Reaction Operator Approach to Non-Abelian Energy Loss

TL;DR

This work develops a reaction-operator formalism to compute non-Abelian energy loss from hard jets in dense QCD media, enabling an all-orders opacity expansion. The authors derive a compact recursion for the inclusive gluon distribution and prove color triviality, allowing results to be expressed in terms of the gluon cross section σ_g and to incorporate evolving geometries and finite kinematic constraints. Analytic and numerical analyses show that the first-order opacity contribution dominates the induced radiation and energy loss for realistic jet energies and medium sizes, with higher orders providing modest corrections except at SPS energies where kinematic bounds suppress energy loss. The formalism is well suited for Monte Carlo implementations, offering a practical, versatile framework for jet quenching phenomenology across RHIC and LHC conditions.

Abstract

A systematic expansion of the induced inclusive gluon radiation associated with jet production in a dense QCD plasma is derived using a reaction operator formalism. Analytic expressions for the transverse momentum and light-cone momentum distributions are derived to all orders in powers of the gluon opacity of the medium, $Nσ_g/A=L/λ_g$. The reaction operator approach also leads to a simple algebraic proof of the ``color triviality'' of single inclusive distributions and to a solvable set of recursion relations. The analytic solution generalizes previous continuum solutions (BDMPS) for applications to mesoscopic QCD plasmas. The solution is furthermore not restricted to uncorrelated geometries and allows for evolving screening scales as well as the inclusion of finite kinematic constraints. The later is particularly important because below LHC energies the kinematic constraints significantly decrease the non-abelian energy loss. Our solution for the inclusive distribution also generalizes the finite order exclusive (tagged) distribution case studied previously (GLV1). The form of the analytic solution is well suited for numerical implementation in Monte Carlo event generators to enable more accurate calculations of jet quenching in ultra-relativistic nuclear collisions. Numerical results illustrating the constributions of the first three orders in opacity are compared to the ``self-quenching'' hard radiation intensity. A surprising result is that the induced gluon radiation intensity is dominated by the (quadratic in $L$) first order opacity contribution for realistic geometries and jet energies in nuclear collisions.