Jet Quenching in Thin Quark-Gluon Plasmas I: Formalism

TL;DR

This paper develops a rigorous, angle-resolved formalism for jet quenching in thin quark-gluon plasmas, focusing on the interference between hard radiation, induced GB radiation, and gluon rescattering. It introduces a static color-screened potential model and an explicit eikonal framework to compute the gluon emission matrix elements for $n_s=1,2,3$ scatterings, including a binary-encoded organization of time-ordered diagrams and detailed color algebra. A key result is a power-law-like enhancement of the angular broadening with increasing $n_s$, modulated by destructive interference from the non-abelian LPM effect, yielding a relatively modest energy loss due to rapid wavefunction renormalization. The work provides a systematic method and quantitative insights that form the basis for Monte-Carlo implementations (to be presented in GLVII) and for connecting parton-level quenching to hadronic observables.

Abstract

The modification and amplification of the gluon angular distribution produced along with hard jets in nuclear collisions is computed. We consider the limit of a thin quark-gluon plasma, where the number of rescatterings of the jet and gluons is small. The focus is on jet quenching associated with the formation of highly off-shell partons in hard scattering events involving nuclei. The interference between the initial hard radiation amplitude, the multiple induced Gunion-Bertsch radiation amplitudes, and gluon rescattering amplitudes leads to an angular distribution that differs considerably from both the standard DGLAP evolution and from the classical limit parton cascading. The cases of a single and double rescattering are considered in detail, and a systematic method to compute all matrix elements for the general case is developed. A simple power law scaling of the angular distribution with increasing number of rescatterings is found and used for estimates of the fractional energy loss as a function of the plasma thickness.