In-medium Gluon Radiation in General Kinematics

In the aftermath of heavy ion collisions, a deconfined state of matter known as the Quark-Gluon Plasma (QGP) is formed. One of the most extensively studied effects arising from the presence of a medium is jet quenching, which refers to the energy loss experienced by jets as they traverse the QGP.

This energy loss is primarily driven by medium-induced interactions that stimulate the emission of partons at large angles. These emitted partons are ultimately detected outside the jet cone, leading to the observed suppression of jet energy. As the precision of jet-quenching observables continues to improve, the need for more precise analytical tools to accurately describe in-medium gluon emissions has become increasingly critical.

This work focuses on the theoretical description of medium-induced emissions within the framework of the BDMPS-Z formalism. Building on recent developments, we extend previous results for the emission spectrum of single medium-induced radiation, which had been restricted to the soft regime. We derive a more generalized expression for the emission spectrum, without relying on the harmonic or single hard approximations, and demonstrate that this expression reduces to the established result in the soft limit.

Additionally, to facilitate further research, we provide a computational routine based on a set of differential equations, designed to simplify the evaluation of the spectrum by avoiding cumbersome numerical integrations. Lastly, we illustrate the application of this routine through the use of the large approximation.