Medium-induced radiative energy loss; equivalence between the BDMPS and Zakharov formalisms

TL;DR

This paper extends the BDMPS framework for medium-induced radiative energy loss to finite gluon momentum fraction x and includes previously neglected virtual terms. It derives a time-evolution (Schrödinger-type) equation for the in-medium quark–gluon system, computes the induced gluon radiation spectrum including hard-scattering contributions, and shows how to extract the energy loss. A central result is the explicit equivalence between the BDMPS formalism and Zakharov’s approach, both in quantitative mapping and in conceptual interpretation via a three-body quark–antiquark–gluon system. The work clarifies the role of virtual corrections, resolves previous discrepancies, and provides a unified framework for understanding jet quenching across hot and cold QCD media.

Abstract

We extend the BDMPS formalism for calculating radiative energy loss to the case when the radiated gluon carries a finite fraction of the quark momentum. Some virtual terms, previously overlooked, are now included. The equivalence between the formalism of BDMPS and that of B.Zakharov is explicitly demonstrated.