$ suppression data from central heavy-ion collisions at RHIC and LHC, yielding good agreement with all available data. We estimate two important theoretical uncertainties in our model, stemming from: the transition between vacuum and hard thermal loop propagators in the collisional energy loss, and from the angular cutoff on the radiated gluon momentum. We find, consistently, that the extracted $α_s$ remains relatively unchanged across heavy- and light-flavor final states and across central, semi-central, and peripheral collisions. We make predictions from our large-system-constrained model for small systems and find good agreement with photon-normalized $R^{π^0}_{d \text{Au}} \simeq 0.75 $ in $0-5\%$ centrality $d$ + Au collisions by PHENIX. However, we find strong disagreement with the measured $R^{h^{\pm}}_{p \text{Pb}} \gtrsim 1$ in $0-5\%$ centrality $p$ + Pb collisions by ALICE and ATLAS; we argue that this disagreement is due, in large part, to centrality bias. We make predictions for the ratio of suppression in ${}^3$He + Au and $p$ + Au collisions, which may in the future be used to disentangle final- from initial-state suppression in small systems. We then compare our results to various subsets of data, which allows us to estimate the preferred: low-$p_T$ scale at which non-perturbative processes become important, scales at which the strong coupling runs, and scale at which vacuum propagators transition to thermally modified propagators in collisional energy loss.

Figures (30)

• Figure 1: Plot of the expectation value $\left\langle R \right\rangle$ of the ratio $R \equiv (\mathbf{k} - \mathbf{q})^2 / (2 x E \sqrt{\mu^2 + \mathbf{q}^2})$ as a function of incident momentum $p_T$. Theoretical radiative energy loss curves are shown for DGLV (solid) and DGLV + SPLC (dashed). The large formation time approximation used in the derivation of DGLV and DGLV + SPLC assumes $R \ll 1$. Theoretical curves are produced for gluons moving through a brick of QGP at constant temperature of $T = 0.3 ~\mathrm{GeV}$ with a constant path length of $L = 1 ~\mathrm{fm}$ (left) and $L = 5 ~\mathrm{fm}$ (right).
• Figure 2: Plot of the expectation value $\left\langle R \right\rangle$ of the ratio $R \equiv \mathbf{k}^2 / (2 x E \sqrt{\mu^2 + \mathbf{q}^2})$ as a function of $p_T$. Theoretical radiative energy loss curves are shown for DGLV (dashed) and DGLV + SPLC (solid) with the upper bound on the transverse radiated gluon momentum from the collinear + large formation time approximation in \ref{['eqn:LFT_coll_upper_bound']}. The large formation time approximation used in the derivation of DGLV and DGLV + SPLC assumes $R \ll 1$.
• Figure 3: $\Delta E / E$ as a function of $E$ for incident gluons moving through a brick of QGP with constant temperature $T = 0.3 ~\mathrm{GeV}$ and constant length $L = 1 ~\mathrm{fm}$ (left) and $L = 5 ~\mathrm{fm}$ (right). Theoretical radiative energy loss curves are shown for DGLV (solid) and DGLV + SPLC (dashed) in conjunction with the upper bound on the transverse radiated gluon momentum from the collinear approximation only (black) and from the collinear + large formation time approximation (red). All curves shown in the left panel are multiplied by 10 for purposes of illustration.
• Figure 4: $\Delta E / E$ as a function of incident parton energy $E$ for gluons traversing a brick of QGP with $L = 5 ~\mathrm{fm}$ and $T = 0.3 ~\mathrm{GeV}$. Band widths are generated by varying the upper bound $|\mathbf{k}|_{\text{max}}$ on the transverse radiated gluon momentum $\mathbf{k}$ by factors of two up and down. Results are shown for $|\mathbf{k}|_{\text{max}}$ determined by ensuring that the collinear approximation is self-consistently satisfied (black) and by ensuring that both the collinear and large formation time approximations are self-consistently satisfied (red). The left figure shows results for DGLV energy loss and the right for DGLV + SPLC energy loss.
• Figure 5: The top panel shows the $p_T$-differential production cross section $d \sigma / d p_T$ in $p + p$ collisions for final state hadrons as a function of final hadron $p_T$. Experimental data are shown for charged hadrons at $\sqrt{s_{NN}} = 200 ~\mathrm{GeV}$PHENIX:2007kqm, charged hadrons ATLAS:2022kqu and charged pions ALICE:2019hno at $\sqrt{s_{NN}} = 5.02 ~\mathrm{TeV}$, $D^0$ mesons at $\sqrt{s_{NN}} = 5.02 ~\mathrm{TeV}$ALICE:2016yta, and $B^{\pm}$ mesons at $\sqrt{s_{NN}} = 5.02 ~\mathrm{TeV}$CMS:2017uoy. Theoretical calculations are shown for pions at $\sqrt{s_{NN}} = 200 ~\mathrm{GeV}$ and $\sqrt{s_{NN}} = 5.5 ~\mathrm{TeV}$, as well as $D$ and $B$ mesons at $\sqrt{s_{NN}} = 5.02 ~\mathrm{TeV}$. Both experimental data and theoretical curves are shifted vertically for visual clarity. The bottom panel shows the ratio of the same experimental data to the theoretical predictions as a function of $p_T$. Statistical uncertainties are represented by bars while systematic uncertainties are represented by shaded boxes.