Energy loss and theoretical uncertainties in small quark-gluon plasmas

TL;DR

This paper develops a perturbative QCD model for energy loss in small quark-gluon plasmas, incorporating size corrections, and analyzes the impact of various theoretical uncertainties on predictions for small collision systems.

Contribution

It introduces a refined energy loss model with size corrections, examines the validity of key approximations, and assesses uncertainties affecting small system collision predictions.

Findings

Size corrections significantly affect high-momentum pion energy loss.

The large formation time approximation is not self-consistent without a transverse momentum cutoff.

Model predictions agree with RHIC small system data but not with LHC results.

Abstract

We present a perturbative-quantum-chromodynamics-based energy loss model with small system size corrections to both radiative and elastic energy loss, incorporating realistic collision geometry, production spectra, and fragmentation. We use the Djordjevic-Gyulassy-Levai-Vitev (DGLV) radiative energy loss model and add back in previously neglected terms suppressed by system size. This small system size correction, derived by Kolbe and Horowitz, is large for high-momentum pions, raising concerns about key approximations in the radiative energy loss. We analyse the self-consistency of these approximations, finding that a particular approximation - the large formation time approximation - is not satisfied self-consistently within the model. We explore a kinematic cutoff on the transverse radiated gluon momentum, which restores the self-consistency of this approximation, but at the cost of an increased sensitivity to the exact cutoff chosen. We investigate the common application of the central limit theorem to approximate the elastic energy loss as a Gaussian distribution. Our results are insensitive to this approximation - understood not by many scatterings, but rather from an expansion of $R_{AA}$ in terms of moments of the energy loss probability distributions. We also explore uncertainty from the crossover between hard thermal loop and vacuum propagators. We perform a one-parameter fit of the strong coupling $\alpha_s$ to RHIC and LHC large-system data, accounting for two important theoretical uncertainties. Most uncertainties can be absorbed into a shift in $\alpha_s$, but residual uncertainty bands remain. Differences in elastic energy loss persist even after the fit, producing distinct $p_T$ and system size dependencies. We show model predictions for $p / d / {}^3 \text{He} + A$ collisions, finding agreement with RHIC small system data but disagreement with LHC results.